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Photonics Papers and Abstracts

See also our main Papers and Publications page, as well as the publications pages of the Fink, Johnson, and Soljacic groups.

[1]
S.-L. Chua, L. Lu, J. Bravo-Abad, J. D. Joannopoulos, and M. Soljačić, “Larger-area single-mode photonic crystal surface-emitting lasers enabled by an accidental dirac point,” OL, vol. 39, pp. 2072–2075, April 2014. [ bib | DOI | .pdf ]
By altering the lattice geometry of the photonic crystal (PhC) surface-emitting lasers (PCSELs), we tune the regular lasing band edges of quadratic dispersions to form a single accidental Dirac point of linear dispersion at the Brillouin zone center. This not only increases the mode spacing by orders of magnitude but also eliminates the distributed in-plane feedback to enable single-mode PCSELs of substantially larger area and thus substantially higher output power. The advantages of using accidental Dirac cones are systematically evaluated through two-dimensional in-plane calculations and confirmed by three-dimensional simulations of PhC slab devices.

[2]
O. D. Miller, C. W. Hsu, M. T. H. Reid, W. Qiu, B. G. DeLacy, J. D. Joannopoulos, M. Soljačić, and S. G. Johnson, “Fundamental limits to extinction by metallic nanoparticles,” Physical Review Letters, vol. 112, p. 123903, March 2014. [ bib | DOI | .pdf ]
We show that there are shape-independent upper bounds to the extinction cross section per unit volume of dilute, randomly arranged nanoparticles, given only material permittivity. Underlying the limits are restrictive sum rules that constrain the distribution of quasistatic eigenvalues. Surprisingly, optimally designed spheroids, with only a single quasistatic degree of freedom, reach the upper bounds for four permittivity values. Away from these permittivities, we demonstrate computationally optimized structures that surpass spheroids and approach the fundamental limits.

[3]
Y. Shen, D. Ye, I. Celanovic, S. G. Johnson, J. D. Joannopoulos, , and M. Soljačić, “Optical broadband angular selectivity,” Science, vol. 343, pp. 1499–1501, March 2014. [ bib | DOI | .pdf ]
Light selection based purely on the angle of propagation is a long-standing scientific challenge. In angularly selective systems, however, the transmission of light usually also depends on the light frequency. We tailored the overlap of the band gaps of multiple one-dimensional photonic crystals, each with a different periodicity, in such a way as to preserve the characteristic Brewster modes across a broadband spectrum. We provide theory as well as an experimental realization with an all–visible spectrum, p-polarized angularly selective material system. Our method enables transparency throughout the visible spectrum at one angle—the generalized Brewster angle—and reflection at every other viewing angle.

[4]
C. W. Hsu, B. Zhen, W. Qiu, O. Shapira, B. G. DeLacy, J. D. Joannopoulos, and M. Soljačić, “Transparent displays enabled by resonant nanoparticle scattering,” Nature Communications, vol. 5, p. 3152, January 2014. [ bib | http | .pdf ]
The ability to display graphics and texts on a transparent screen can enable many useful applications. Here we create a transparent display by projecting monochromatic images onto a transparent medium embedded with nanoparticles that selectively scatter light at the projected wavelength. We describe the optimal design of such nanoparticles, and experimentally demonstrate this concept with a blue-color transparent display made of silver nanoparticles in a polymer matrix. This approach has attractive features including simplicity, wide viewing angle, scalability to large sizes and low cost.

[5]
V. Stelmakh, V. Rinnerbauer, J. D. Joannopoulos, M. Soljačić, I. Celanovic, J. J. Senkevich, C. Tucker, T. Ives, and R. Shrader, “Evolution of sputtered tungsten coatings at high temperature,” Journal of Vacuum Science Technology A: Vacuum, Surfaces, and Films, vol. 31, p. 061505, November 2013. [ bib | DOI | .pdf ]
Sputtered tungsten (W) coatings were investigated as potential high temperature nanophotonic material to replace bulk refractory metal substrates. Of particular interest are materials and coatings for thermophotovoltaic high-temperature energy conversion applications. For such applications, high reflectance of the substrate in the infrared wavelength range is critical in order to reduce losses due to waste heat. Therefore, the reflectance of the sputtered W coatings was characterized and compared at different temperatures. In addition, the microstructural evolution of sputtered W coatings (1 and 5 μm thick) was investigated as a function of anneal temperature from room temperature to 1000 °C. Using in situ x-ray diffraction analysis, the microstrain in the two samples was quantified, ranging from 0.33% to 0.18% for the 1 μm sample and 0.26% to 0.20% for the 5 μm sample, decreasing as the temperature increased. The grain growth could not be as clearly quantified due to the dominating presence of microstrain in both samples but was in the order of 20 to 80 nm for the 1 μm sample and 50 to 100 nm for the 5 μm sample, as deposited. Finally, the 5 μm thick layer was found to be rougher than the 1 μm thick layer, with a lower reflectance at all wavelengths. However, after annealing the 5 μm sample at 900 °C for 1 h, its reflectance exceeded that of the 1 μm sample and approached that of bulk W found in literature. Overall, the results of this study suggest that thick coatings are a promising alternative to bulk substrates as a low cost, easily integrated platform for nanostructured devices for high-temperature applications, if the problem of delamination at high temperature can be overcome.

[6]
Y. X. Yeng, W. R. Chan, V. Rinnerbauer, J. D. Joannopoulos, M. Soljačić, and I. Celanovic, “Performance analysis of experimentally viable photonic crystal enhanced thermophotovoltaic systems,” OE, vol. 21, pp. A1035–A1051, November 2013. [ bib | DOI | http | .pdf ]
One of the keys towards high efficiency thermophotovoltaic (TPV) energy conversion systems lies in spectral control. Here, we present detailed performance predictions of realistic TPV systems incorporating experimentally demonstrated advanced spectral control components. Compared to the blackbody emitter, the optimized two-dimensional (2D) tantalum (Ta) photonic crystal (PhC) selective emitter enables up to 100% improvement in system efficiency. When combined with the well characterized cold side tandem filter and the latest InGaAs TPV cells, a TPV energy conversion system with radiant heat-to-electricity efficiency of 25% and power density of 0.68 W cm−2 is achievable today even at a relatively low temperature of 1320 K. The efficiency could be increased to ∼ 40% (the theoretical 0.62 eV single bandgap TPV thermodynamic limit at 1320 K is 55%) as future implementation of more optimized TPV cells approach their theoretical thermodynamic limit.

[7]
V. Stelmakh, V. Rinnerbauer, R. D. Geil, P. R. Aimone, J. J. Senkevich, J. D. Joannopoulos, M. Soljačić, and I. Celanovic, “High-temperature tantalum tungsten alloy photonic crystals: Stability, optical properties, and fabrication,” APL, vol. 103, p. 123903, September 2013. [ bib | DOI | http | .pdf ]
[8]
B. G. DeLacy, W. Qiu, M. Soljačić, C. W. Hsu, O. D. Miller, S. G. Johnson, and J. D. Joannopoulos, “Layer-by-layer self-assembly of plexcitonic nanoparticles,” Optics Express, vol. 21, pp. 19103–19112, August 2013. [ bib | DOI | http ]
Colloidal suspensions of multilayer nanoparticles composed of a silver core, a polyelectrolyte spacer layer (inner shell), and a J-aggregate cyanine dye outer shell have been prepared for the first time. Absorption properties of the colloid were measured in the visible region. This multilayer architecture served as a framework for examining the coupling of the localized surface plasmon resonance exhibited by the silver core with the molecular exciton exhibited by the J-aggregate outer shell. The polyelectrolyte spacer layer promotes the formation of an excitonic J-aggregate while serving as a means of controlling the plasmon-exciton (i.e. plexciton) coupling strength through changing the distance between the core and the shell. An analytical expression based on Mie Theory and the Transfer Matrix Method was obtained for describing the optical response of these multilayered nanostructures. Computational and experimental results indicate that the absorption wavelength of the J-aggregate form of the dye is dependent on both the distance of the dye layer from the silver core and the degree of dye aggregation.

[9]
B. Zhen, S.-L. Chua, J. Lee, A. W. Rodriguez, X. Liang, S. G. Johnson, J. D. Joannopoulos, M. Soljačić, and O. Shapira, “Enabling enhanced emission and low-threshold lasing of organic molecules using special Fano resonances of macroscopic photonic crystals,” Proceedings of the National Academy of Sciences, vol. 110, pp. 13711–13716, August 2013. [ bib | DOI | .pdf ]
The nature of light interaction with matter can be dramatically altered in optical cavities, often inducing nonclassical behavior. In solid-state systems, excitons need to be spatially incorporated within nanostructured cavities to achieve such behavior. Although fascinating phenomena have been observed with inorganic nanostructures, the incorporation of organic molecules into the typically inorganic cavity is more challenging. Here, we present a unique optofluidic platform comprising organic molecules in solution suspended on a photonic crystal surface, which supports macroscopic Fano resonances and allows strong and tunable interactions with the molecules anywhere along the surface. We develop a theoretical framework of this system and present a rigorous comparison with experimental measurements, showing dramatic spectral and angular enhancement of emission. We then demonstrate that these enhancement mechanisms enable lasing of only a 100-nm thin layer of diluted solution of organic molecules with substantially reduced threshold intensity, which has important implications for organic light-emitting devices and molecular sensing.

[10]
C. W. Hsu, B. Zhen, J. Lee, S.-L. Chua, S. G. Johnson, J. D. Joannopoulos, and M. Soljačić, “Observation of trapped light within the radiation continuum,” Nature, vol. 499, pp. 188–191, July 2013. [ bib | DOI | .pdf ]
The ability to confine light is important both scientifically and technologically. Many light confinement methods exist, but they all achieve confinement with materials or systems that forbid outgoing waves. These systems can be implemented by metallic mirrors, by photonic band-gap materials, by highly disordered media (Anderson localization) and, for a subset of outgoing waves, by translational symmetry (total internal reflection1) or by rotational or reflection symmetry. Exceptions to these examples exist only in theoretical proposals. Here we predict and show experimentally that light can be perfectly confined in a patterned dielectric slab, even though outgoing waves are allowed in the surrounding medium. Technically, this is an observation of an ‘embedded eigenvalue—namely, a bound state in a continuum of radiation modes—that is not due to symmetry incompatibility. Such a bound state can exist stably in a general class of geometries in which all of its radiation amplitudes vanish simultaneously as a result of destructive interference. This method to trap electromagnetic waves is also applicable to electronic and mechanical waves.

[11]
C. W. Hsu, B. Zhen, S.-L. Chua, S. G. Johnson, J. D. Joannopoulos, and M. Soljačić, “Bloch surface eigenstates within the radiation continuum,” Light: Science & Applications, vol. 2, p. e84, July 2013. Invited paper. [ bib | DOI | .pdf ]
From detailed numerical calculations, we demonstrate that in simple photonic crystal structures, a discrete number of Bloch surface-localized eigenstates can exist inside the continuum of free-space modes. Coupling to the free space causes the surface modes to leak, but the forward and back-reflected leakage may interfere destructively to create a perfectly bound surface state with zero leakage. We perform analytical temporal coupled-mode theory analysis to show the generality of such phenomenon and its robustness from variations of system parameters. Periodicity, time-reversal invariance, two-fold rotational symmetry and a perfectly reflecting boundary are necessary for these unique states.

[12]
V. Rinnerbauer, Y. X. Yeng, W. R. Chan, J. J. Senkevich, J. D. Joannopoulos, M. Soljačić, and I. Celanovic, “High-temperature stability and selective thermal emission of polycrystalline tantalum photonic crystals,” OE, vol. 21, pp. 11482–11491, May 2013. [ bib | DOI | http | .pdf ]
We present the results of extensive characterization of selective emitters at high temperatures, including thermal emission measurements and thermal stability testing at 1000°C for 1h and 900°C for up to 144h. The selective emitters were fabricated as 2D photonic crystals (PhCs) on polycrystalline tantalum (Ta), targeting large-area applications in solid-state heat-to-electricity conversion. We characterized spectral emission as a function of temperature, observing very good selectivity of the emission as compared to flat Ta, with the emission of the PhC approaching the blackbody limit below the target cut-off wavelength of 2 μm, and a steep cut-off to low emission at longer wavelengths. In addition, we study the use of a thin, conformal layer (20 nm) of HfO2 deposited by atomic layer deposition (ALD) as a surface protective coating, and confirm experimentally that it acts as a diffusion inhibitor and thermal barrier coating, and prevents the formation of Ta carbide on the surface. Furthermore, we tested the thermal stability of the nanostructured emitters and their optical properties before and after annealing, observing no degradation even after 144h (6 days) at 900°C, which demonstrates the suitability of these selective emitters for high-temperature applications.

[13]
L. Lu, L. Fu, J. D. Joannopoulos, and M. Soljačić, “Weyl points and line nodes in gyroid photonic crystals,” Nature Photonics, vol. 7, pp. 294–299, April 2013. [ bib | http | .pdf ]
[14]
A. W. Rodriguez, M. T. H. Reid, J. Varela, J. D. Joannopoulos, F. Capasso, and S. G. Johnson, “Anomalous near-field heat transfer between a cylinder and a perforated surface,” Physical Review Letters, vol. 110, p. 014301, January 2013. [ bib | DOI | .pdf ]
We predict that the radiative heat-transfer rate between a cylinder and a perforated surface depends non-monotonically on their separation. This anomalous behavior, which arises due to evanescent-wave effects, is explained using a heuristic model based on the interaction of a dipole with a plate. We show that nonmonotonicity depends not only on geometry and temperature but also on material dispersion—for micron and submicron objects, nonmonotonicity is present in polar dielectrics but absent in metals with small skin depths.

[15]
W. R. Chan, P. Bermel, R. C. N. Pilawa-Podgurski, C. H. Marton, K. F. Jensen, J. J. Senkevich, J. D. Joannopoulos, M. Soljačić, and I. Celanovic, “Toward high-energy-density, high-efficiency, and moderate-temperature chip-scale thermophotovoltaics,” PNAS, vol. 110, pp. 5309–5314, January 2013. [ bib | DOI | http | .pdf ]
The challenging problem of ultra-high-energy-density, high-efficiency, and small-scale portable power generation is addressed here using a distinctive thermophotovoltaic energy conversion mechanism and chip-based system design, which we name the microthermophotovoltaic (μTPV) generator. The approach is predicted to be capable of up to 32% efficient heat-to-electricity conversion within a millimeter-scale form factor. Although considerable technological barriers need to be overcome to reach full performance, we have performed a robust experimental demonstration that validates the theoretical framework and the key system components. Even with a much-simplified μTPV system design with theoretical efficiency prediction of 2.7%, we experimentally demonstrate 2.5% efficiency. The μTPV experimental system that was built and tested comprises a silicon propane microcombustor, an integrated high-temperature photonic crystal selective thermal emitter, four 0.55-eV GaInAsSb thermophotovoltaic diodes, and an ultra-high-efficiency maximum power-point tracking power electronics converter. The system was demonstrated to operate up to 800 °C (silicon microcombustor temperature) with an input thermal power of 13.7 W, generating 344 mW of electric power over a 1-cm2 area.

[16]
V. Rinnerbauer, S. Ndao, Y. Xiang Yeng, J. J. Senkevich, K. F. Jensen, J. D. Joannopoulos, M. Soljačić, I. Celanovic, and R. D. Geil, “Large-area fabrication of high aspect ratio tantalum photonic crystals for high-temperature selective emitters,” Journal of Vacuum Science & Technology B, vol. 31, p. 011802, January 2013. [ bib | DOI | http | .pdf ]
[17]
V. Rinnerbauer, J. J. Senkevich, J. D. Joannopoulos, M. Soljačić, I. Celanovic, R. R. Harl, and B. R. Rogers, “Low emissivity high-temperature tantalum thin film coatings for silicon devices,” Journal of Vacuum Science & Technology A, vol. 31, p. 011501, January 2013. [ bib | DOI | http | .pdf ]
[18]
D. Jukić, H. Buljan, D.-H. Lee, J. D. Joannopoulos, and M. Soljačić, “Flat photonic surface bands pinned between Dirac points,” Optics Letters, vol. 37, pp. 5262–5264, December 2012. [ bib | DOI | .pdf ]
We point out that 2D photonic crystals (PhCs) can support surface bands that are pinned to Dirac points. These bands can be made very flat by optimizing the parameters of the system. Surface modes are found at the interface of two different cladding materials: one is a PhC with Dirac linear dispersion for the TE mode, and the other is a PhC that has a broad TE gap at the Dirac frequency.

[19]
L. Lu, L. L. Cheong, H. I. Smith, S. G. Johnson, J. D. Joannopoulos, and M. Soljačić, “Three-dimensional photonic crystals by large-area membrane stacking,” Optics Letters, vol. 37, pp. 4726–4728, November 2012. [ bib | http | .pdf ]
We designed and analyzed a “mesh-stack” three-dimensional photonic crystal of a 12.4% bandgap with a dielectric constant ratio of 12∶1. The mesh-stack consists of four offset identical square-lattice air-hole patterned membranes in each vertical period that is equal to the in-plane period of the square lattice. This design is fully compatible with the membrane-stacking fabrication method, which is based on alignment and stacking of large-area single-crystal membranes containing engineered defects. A bandgap greater than 10% is preserved as long as the membranes are subjected to in-plane misalignment less than 3% of the square period. By introducing a linear defect with a nonsymmorphic symmetry into the mesh-stack, we achieved a single-mode waveguide over a wide bandwidth.

[20]
A. Oskooi, A. Mutapcic, S. Noda, J. D. Joannopoulos, S. P. Boyd, and S. G. Johnson, “Robust optimization of adiabatic tapers for coupling to slow-light photonic-crystal waveguides,” Optics Express, vol. 20, pp. 21558–21575, September 2012. [ bib | http ]
We investigate the design of taper structures for coupling to slow-light modes of various photonic-crystal waveguides while taking into account parameter uncertainties inherent in practical fabrication. Our short-length (11 periods) robust tapers designed for λ= 1.55μm and a slow-light group velocity of c/34 have a total loss of < 20 dB even in the presence of nanometer-scale surface roughness, which outperform the corresponding non-robust designs by an order of magnitude. We discover a posteriori that the robust designs have smooth profiles that can be parameterized by a few-term (intrinsically smooth) sine series which helps the optimization to further boost the performance slightly. We ground these numerical results in an analytical foundation by deriving the scaling relationships between taper length, taper smoothness, and group velocity with the help of an exact equivalence with Fourier analysis.

[21]
J. Lee, B. Zhen, S.-L. Chua, W. Qiu, J. D. Joannopoulos, M. Soljačić, and O. Shapira, “Observation and differentiation of unique high-q optical resonances near zero wave vector in macroscopic photonic crystal slabs,” Physical Review Letters, vol. 109, p. 067401, August 2012. [ bib | DOI | .pdf ]
We demonstrate and distinguish experimentally the existence of a special type of Fano resonances at k ≈0 in a macroscopic two-dimensional photonic crystal slab. We fabricate a square lattice array of holes in a silicon nitride layer and perform an angular resolved spectral analysis of the various Fano resonances. We elucidate their radiation behavior using temporal coupled-mode theory and symmetry considerations. The unique simplicity of this system whereby an ultralong lifetime delocalized electromagnetic field can exist above the surface and consequently easily interact with added matter, provides exciting new opportunities for the study of light and matter interaction.

[22]
Z. Wang, Z. Wang, J. Wang, B. Zhang, J. Huangfu, J. D. Joannopoulos, M. Soljačić, and L. Ran, “Gyrotropic response in the absence of a bias field,” Proceedings of the National Academy of Sciences, vol. 109, pp. 13194–13197, August 2012. [ bib | DOI | .pdf ]
Electromagnetic materials lacking local time-reversal symmetry, such as gyrotropic materials, are of keen interest and importance both scientifically and technologically. Scientifically, topologically nontrivial phenomena, such as photonic chiral edge states, allow for reflection-free transport even in the presence of large disorder. Technologically, nonreciprocal photonic devices, such as optical isolators and circulators, play critical roles in optical communication and computing technologies because of their ability to eliminate cross-talk and feedback. Nevertheless, most known natural materials that lack local time-reversal symmetry require strong external fields and function only in a limited range of the electromagnetic spectrum. By taking advantage of metamaterials capable of translating the property of unidirectional active electronic circuits into effective dielectric response, we introduce a microwave gyrotropic metamaterial that does not require an external magnetic bias. Strong bulk Faraday-like effects, observed in both simulations and experiments, confirm nonreciprocity of the effective medium. This approach is scalable to many other wavelengths, and it also illustrates an opportunity to synthesize exotic electromagnetic materials.

[23]
V. Rinnerbauer, S. Ndao, Y. X. Yeng, W. R. Chan, J. J. Senkevich, J. D. Joannopoulos, M. Soljačić, and I. Celanovic, “Recent developments in high-temperature photonic crystals for energy conversion,” Energy & Environmental Science, vol. 5, pp. 8815–8823, August 2012. [ bib | DOI | http | .pdf ]
After decades of intense studies focused on cryogenic and room temperature nanophotonics, scientific interest is also growing in high-temperature nanophotonics aimed at solid-state energy conversion. These latest extensive research efforts are spurred by a renewed interest in high temperature thermal-to-electrical energy conversion schemes including thermophotovoltaics (TPV), solar-thermophotovoltaics, solar-thermal, and solar-thermochemical energy conversion systems. This field is profiting tremendously from the outstanding degree of control over the thermal emission properties that can be achieved with nanoscale photonic materials. The key to obtaining high efficiency in this class of high temperature energy conversion is the spectral and angular matching of the radiation properties of an emitter to those of an absorber. Together with the achievements in the field of high-performance narrow bandgap photovoltaic cells, the ability to tailor the radiation properties of thermal emitters and absorbers using nanophotonics facilitates a route to achieving the impressive efficiencies predicted by theoretical studies. In this review, we will discuss the possibilities of emission tailoring by nanophotonics in the light of high temperature thermal-to-electrical energy conversion applications, and give a brief introduction to the field of TPV. We will show how a class of large area 2D metallic photonic crystals can be designed and employed to efficiently control and tailor the spectral and angular emission properties, paving the way towards new and highly efficient thermophotovoltaic systems and enabling other energy conversion schemes based on high-performance high-temperature nanoscale photonic materials.

[24]
W. Qiu, B. G. DeLacy, S. G. Johnson, J. D. Joannopoulos, and M. Soljačić, “Optimization of broadband optical response of multilayer nanospheres,” Optics Express, vol. 20, pp. 18494–18504, July 2012. [ bib | DOI ]
We propose an optimization-based theoretical approach to tailor the optical response of silver/silica multilayer nanospheres over the visible spectrum. We show that the structure that provides the largest cross-section per volume/mass, averaged over a wide frequency range, is the silver coated silica sphere. We also show how properly chosen mixture of several species of different nanospheres can have an even larger minimal cross-section per volume/mass over the entire visible spectrum.

[25]
H. Hashemi, C. W. Qiu, A. P. McCauley, J. D. Joannopoulos, and S. G. Johnson, “Diameter–bandwidth product limitation of isolated-object cloaking,” Physical Review A, vol. 86, p. 013804, July 2012. [ bib | DOI | .pdf ]
We show that cloaking of isolated objects using transformation-based cloaks is subject to a diameter–bandwidth product limitation: as the size of the object increases, the bandwidth of good (small cross-section) cloaking decreases inversely with the diameter, as a consequence of causality constraints even for perfect fabrication and materials with negligible absorption. This generalizes a previous result that perfect cloaking of isolated objects over a nonzero bandwidth violates causality. Furthermore, we demonstrate broader causality-based scaling limitations on any bandwidth-averaged cloaking cross-section, using complex analysis and the optical theorem to transform the frequency-averaged problem into a single scattering problem with transformed materials.

[26]
L. Lu, J. D. Joannopoulos, and M. Soljačić, “Waveguiding at the edge of a three-dimensional photonic crystal,” Physical Review Letters, vol. 108, p. 243901, June 2012. [ bib | DOI | .pdf ]
We find that electromagnetic waves can be guided at the edge of a three-dimensional photonic crystal in air. When the waveguide is defined by the intersection of two surface planes, the edge modes are associated with the corresponding surface bands. A simple cell counting approach is presented to describe the periodic evolution of the system with interesting interplays among edge, surface, and bulk states.

[27]
J. Bravo-Abad, J. D. Joannopoulos, and M. Soljačić, “Enabling single-mode behavior over large areas with photonic Dirac cones,” Proceedings of the National Academy of Sciences, vol. 109, pp. 9761–9765, June 2012. [ bib | DOI | .pdf ]
Many of graphene’s unique electronic properties emerge from its Dirac-like electronic energy spectrum. Similarly, it is expected that a nanophotonic system featuring Dirac dispersion (two conical bands touching at a single point, the so-called Dirac point) will open a path to a number of important research avenues. To date, however, all proposed realizations of a photonic analog of graphene lack fully omnidirectional out-of-plane light confinement, which has prevented creating truly realistic implementations of this class of systems able to mimic the two-dimensional transport properties of graphene. Here we report on a novel route to achieve all-dielectric three-dimensional photonic materials featuring Dirac-like dispersion in a quasi-two-dimensional system. We further discuss how this finding could enable a dramatic enhancement of the spontaneous emission coupling efficiency (the β-factor) over large areas, defying the common wisdom that the β-factor degrades rapidly as the size of the system increases. These results might enable general new classes of large-area ultralow-threshold lasers, single-photon sources, quantum information processing devices and energy harvesting systems.

[28]
A. M. Stolyarov, A. Gumennik, W. McDaniel, O. Shapira, B. Schell, F. Sorin, K. Kuriki, G. Benoit, A. Rose, J. D. Joannopoulos, and Y. Fink, “Enhanced chemiluminescent detection scheme for trace vapor sensing in pneumatically-tuned hollow core photonic bandgap fibers,” Optics Express, vol. 20, pp. 12407–12415, May 2012. [ bib | DOI ]
We demonstrate an in-fiber gas phase chemical detection architecture in which a chemiluminescent (CL) reaction is spatially and spectrally matched to the core modes of hollow photonic bandgap (PBG) fibers in order to enhance detection efficiency. A peroxide-sensitive CL material is annularly shaped and centered within the fiber’s hollow core, thereby increasing the overlap between the emission intensity and the intensity distribution of the low-loss fiber modes. This configuration improves the sensitivity by 0.9 dB/cm compared to coating the material directly on the inner fiber surface, where coupling to both higher loss core modes and cladding modes is enhanced. By integrating the former configuration with a custom-built optofluidic system designed for concomitant controlled vapor delivery and emission measurement, we achieve a limit-of-detection of 100 parts per billion (ppb) for hydrogen peroxide vapor. The PBG fibers are produced by a new fabrication method whereby external gas pressure is used as a control knob to actively tune the transmission bandgaps through the entire visible range during the thermal drawing process.

[29]
O. Ilic, M. Jablan, J. D. Joannopoulos, I. Celanovic, and M. Soljačić, “Near-field thermal radiation transfer controlled by plasmons in graphene,” Physical Review B, vol. 85, p. 155422, April 2012. [ bib | DOI | .pdf ]
It is shown that thermally excited plasmon-polariton modes can strongly mediate, enhance, and tune the near-field radiation transfer between two closely separated graphene sheets. The dependence of near-field heat exchange on doping and electron relaxation time is analyzed in the near infrared within the framework of fluctuational electrodynamics. The dominant contribution to heat transfer can be controlled to arise from either interband or intraband processes. We predict maximum transfer at low doping and for plasmons in two graphene sheets in resonance, with orders-of-magnitude enhancement (e.g., 102 to 103 for separations between 0.1 μm and 10 nm) over the Stefan-Boltzmann law, known as the far-field limit. Strong, tunable, near-field transfer offers the promise of an externally controllable thermal switch as well as a novel hybrid graphene-graphene thermoelectric/thermophotovoltaic energy conversion platform.

[30]
O. Ilic, M. Jablan, J. D. Joannopoulos, I. Celanovic, and M. Soljačić, “Overcoming the black body limit in plasmonic and graphene near-field thermophotovoltaic systems,” Optics Express, vol. 20, pp. A366–A384, March 2012. [ bib | DOI | .pdf ]
Near-field thermophotovoltaic (TPV) systems with carefully tailored emitter-PV properties show large promise for a new temperature range (600–1200 K) solid state energy conversion, where conventional thermoelectric (TE) devices cannot operate due to high temperatures and far-field TPV schemes suffer from low efficiency and power density. We present a detailed theoretical study of several different implementations of thermal emitters using plasmonic materials and graphene. We find that optimal improvements over the black body limit are achieved for low bandgap semiconductors and properly matched plasmonic frequencies. For a pure plasmonic emitter, theoretically predicted generated power density of 14 W/cm2 and efficiency of 36% can be achieved at 600 K (hot-side), for 0.17 eV bandgap (InSb). Developing insightful approximations, we argue that large plasmonic losses can, contrary to intuition, be helpful in enhancing the overall near-field transfer. We discuss and quantify the properties of an optimal near-field photovoltaic (PV) diode. In addition, we study plasmons in graphene and show that doping can be used to tune the plasmonic dispersion relation to match the PV cell bangap. In case of graphene, theoretically predicted generated power density of 6(120) W/cm2 and efficiency of 35(40)% can be achieved at 600(1200) K, for 0.17 eV bandgap. With the ability to operate in intermediate temperature range, as well as high efficiency and power density, near-field TPV systems have the potential to complement conventional TE and TPV solid state heat-to-electricity conversion devices.

[31]
Y. X. Yeng, M. Ghebrebrhan, P. Bermel, W. R. Chan, J. D. Joannopoulos, M. Soljačić, and I. Celanovic, “Enabling high-temperature nanophotonics for energy applications,” Proceedings of the National Academy of Sciences, December 2011. Published online before print. [ bib | DOI | .pdf ]
The nascent field of high-temperature nanophotonics could potentially enable many important solid-state energy conversion applications, such as thermophotovoltaic energy generation, selective solar absorption, and selective emission of light. However, special challenges arise when trying to design nanophotonic materials with precisely tailored optical properties that can operate at high-temperatures (> 1,100 K). These include proper material selection and purity to prevent melting, evaporation, or chemical reactions; severe minimization of any material interfaces to prevent thermomechanical problems such as delamination; robust performance in the presence of surface diffusion; and long-range geometric precision over large areas with severe minimization of very small feature sizes to maintain structural stability. Here we report an approach for high-temperature nanophotonics that surmounts all of these difficulties. It consists of an analytical and computationally guided design involving high-purity tungsten in a precisely fabricated photonic crystal slab geometry (specifically chosen to eliminate interfaces arising from layer-by-layer fabrication) optimized for high performance and robustness in the presence of roughness, fabrication errors, and surface diffusion. It offers near-ultimate short-wavelength emittance and low, ultra-broadband long-wavelength emittance, along with a sharp cutoff offering 4∶1 emittance contrast over 10% wavelength separation. This is achieved via Q-matching, whereby the absorptive and radiative rates of the photonic crystal’s cavity resonances are matched. Strong angular emission selectivity is also observed, with short-wavelength emission suppressed by 50% at 75o compared to normal incidence. Finally, a precise high-temperature measurement technique is developed to confirm that emission at 1,225 K can be primarily confined to wavelengths shorter than the cutoff wavelength.

[32]
P. Bermel, M. Ghebrebrhan, M. Harradon, Y. X. Yeng, I. Celanovic, J. D. Joannopoulos, and M. Soljačić, “Tailoring photonic metamaterial resonances for thermal radiation,” Nanoscale Research Letters, vol. 6, p. 549, October 2011. [ bib | http | .pdf ]
Selective solar absorbers generally have limited effectiveness in unconcentrated sunlight, because of reradiation losses over a broad range of wavelengths and angles. However, metamaterials offer the potential to limit radiation exchange to a proscribed range of angles and wavelengths, which has the potential to dramatically boost performance. After globally optimizing one particular class of such designs, we find thermal transfer efficiencies of 78% at temperatures over 1,000o C, with overall system energy conversion efficiencies of 37%, exceeding the Shockley-Quiesser efficiency limit of 31% for photovoltaic conversion under unconcentrated sunlight. This represents a 250% increase in efficiency and 94% decrease in selective emitter area compared to a standard, angular-insensitive selective absorber.

[33]
M. Araghchini, Y. X. Yeng, N. Jovanovic, P. Bermel, L. A. Kolodziejski, M. Soljačić, I. Celanovic, and J. D. Joannopoulos, “Fabrication of two-dimensional tungsten photonic crystals for high-temperature applications,” Journal of Vacuum Science and Technology B, vol. 29, p. 061402, October 2011. [ bib | DOI | .pdf ]
This article details microfabrication of two-dimensional tungsten photonic crystals (2D W PhCs) for high-temperature applications such as selective thermal emitters for thermophotovoltaic energy conversion. In particular, interference lithography and reactive ion etching are used to produce large area single crystal tungsten 2D PhCs. For this investigation, we fabricated a 2D W PhC sample consisting of an array of cylindrical cavities with 800 nm diameter, 1.2 μm depth, and 1.2 μm period. Extensive characterization and calibration of all microfabrication steps are presented. Experimentally obtained thermal emissivity spectrum is shown to match well with numerical simulations.

[34]
A. W. Rodriguez, O. Ilic, P. Bermel, I. Celanovic, J. D. Joannopoulos, M. Soljačić, and S. G. Johnson, “Frequency-selective near-field radiative heat transfer between photonic crystal slabs: A computational approach for arbitrary geometries and materials,” Physical Review Letters, vol. 107, p. 114302, September 2011. [ bib | DOI | .pdf ]
We demonstrate the possibility of achieving enhanced frequency-selective near-field radiative heat transfer between patterned (photonic-crystal) slabs at designable frequencies and separations, exploiting a general numerical approach for computing heat transfer in arbitrary geometries and materials based on the finite-difference time-domain method. Our simulations reveal a tradeoff between selectivity and near-field enhancement as the slab-slab separation decreases, with the patterned heat transfer eventually reducing to the unpatterned result multiplied by a fill factor (described by a standard proximity approximation). We also find that heat transfer can be further enhanced at selective frequencies when the slabs are brought into a glide-symmetric configuration, a consequence of the degeneracies associated with the nonsymmorphic symmetry group.

[35]
H. Hashemi, A. Oskooi, J. D. Joannopoulos, and S. G. Johnson, “General scaling limitations of ground-plane and isolated-object cloaks,” Physical Review A, vol. 84, p. 023815, August 2011. [ bib | DOI | .pdf ]
We prove that, for arbitrary three-dimensional transformation-based invisibility cloaking of an object above a ground plane or of isolated object, there are practical constraints that increase with the object size. In particular, we show that the cloak thickness must scale proportional to the thickness of the object being cloaked, assuming bounded refractive indices, and that absorption discrepancies and other imperfections must scale inversely with the object thickness. For isolated objects, we also show that bounded refractive indices imply a lower bound on the effective cross-section.

[36]
A. Kurs, J. D. Joannopoulous, M. Soljačić, and S. G. Johnson, “Abrupt coupling between strongly dissimilar waveguides with 100% transmission,” Optics Express, vol. 19, pp. 13714–13721, June 2011. [ bib | http ]
We present numerical experiments showing how coupled-mode theory can be systematically applied to join very dissimilar photonic crystal waveguides with 100% transmission. Our approach relies on appropriately tuning the coupling of the evanescent tail of a cavity mode to each waveguide. The transition region between the waveguides may be as short as a few lattice spacings. Moreover, this technique only requires varying a small number of parameters (two for each waveguide in our example) and the tuning to each waveguide may be done separately, greatly simplifying the computations involved.

[37]
A. P. McCauley, F. S. S. Rosa, A. W. Rodriguez, J. D. Joannopoulos, D. A. R. Dalvit, and S. G. Johnson, “Structural anisotropy and orientation-induced Casimir repulsion in fluids,” Physical Review A, vol. 83, p. 052503, May 2011. [ bib | DOI | .pdf ]
In this work we theoretically consider the Casimir force between two periodic arrays of nanowires (both in vacuum, and on a substrate separated by a fluid) at separations comparable to the period. Specifically, we compute the dependence of the exact Casimir force between the arrays under both lateral translations and rotations. Although typically the force between such structures is well characterized by the proximity force approximation (PFA), we find that in the present case the microstructure modulates the force in a way qualitatively inconsistent with PFA. We find instead that effective-medium theory, in which the slabs are treated as homogeneous, anisotropic dielectrics, gives a surprisingly accurate picture of the force, down to separations of half the period. This includes a situation for identical, fluid-separated slabs in which the exact force changes sign with the orientation of the wire arrays, whereas PFA predicts attraction. We discuss the possibility of detecting these effects in experiments, concluding that this effect is strong enough to make detection possible in the near future.

[38]
S.-L. Chua, C. A. Caccamise, D. J. Phillips, J. D. Joannopoulos, M. Soljačić, H. O. Everitt, and J. Bravo-Abad, “Spatio-temporal theory of lasing action in optically-pumped rotationally excited molecular gases,” Optics Express, vol. 19, pp. 7513–7529, April 2011. [ bib | http | .pdf ]
We investigate laser emission from optically-pumped rotationally excited molecular gases confined in a metallic cavity. To this end, we have developed a theoretical framework able to accurately describe, both in the spatial and temporal domains, the molecular collisional and diffusion processes characterizing the operation of this class of lasers. The effect on the main lasing features of the spatial variation of the electric field intensity and the ohmic losses associated to each cavity mode are also included in our analysis. Our simulations show that, for the exemplary case of methyl fluoride gas confined in a cylindrical copper cavity, the region of maximum population inversion is located near the cavity walls. Based on this fact, our calculations show that the lowest lasing threshold intensity corresponds to the cavity mode that, while maximizing the spatial overlap between the corresponding population inversion and electric-field intensity distributions, simultaneously minimizes the absorption losses occurring at the cavity walls. The dependence of the lasing threshold intensity on both the gas pressure and the cavity radius is also analyzed and compared with experiment. We find that as the cavity size is varied, the interplay between the overall gain of the system and the corresponding ohmic losses allows for the existence of an optimal cavity radius which minimizes the intensity threshold for a large range of gas pressures. The theoretical analysis presented in this work expands the current understanding of lasing action in optically-pumped far-infrared lasers and, thus, could contribute to the development of a new class of compact far-infrared and terahertz sources able to operate efficiently at room temperature.

[39]
D. Ramirez, A. W. Rodriguez, H. Hashemi, J. Joannopoulos, M. Soljačić, and S. G. Johnson, “Degenerate four-wave mixing in triply-resonant Kerr cavities,” Physical Review A, vol. 83, p. 033834, March 2011. [ bib | DOI | .pdf ]
We demonstrate theoretical conditions for highly-efficient degenerate four-wave mixing in triply-resonant nonlinear (Kerr) cavities. We employ a general and accurate temporal coupled-mode analysis in which the interaction of light in arbitrary microcavities is expressed in terms a set of coupling coefficients that we rigorously derive from the full Maxwell equations. Using the coupled-mode theory, we show that light consisting of an input signal of frequency ω0-Δω can, in the presence of pump light at ω0, be converted with quantum-limited efficiency into an output shifted signal of frequency ω0 + Δω, and we derive expressions for the critical input powers at which this occurs. We find that critical powers in the order of 10mW assuming very conservative cavity parameters (modal volumes ∼10 cubic wavelengths and quality factors ∼1000. The standard Manley-Rowe efficiency limits are obtained from the solution of the classical coupled-mode equations, although we also derive them from simple photon-counting “quantum” arguments. Finally, using a linear stability analysis, we demonstrate that maximal conversion efficiency can be retained even in the presence of self- and cross-phase modulation effects that generally act to disrupt the resonance condition.

[40]
M. Ghebrebrhan, P. Bermel, Y. X. Yeng, I. Celanovic, M. Soljačić, and J. D. Joannopoulos, “Tailoring thermal emission via q matching of photonic crystal resonances,” Physical Review A, vol. 83, p. 033810, March 2011. [ bib | DOI | .pdf ]
We develop a model for predicting the thermal emission spectrum of a two-dimensional metallic photonic crystal for arbitrary angles based on coupled-mode theory. Calculating the appropriate coupled-mode parameters over a range of geometrical parameters allows one to tailor the emissivity spectrum to a specific application. As an example, we design an emitter with a step-function cutoff suppressing long-wavelength emission, which is necessary for high-efficiency thermophotovoltaic systems. We also confirm the accuracy of the results of our model with finite-difference time-domain simulations.

[41]
S. Danto, Z. Ruff, Z. Wang, J. D. Joannopoulos, and Y. Fink, “Ovonic memory switching in multimaterial fibers,” Advanced Functional Materials, vol. 21, pp. 1095–1101, March 2011. [ bib | DOI ]
We demonstrate the first rewritable memory in thermally drawn fibers. A high tellurium-content chalcogenide glass, contacted by metallic electrodes internal to the fiber structure, is drawn from a macroscopic preform. An externally applied voltage is utilized to switch between a high resistance (OFF) and a low resistance (ON) state; this in turn allows the fibers to function as a memory device reminiscent of the ovonic switch. The difference between the ON and OFF states is found to be four orders of magnitude. The glass–crystal phase transition is localized to micrometer-wide filaments, whose position can be optically controlled along the fiber axis. An architecture that enabled the encoding of multiple bits per fiber is described.

[42]
D. Chester, P. Bermel, J. D. Joannopoulos, M. Soljačić, and I. Celanovic, “Design and global optimization of high-efficiency solar thermal systems with tungsten cermets,” Optics Express, vol. 19, pp. A245–A257, March 2011. [ bib | http | .pdf ]
Solar thermal, thermoelectric, and thermophotovoltaic (TPV) systems have high maximum theoretical efficiencies; experimental systems fall short because of losses by selective solar absorbers and TPV selective emitters. To improve these critical components, we study a class of materials known as cermets. While our approach is completely general, the most promising cermet candidate combines nanoparticles of silica and tungsten. We find that 4-layer silica-tungsten cermet selective solar absorbers can achieve thermal transfer efficiencies of 84.3% at 400 K, and 75.59% at 1000 K, exceeding comparable literature values. Three layer silica-tungsten cermets can also be used as selective emitters for InGaAsSb-based thermophotovoltaic systems, with projected overall system energy conversion efficiencies of 10.66% at 1000 K using realistic design parameters. The marginal benefit of adding more than 4 cermet layers is small (less than 0.26%, relative).

[43]
K. Y. K. Lee, M. K. Nyein, D. F. Moore, J. D. Joannopoulos, S. Socrate, T. Imholt, R. Radovitzky, and S. G. Johnson, “Blast-induced electromagnetic fields in the brain from bone piezoelectricity,” NeuroImage, vol. 54, pp. S30–S36, January 2011. Invited paper, published online June 2010. [ bib | DOI ]
In this paper, we show that bone piezoelectricity—a phenomenon in which bone polarizes electrically in response to an applied mechanical stress and produces a short-range electric field—may be a source of intense blast-induced electric fields in the brain, with magnitudes and timescales comparable to fields with known neurological effects. We compute the induced charge density in the skull from stress data on the skull from a finite-element full-head model simulation of a typical IED-scale blast wave incident on an unhelmeted human head as well as a human head protected by a kevlar helmet, and estimate the resulting electric fields in the brain in both cases to be on the order of 10 V/m in millisecond pulses. These fields are more than 10 times stronger than the IEEE safety guidelines for controlled environments (IEEE Standards Coordinating Committee 28, 2002) and comparable in strength and timescale to fields from repetitive Transcranial Magnetic Stimulation (rTMS) that are designed to induce neurological effects (Wagner et al., 2006a). They can be easily measured by RF antennas, and may provide the means to design a diagnostic tool that records a quantitative measure of the head's exposure to blast insult.

[44]
N. D. Orf, O. Shapira, F. Sorin, S. Danto, M. A. Baldo, J. D. Joannopoulos, and Y. Fink, “Fiber draw synthesis,” Proceedings of the National Academy of Sciences, vol. 108, pp. 4743–4747, January 2011. [ bib | DOI ]
The synthesis of a high-melting temperature semiconductor in a low-temperature fiber drawing process is demonstrated, substantially expanding the set of materials that can be incorporated into fibers. Reagents in the solid state are arranged in proximate domains within a fiber preform. The preform is fluidized at elevated temperatures and drawn into fiber, reducing the lateral dimensions and bringing the domains into intimate contact to enable chemical reaction. A polymer preform containing a thin layer of selenium contacted by tin–zinc wires is drawn to yield electrically contacted crystalline ZnSe domains of sub-100-nm scales. The in situ synthesized compound semiconductor becomes the basis for an electronic heterostructure diode of arbitrary length in the fiber. The ability to synthesize materials within fibers while precisely controlling their geometry and electrical connectivity at submicron scales presents new opportunities for increasing the complexity and functionality of fiber structures.

[45]
F. Sorin, G. Lestoquoy, S. Danto, J. D. Joannopoulos, and Y. Fink, “Resolving optical illumination distributions along an axially symmetric photodetecting fiber,” Optics Express, vol. 18, pp. 24264–24275, November 2010. [ bib | http ]
Photodetecting fibers of arbitrary length with internal metal, semiconductor and insulator domains have recently been demonstrated. These semiconductor devices exhibit a continuous translational symmetry which presents challenges to the extraction of spatially resolved information. Here, we overcome this seemingly fundamental limitation and achieve the detection and spatial localization of a single incident optical beam at sub-centimeter resolution, along a one-meter fiber section. Using an approach that breaks the axial symmetry through the constuction of a convex electrical potential along the fiber axis, we demonstrate the full reconstruction of an arbitrary rectangular optical wave profile. Finally, the localization of up to three points of illumination simultaneously incident on a photodetecting fiber is achieved.

[46]
M. K. Nyein, A. M. Jason, L. Yu, C. M. Pita, J. D. Joannopoulos, D. F. Moore, and R. A. Radovitzky, “In silico investigation of intracranial blast mitigation with relevance to military traumatic brain injury,” Proceedings of the National Academy of Sciences, vol. 107, pp. 20703–20708, November 2010. [ bib | DOI ]
Blast-induced traumatic brain injury is the most prevalent military injury in Iraq and Afghanistan, yet little is known about the mechanical effects of blasts on the human head, and still less is known about how personal protective equipment affects the brain’s response to blasts. In this study we investigated the effect of the Advanced Combat Helmet (ACH) and a conceptual face shield on the propagation of stress waves within the brain tissue following blast events. We used a sophisticated computational framework for simulating coupled fluid–solid dynamic interactions and a three-dimensional biofidelic finite element model of the human head and intracranial contents combined with a detailed model of the ACH and a conceptual face shield. Simulations were conducted in which the unhelmeted head, head with helmet, and head with helmet and face shield were exposed to a frontal blast wave with incident overpressure of 10 atm. Direct transmission of stress waves into the intracranial cavity was observed in the unprotected head and head with helmet simulations. Compared to the unhelmeted head, the head with helmet experienced slight mitigation of intracranial stresses. This suggests that the existing ACH does not significantly contribute to mitigating blast effects, but does not worsen them either. By contrast, the helmet and face shield combination impeded direct transmission of stress waves to the face, resulting in a delay in the transmission of stresses to the intracranial cavity and lower intracranial stresses. This suggests a possible strategy for mitigating blast waves often associated with military concussion.

[47]
A. P. McCauley, R. Zhao, M. T. H. Reid, A. W. Rodriguez, J. Zhou, F. S. S. Rosa, J. D. Joannopoulos, D. A. R. Dalvit, C. M. Soukoulis, and S. G. Johnson, “Microstructure effects for Casimir forces in chiral metamaterials,” Physical Review B, vol. 82, p. 165108, October 2010. [ bib | DOI | .pdf ]
We examine a recent prediction for the chirality dependence of the Casimir force in chiral metamaterials by numerical computation of the forces between the exact microstructures, rather than homogeneous approximations. Although repulsion in the metamaterial regime is rigorously impossible, it is unknown whether a reduction in the attractive force can be achieved through suitable material engineering. We compute the exact force for a chiral bent-cross pattern, as well as forces for an idealized “omega”-particle medium in the dilute approximation and identify the effects of structural inhomogeneity (i.e., proximity forces and anisotropy). We find that these microstructure effects dominate the force for separations where chirality was predicted to have a strong influence. At separations where the homogeneous approximation is valid, in even the most ideal circumstances the effects of chirality are less than 10−4 of the total force, making them virtually undetectable in experiments.

[48]
S. Danto, F. Sorin, N. D. Orf, Z. Wang, S. A. Speakman, J. D. Joannopoulos, and Y. Fink, “Fiber field-effect device via in situ channel crystallization,” Advanced Materials, vol. 22, pp. 4162–4166, October 2010. [ bib | DOI ]
The in situ crystallization of the incorporated amorphous semiconductor within the multimaterial fiber device yields a large decrease in defect density and a concomitant five-order-of-magnitude decrease in resistivity of the novel metal-insulator-crystalline semiconductor structure. Using a post-drawing crystallization process, the first tens-of-meters-long single-fiber field-effect device is demonstrated. This work opens significant opportunities for incorporating higher functionality in functional fibers and fabrics.

[49]
A. W. Rodriguez, D. Woolf, A. P. McCauley, F. Capasso, J. D. Joannopoulos, and S. G. Johnson, “Achieving a strongly temperature-dependent Casimir effect,” Physical Review Letters, vol. 105, p. 060401, August 2010. [ bib | DOI | .pdf ]
We propose a method of achieving large temperature T sensitivity in the Casimir force that involves measuring the stable separation between dielectric objects immersed in a fluid. We study the Casimir force between slabs and spheres using realistic material models, and find large >2 nm/K variations in their stable separations (hundreds of nanometers) near room temperature. In addition, we analyze the effects of Brownian motion on suspended objects, and show that the average separation is also sensitive to changes in T. Finally, this approach also leads to rich qualitative phenomena, such as irreversible transitions, from suspension to stiction, as T is varied.

[50]
P. Bermel, M. Ghebrebrhan, W. Chan, Y. X. Yeng, M. Araghchini, R. Hamam, C. H. Marton, K. F. Jensen, M. Soljačić, J. D. Joannopoulos, S. G. Johnson, and I. Celanovic, “Design and global optimization of high-efficiency thermophotovoltaic systems,” Optics Express, vol. 18, pp. A314–A334, August 2010. [ bib | http | .pdf ]
Despite their great promise, small experimental thermophotovoltaic (TPV) systems at 1000 K generally exhibit extremely low power conversion efficiencies (approximately 1%), due to heat losses such as thermal emission of undesirable mid-wavelength infrared radiation. Photonic crystals (PhC) have the potential to strongly suppress such losses. However, PhC-based designs present a set of non-convex optimization problems requiring efficient objective function evaluation and global optimization algorithms. Both are applied to two example systems: improved micro-TPV generators and solar thermal TPV systems. Micro-TPV reactors experience up to a 27-fold increase in their efficiency and power output; solar thermal TPV systems see an even greater 45-fold increase in their efficiency (exceeding the Shockley–Quiesser limit for a single-junction photovoltaic cell).

[51]
S. Egusa, Z. Wang, N. Chocat, Z. M. Ruff, A. M. Stolyarov, D. Shemuly, F. Sorin, P. T. Rakich, J. D. Joannopoulos, and Y. Fink, “Multimaterial piezoelectric fibres,” Nature Materials, vol. 9, pp. 643–648, July 2010. [ bib | DOI ]
Fibre materials span a broad range of applications ranging from simple textile yarns to complex modern fibre-optic communication systems. Throughout their history, a key premise has remained essentially unchanged: fibres are static devices, incapable of controllably changing their properties over a wide range of frequencies. A number of approaches to realizing time-dependent variations in fibres have emerged, including refractive index modulation, nonlinear optical mechanisms in silica glass fibres and electroactively modulated polymer fibres. These approaches have been limited primarily because of the inert nature of traditional glassy fibre materials. Here we report the composition of a phase internal to a composite fibre structure that is simultaneously crystalline and non-centrosymmetric. A ferroelectric polymer layer of 30 μm thickness is spatially confined and electrically contacted by internal viscous electrodes and encapsulated in an insulating polymer cladding hundreds of micrometres in diameter. The structure is thermally drawn in its entirety from a macroscopic preform, yielding tens of metres of piezoelectric fibre. The fibres show a piezoelectric response and acoustic transduction from kilohertz to megahertz frequencies. A single-fibre electrically driven device containing a high-quality-factor Fabry–Perot optical resonator and a piezoelectric transducer is fabricated and measured.

[52]
H. Hashemi, B. Zhang, J. D. Joannopoulos, and S. G. Johnson, “Delay-bandwidth and delay-loss limitations for cloaking of large objects,” Physical Review Letters, vol. 104, p. 253903, June 2010. [ bib | DOI | .pdf ]
We show that the difficulty of cloaking is fundamentally limited by delay-loss and delay-bandwidth limitations that worsen as the size of the object to be cloaked increases relative to the wavelength, using a simple model of ground-plane cloaking. These limitations must be considered when scaling experimental cloaking demonstrations up from wavelength-scale objects.

[53]
A. W. Rodriguez, A. P. McCauley, J. D. Joannopoulos, and S. G. Johnson, “Theoretical ingredients of a Casimir analog computer,” Proceedings of the National Academy of Sciences, vol. 107, pp. 9531–9536, May 2010. [ bib | DOI | .pdf ]
We derive a correspondence between the contour integration of the Casimir stress tensor in the complex-frequency plane and the electromagnetic response of a physical dissipative medium in a finite real-frequency bandwidth. The consequences of this correspondence are at least threefold: First, the correspondence makes it easier to understand Casimir systems from the perspective of conventional classical electromagnetism, based on real-frequency responses, in contrast to the standard imaginary-frequency point of view based on Wick rotations. Second, it forms the starting point of finite-difference time-domain numerical techniques for calculation of Casimir forces in arbitrary geometries. Finally, this correspondence is also key to a technique for computing quantum Casimir forces at micrometer scales using antenna measurements at tabletop (e.g., centimeter) scales, forming a type of analog computer for the Casimir force. Superficially, relationships between the Casimir force and the classical electromagnetic Green’s function are well known, so one might expect that any experimental measurement of the Green’s function would suffice to calculate the Casimir force. However, we show that the standard forms of this relationship lead to infeasible experiments involving infinite bandwidth or exponentially growing fields, and a fundamentally different formulation is therefore required.

[54]
O. Shapira, A. F. Abouraddy, Q. Hu, D. Shemuly, J. D. Joannopoulos, and Y. Fink, “Enabling coherent superpositions of iso-frequency optical states in multimode fibers,” Optics Express, vol. 18, pp. 12622–12629, May 2010. [ bib | http ]
The ability to precisely and selectively excite superpositions of specific fiber eigenmodes allows one in principle to control the three dimensional field distribution along the length of a fiber. Here we demonstrate the dynamic synthesis and controlled transmission of vectorial eigenstates in a hollow core cylindrical photonic bandgap fiber, including a coherent superposition of two different angular momentum states. The results are verified using a modal decomposition algorithm that yields the unique complex superposition coefficients of the eigenstate space.

[55]
A. W. Rodriguez, A. P. McCauley, D. Woolf, F. Capasso, J. D. Joannopoulos, and S. G. Johnson, “Non-touching nanoparticle diclusters bound by repulsive and attractive Casimir forces,” Physical Review Letters, vol. 104, p. 160402, April 2010. [ bib | http | .pdf ]
We present a scheme for obtaining stable Casimir suspension of dielectric nontouching objects immersed in a fluid, validated here in various geometries consisting of ethanol-separated dielectric spheres and semi-infinite slabs. Stability is induced by the dispersion properties of real dielectric (monolithic) materials. A consequence of this effect is the possibility of stable configurations (clusters) of compact objects, which we illustrate via a molecular two-sphere dicluster geometry consisting of two bound spheres levitated above a gold slab. Our calculations also reveal a strong interplay between material and geometric dispersion, and this is exemplified by the qualitatively different stability behavior observed in planar versus spherical geometries.

[56]
J. Bravo-Abad, A. W. Rodriguez, J. D. Joannopoulos, P. T. Rakich, S. G. Johnson, and M. Soljačić, “Efficient low-power terahertz generation via on-chip triply-resonant nonlinear frequency mixing,” Applied Physics Letters, vol. 96, p. 101110, March 2010. [ bib | DOI | .pdf ]
In this letter, we show theoretically how the light-confining properties of triply-resonant photonic resonators can be tailored to enable dramatic enhancements of the conversion efficiency of terahertz (THz) generation via nonlinear frequency down-conversion processes. Using detailed numerical calculations, we predict that this approach can be used to reduce up to three orders of magnitude the pump powers required to reach quantum-limited conversion efficiency of THz generation in conventional nonlinear optical material systems. Furthermore, we propose a realistic design readily accessible experimentally, both for fabrication and demonstration of optimal THz conversion efficiency at sub-W power levels.

[57]
W. Chan, R. Huang, C. Wang, J. Kassakian, J. Joannopoulos, and I. Celanovic, “Modeling low-bandgap thermophotovoltaic diodes for high-efficiency portable power generators,” Solar Energy Materials and Solar Cells, vol. 94, pp. 509–514, March 2010. [ bib | DOI ]
To aid in the design of low-temperature high-efficiency thermophotovoltaic (TPV) systems, based on low-bandgap photovoltaic (PV) diodes and selective thermal emitters, we developed a detailed model of GaSb and GaInAsSb PV diodes. An equivalent circuit model describes the electrical behavior of the diode as a function of the operating point defined by a photocurrent and a junction temperature. The single diode equivalent circuit model has five variable parameters: photocurrent, dark current, ideality, and series and shunt resistance. The model accurately predicts the circuit parameters for a given operating point. In addition, parameterized quantum efficiency is used to calculate photocurrent while accounting for temperature induced bandgap narrowing. Models show very good agreement with experimental results obtained with calibrated blackbody source. Although we focus on TPV systems, these methods and results are applicable to solar-thermophotovotaic and concentrator photovoltaic systems.

[58]
I. D. Hosein, M. Ghebrebrhan, J. D. Joannopoulos, and C. M. Liddell, “Dimer shape anisotropy: A nonspherical colloidal approach to omnidirectonal photonic band gaps,” Langmuir, vol. 26, pp. 2151–2159, February 2010. [ bib | DOI ]
Theoretical calculations of the photonic band gap forming properties are reported for a class of colloidal dimer-based structures with similarity to zinc blende and which map onto diamond or opalline face-centered cubic structures at the extrema in shape parameters. Inspired by the range of nonspherical building blocks for self-assembly synthesized using seeded emulsion polymerization and sol−gel techniques, we explore in particular the band structures as a function of dimer lobe symmetry and the degree of lobe interpenetration for tangent dimers. Complete photonic band gaps were observed between the second and third, fifth and sixth, or eighth and ninth bands for various shape classes. As well, select inverted and direct dimer-based structures showed two complete band gaps simultaneously.

[59]
A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method,” Computer Physics Communications, vol. 181, pp. 687–702, January 2010. [ bib | DOI | .pdf ]
This paper describes Meep, a popular free implementation of the finite-difference time-domain (FDTD) method for simulating electromagnetism. In particular, we focus on aspects of implementing a full-featured FDTD package that go beyond standard textbook descriptions of the algorithm, or ways in which Meep differs from typical FDTD implementations. These include pervasive interpolation and accurate modeling of subpixel features, advanced signal processing, support for nonlinear materials via Padé approximants, and flexible scripting capabilities.

[60]
A. P. McCauley, A. W. Rodriguez, J. D. Joannopoulos, and S. G. Johnson, “Casimir forces in the time domain: Applications,” Physical Review A, vol. 81, p. 012119, January 2010. [ bib | http | .pdf ]
Our previous article [Phys. Rev. A 80, 012115 (2009)] introduced a method to compute Casimir forces in arbitrary geometries and for arbitrary materials that was based on a finite-difference time-domain (FDTD) scheme. In this article, we focus on the efficient implementation of our method for geometries of practical interest and extend our previous proof-of-concept algorithm in one dimension to problems in two and three dimensions, introducing a number of new optimizations. We consider Casimir pistonlike problems with nonmonotonic and monotonic force dependence on sidewall separation, both for previously solved geometries to validate our method and also for new geometries involving magnetic sidewalls and/or cylindrical pistons. We include realistic dielectric materials to calculate the force between suspended silicon waveguides or on a suspended membrane with periodic grooves, also demonstrating the application of perfectly matched layer (PML) absorbing boundaries and/or periodic boundaries. In addition, we apply this method to a realizable three-dimensional system in which a silica sphere is stably suspended in a fluid above an indented metallic substrate. More generally, the method allows off-the-shelf FDTD software, already supporting a wide variety of materials (including dielectric, magnetic, and even anisotropic materials) and boundary conditions, to be exploited for the Casimir problem.

[61]
D. S. Deng, N. D. Orf, S. Danto, A. F. Abouraddy, J. D. Joannopoulos, and Y. Fink, “Processing and properties of centimeter-long, in-fiber, crystalline-selenium filaments,” Applied Physics Letters, vol. 96, p. 023102, January 2010. [ bib | DOI ]
We report on the fabrication and characterization of globally ordered crystalline selenium filaments with diameters about 200 nm and aspect ratios upwards of 105. Amorphous Se filaments are fabricated by a recently developed approach in which a thin film evolves into an ordered array of filaments in fiber. Single-crystal and polycrystalline filaments are attained with a postdrawing annealing procedure. Arrays of two-cm-long crystalline nanowires, electrically contacted to external circuitry through the fiber end facets, exhibit a two-orders-of-magnitude change in conductivity between dark and illuminated states. These results hold promise for the fabrication of filament-detector arrays that may be integrated with large-area electronics.

[62]
C. Qiu, L. Gao, J. Joannopoulos, and M. Soljačić, “Light scattering from anisotropic particles: propagation, localization, and nonlinearity,” Laser & Photon. Rev., vol. 4, no. 2, pp. 268–282, 2010. [ bib | .pdf ]
Plasmon resonances and extraordinary light scatter- ings of a nanoparticle with radial anisotropy are studied and summarized. The coupling between localized surface plasmons and far-field quantities is discussed. It is found that the presence of radial anisotropy redistributes the localization of plasmons and also results in certain novel phenomena in the far zone, which provide the possibility of scattering control such as elec- tromagnetic transparency, enhanced scattering cross section, etc. The nonlinear optical response is explored in order to yield deeper physical insight into the interaction between plasmons and incident light.

[63]
Z. Wang, Y. Chong, J. D. Joannopoulos, and M. Soljačić, “Observation of unidirectional backscattering-immune topological electromagnetic states,” Nature, vol. 461, pp. 772–775, October 2009. [ bib | DOI ]
One of the most striking phenomena in condensed-matter physics is the quantum Hall effect, which arises in two-dimensional electron systems subject to a large magnetic field applied perpendicular to the plane in which the electrons reside. In such circumstances, current is carried by electrons along the edges of the system, in so-called chiral edge states (CESs). These are states that, as a consequence of nontrivial topological properties of the bulk electronic band structure, have a unique directionality and are robust against scattering from disorder. Recently, it was theoretically predicted that electromagnetic analogues of such electronic edge states could be observed in photonic crystals, which are materials having refractive-index variations with a periodicity comparable to the wavelength of the light passing through them. Here we report the experimental realization and observation of such electromagnetic CESs in a magneto-optical photonic crystal fabricated in the microwave regime. We demonstrate that, like their electronic counterparts, electromagnetic CESs can travel in only one direction and are very robust against scattering from disorder; we find that even large metallic scatterers placed in the path of the propagating edge modes do not induce reflections. These modes may enable the production of new classes of electromagnetic device and experiments that would be impossible using conventional reciprocal photonic states alone. Furthermore, our experimental demonstration and study of photonic CESs provides strong support for the generalization and application of topological band theories to classical and bosonic systems, and may lead to the realization and observation of topological phenomena in a generally much more controlled and customizable fashion than is typically possible with electronic systems.

[64]
A. F. Oskooi, C. Kottke, and S. G. Johnson, “Accurate finite-difference time-domain simulation of anisotropic media by subpixel smoothing,” Optics Letters, vol. 34, pp. 2778–2780, September 2009. [ bib | http | .pdf ]
Finite-difference time-domain methods suffer from reduced accuracy when discretizing discontinuous materials. We previously showed that accuracy can be significantly improved by using subpixel smoothing of the isotropic dielectric function, but only if the smoothing scheme is properly designed. Using recent developments in perturbation theory that were applied to spectral methods, we extend this idea to anisotropic media and demonstrate that the generalized smoothing consistently reduces the errors and even attains second-order convergence with resolution.

[65]
R. E. Hamam, A. Karalis, J. D. Joannopoulos, and M. Soljačić, “Efficient weakly-radiative wireless energy transfer: An EIT-like approach,” Annals of Physics, vol. 324, pp. 1783–1795, August 2009. [ bib | DOI | .pdf ]
Inspired by a quantum interference phenomenon known in the atomic physics community as electromagnetically induced transparency (EIT), we propose an efficient weakly radiative wireless energy transfer scheme between two identical classical resonant objects, strongly coupled to an intermediate classical resonant object of substantially different properties, but with the same resonance frequency. The transfer mechanism essentially makes use of the adiabatic evolution of an instantaneous (so called “dark”) eigenstate of the coupled 3-object system. Our analysis is based on temporal coupled mode theory (CMT), and is general enough to be valid for various possible sorts of coupling, including the resonant inductive coupling on which witricity-type wireless energy transfer is based. We show that in certain parameter regimes of interest, this scheme can be more efficient, and/or less radiative than other, more conventional approaches. A concrete example of wireless energy transfer between capacitively-loaded metallic loops is illustrated at the beginning, as a motivation for the more general case. We also explore the performance of the currently proposed EIT-like scheme, in terms of improving efficiency and reducing radiation, as the relevant parameters of the system are varied.

[66]
M. T. H. Reid, A. W. Rodriguez, J. White, and S. G. Johnson, “Efficient computation of Casimir interactions between arbitrary 3d objects,” Physical Review Letters, vol. 103, p. 040401, July 2009. Invited paper in August 3, 2009, issue of the Virtual Journal of Nanoscale Science & Technology. [ bib | http | .pdf ]
We introduce an efficient technique for computing Casimir energies and forces between objects of arbitrarily complex 3D geometries. In contrast to other recently developed methods, our technique easily handles non-spheroidal, non-axisymmetric objects and objects with sharp corners. Using our new technique, we obtain the first predictions of Casimir interactions in a number of experimentally relevant geometries, including crossed cylinders and tetrahedral nanoparticles.

[67]
C. Qiu, L. Hu, B. Zhang, B.-I. Wu, S. G. Johnson, and J. D. Joannopoulos, “Spherical cloaking using nonlinear transformations for improved segmentation into concentric isotropic coatings,” Optics Express, vol. 17, pp. 13467–13478, July 2009. [ bib | http ]
Two novel classes of spherical invisibility cloaks based on nonlinear transformation have been studied. The cloaking characteristics are presented by segmenting the nonlinear transformation based spherical cloak into concentric isotropic homogeneous coatings. Detailed investigations of the optimal discretization (e.g., thickness control of each layer, nonlinear factor, etc.) are presented for both linear and nonlinear spherical cloaks and their effects on invisibility performance are also discussed. The cloaking properties and our choice of optimal segmentation are verified by the numerical simulation of not only near-field electric-field distribution but also the far-field radar cross section (RCS).

[68]
A. W. Rodriguez, A. P. McCauley, J. D. Joannopoulos, and S. G. Johnson, “Casimir forces in the time domain: Theory,” Physical Review A, vol. 80, p. 012115, July 2009. [ bib | http | .pdf ]
We present a method to compute Casimir forces in arbitrary geometries and for arbitrary materials based on the finite-difference time-domain (FDTD) scheme. The method involves the time evolution of electric and magnetic fields in response to a set of current sources, in a modified medium with frequency-independent conductivity. The advantage of this approach is that it allows one to exploit existing FDTD software, without modification, to compute Casimir forces. In this paper, we focus on the derivation, implementation choices, and essential properties of the time-domain algorithm, both considered analytically and illustrated in the simplest parallel-plate geometry.

[69]
A. Karalis, J. D. Joannopoulos, and M. Soljačić, “Plasmonic-dielectric systems for high-order dispersionless slow or stopped subwavelength light,” Physical Review Letters, vol. 103, p. 043906, July 2009. Invited paper in July 2009 issue of the Virtual Journal of Nanoscale Science & Technology. [ bib | DOI | .pdf ]
A material platform of multilayered surface-plasmon-dielectric-polariton systems is introduced, along with a new physical mechanism enabling simultaneous cancellation of group-velocity and attenuation dispersion to extremely high orders for subwavelength light of any small positive, negative, or zero group velocity. These dispersion-free systems could have significant impact on the development of nanophotonics, e.g., in the design of efficient and very compact delay lines and active devices. The same dispersion-manipulation mechanism can be employed to tailor at will exotic slow-light dispersion relations.

[70]
A. F. Oskooi, J. D. Joannopoulos, and S. G. Johnson, “Zero–group-velocity modes in chalcogenide holey photonic-crystal fibers,” Optics Express, vol. 17, pp. 10082–10090, June 2009. [ bib | http ]
We demonstrate that a holey photonic-crystal fiber with chalcogenide-glass index contrast can be designed to have a complete gap at a propagation constant β= 0 that also extends into the non-zero β region. This type of bandgap (previously identified only at index contrasts unattainable in glasses) opens up a regime for guiding zero–group-velocity modes not possible in holey fibers with the more common finger-like gaps originating from β→∞. Such modes could be used to enhance nonlinear and other material interactions, such as for hollow-core fibers in gas-sensor applications.

[71]
P.-R. Loh, A. F. Oskooi, M. Ibanescu, M. Skorobogatiy, and S. G. Johnson, “Fundamental relation between phase and group velocity, and application to the failure of perfectly matched layers in backward-wave structures,” Physical Review E, vol. 79, p. 065601(R), June 2009. [ bib | http | .pdf ]
We demonstrate that the ratio of group to phase velocity has a simple relationship to the orientation of the electromagnetic field. In nondispersive materials, opposite group and phase velocity corresponds to fields that are mostly oriented in the propagation direction. More generally, this relationship (including the case of dispersive and negative-index materials) offers a perspective on the phenomena of backward waves and left-handed media. As an application of this relationship, we demonstrate and explain an irrecoverable failure of perfectly matched layer absorbing boundaries in computer simulations for constant cross-section waveguides with backward-wave modes and suggest an alternative in the form of adiabatic isotropic absorbers.

[72]
I. B. Burgess, A. W. Rodriguez, M. W. McCutcheon, J. Bravo-Abad, Y. Zhang, S. G. Johnson, and M. Lončar, “Difference-frequency generation with quantum-limited efficiency in triply-resonant nonlinear cavities,” Optics Express, vol. 17, pp. 9241–9251, May 2009. [ bib | http ]
We present a comprehensive study of second-order nonlinear difference frequency generation in triply resonant cavities using a theoretical framework based on coupled-mode theory. We show that optimal quantum-limited conversion efficiency can be achieved at any pump power when the powers at the pump and idler frequencies satisfy a critical relationship. We demonstrate the existence of a broad parameter range in which all triply-resonant DFG processes exhibit monostable conversion. We also demonstrate the existence of a geometry-dependent bistable region.

[73]
A. Mutapcic, S. Boyd, A. Farjadpour, S. G. Johnson, and Y. Avniel, “Robust design of slow-light tapers in periodic waveguides,” Engineering Optimization, vol. 41, pp. 365–384, April 2009. [ bib | DOI | .html ]
This article concerns the design of tapers for coupling power between uniform and slow-light periodic waveguides. New optimization methods are described for designing robust tapers, which not only perform well under nominal conditions, but also over a given set of parameter variations. When the set of parameter variations models the inevitable variations typical in the manufacture or operation of the coupler, a robust design is one that will have a high yield, despite these parameter variations. The ideas of successive refinement, and robust optimization based on multi-scenario optimization with iterative sampling of uncertain parameters, using a fast method for approximately evaluating the reflection coefficient, are introduced. Robust design results are compared to a linear taper, and to optimized tapers that do not take parameter variation into account. Finally, robust performance of the resulting designs is verified using an accurate, but much more expensive, method for evaluating the reflection coefficient.

[74]
R. E. Hamam, M. Ibanescu, S. G. Johnson, J. D. Joannopoulos, and M. Soljačić, “Broadband super-collimation in a hybrid photonic crystal structure,” Optics Express, vol. 17, pp. 8109–8118, April 2009. [ bib | http ]
We propose a two dimensional (2D) photonic crystal (PhC) structure that supports super-collimation over a large frequency range (over 4 times that of a traditional square lattice of holes). We theoretically and numerically investigate the collimation mechanism in our 2D structure, in comparison to that of two other frequently used related PhC structures. We also point out the potential importance of our proposed structure in the design of super-collimation-based devices for both monochromatic and polychromatic light.

[75]
M. Ghebrebrhan, P. Bermel, Y. Avniel, J. D. Joannopoulos, and S. G. Johnson, “Global optimization of silicon photovoltaic cell front coatings,” Optics Express, vol. 17, pp. 7505–7518, April 2009. [ bib | http ]
The front-coating (FC) of a solar cell controls its efficiency, determining admission of light into the absorbing material and potentially trapping light to enhance thin absorbers. Single-layer FC designs are well known, especially for thick absorbers where their only purpose is to reduce reflections. Multilayer FCs could improve performance, but require global optimization to design. For narrow bandwidths, one can always achieve nearly 100% absorption. For the entire solar bandwidth, however, a second FC layer improves performance by 6.1% for 256 μm wafer-based cells, or by 3.6% for 2 μm thin-film cells, while additional layers yield rapidly diminishing returns.

[76]
H. Hashemi, A. W. Rodriguez, J. D. Joannopoulos, M. Soljačić, and S. G. Johnson, “Nonlinear harmonic generation and devices in doubly-resonant Kerr cavities,” Physical Review A, vol. 79, p. 013812, January 2009. [ bib | http | .pdf ]
We describe a theoretical analysis of the nonlinear dynamics of third-harmonic generation (ω→3ω) via Kerr (χ(3)) nonlinearities in a resonant cavity with resonances at both ω and 3ω. Such a doubly resonant cavity greatly reduces the required power for efficient harmonic generation, by a factor of ∼V/Q2 where V is the modal volume and Q is the lifetime, and can even exhibit 100% harmonic conversion efficiency at a critical input power. However, we show that it also exhibits a rich variety of nonlinear dynamics, such as multistable solutions and long-period limit cycles. We describe how to compensate for self- and cross-phase modulation (which otherwise shifts the cavity frequencies out of resonance), and how to excite the different stable solutions (and especially the high-efficiency solutions) by specially modulated input pulses.

[77]
C. Jiang, M. Ibanescu, J. D. Joannopoulos, and M. Soljačić, “Zero-group-velocity modes in longitudinally uniform waveguides,” Applied Physics Letters, vol. 93, p. 241111, December 2008. [ bib | http ]
We present a longitudinally uniform slow light waveguide, which consists of transverse periodic dielectric strips with a few defect layers. The parameters of the proposed waveguide can be tuned to have two anomalous dispersion curves with extreme points which have zero-group-velocity frequencies at nonzero wave vector in uniform-index direction. The group velocity and group velocity dispersion of the two photonic bands are analyzed, and the propagation of the slow mode with a given bandwidth is demonstrated theoretically.

[78]
L. Zeng, P. Bermel, Y. Yi, B. A. Alamariu, K. A. Broderick, J. Liu, C. Hong, X. Duan, J. Joannopoulos, and L. C. Kimerling, “Demonstration of enhanced absorption in thin film Si solar cells with textured photonic crystal back reflector,” Applied Physics Letters, p. 221105, December 2008. [ bib | http ]
Herein the authors report the experimental application of a powerful light trapping scheme, the textured photonic crystal (TPC) backside reflector, to thin film Si solar cells. TPC combines a one-dimensional photonic crystal as a distributed Bragg reflector with a diffraction grating. Light absorption is strongly enhanced by high reflectivity and large angle diffraction, as designed with scattering matrix analysis. 5 μm thick monocrystalline thin film Si solar cells integrated with TPC were fabricated through an active layer transfer technique. Measured short circuit current density Jsc was increased by 19%, compared to a theoretical prediction of 28%.

[79]
A. W. Rodriguez, J. N. Munday, J. D. Joannopoulos, F. Capasso, D. A. R. Dalvit, and S. G. Johnson, “Stable suspension and dispersion-induced transitions from repulsive Casimir forces between fluid-separated eccentric cylinders,” Physical Review Letters, vol. 101, p. 190404, November 2008. [ bib | http | .pdf ]
We numerically demonstrate a stable mechanical suspension of a silica cylinder within a metallic cylinder separated by ethanol, via a repulsive Casimir force between the silica and the metal. We investigate cylinders with both circular and square cross sections, and show that the latter exhibit a stable orientation as well as a stable position, via a method to compute Casimir torques for finite objects. Furthermore, the stable orientation of the square cylinder undergoes a 45o transition as the separation length scale is varied, which is explained as a consequence of material dispersion.

[80]
D. S. Deng, N. D. Orf, A. F. Abouraddy, A. M. Stolyarov, J. D. Joannopoulos, H. A. Stone, and Y. Fink, “In-fiber semiconductor filament arrays,” Nano Letters, vol. 8, pp. 4265–4269, October 2008. [ bib | DOI ]
We report a novel physical phenomenon in which a cylindrical shell undergoing a scaling process evolves into an ordered array of filaments upon reaching a characteristic thickness. We observe that the tendency to breakup is related to the material viscosity in a manner reminiscent of capillary instability. However, unlike the classical breakup of a fluid cylinder into droplets, the structural evolution in our system occurs exclusively in the cross sectional plane while uniformity is maintained in the axial direction. We propose a fluid front instability mechanism to account for the observed phenomena. The fleeting evolution of fluid breakup from a thin film to a filament array is captured in the frozen state by a thermal drawing process which results in extended lengths of solid sub-100 nm filaments encapsulated within a polymer fiber. Hundreds of glassy semiconductor filament arrays are precisely oriented within a polymer fiber matrix making electrical connections trivial. This approach offers unique opportunities for fabrication of nanometer scale devices of unprecedented lengths allowing simplified access and connectivity.

[81]
K. K. Lee, Y. Avniel, and S. G. Johnson, “Design strategies and rigorous conditions for single-polarization single-mode waveguides,” Optics Express, vol. 16, pp. 15170–15184, September 2008. [ bib | http ]
We establish rigorous necessary analytical conditions for the existence of single-polarization single-mode (SPSM) bandwidths in index-guided microstructured waveguides (such as photonic-crystal fibers). These conditions allow us to categorize designs for SPSM waveguides into four strategies, at least one of which seems previously unexplored. Conversely, we obtain rigorous sufficient conditions for the existence of two cutoff-free index-guided modes in a wide variety of microstructured dielectric waveguides with arbitrary periodic claddings, based on the existence of a degenerate fundamental mode of the cladding (a degenerate light line). We show how such a degenerate light line, in turn, follows from the symmetry of the cladding.

[82]
R. E. Hamam, M. Ibanescu, E. J. Reed, P. Bermel, S. G. Johnson, E. Ippen, J. D. Joannopoulos, and M. Soljačić, “Purcell effect in nonlinear photonic structures: a coupled mode theory analysis,” Optics Express, vol. 16, pp. 12523–12537, August 2008. [ bib | http ]
We develop a coupled mode theory (CMT) model of the behavior of a polarization source in a general photonic structure, and obtain an analytical expression for the resulting generated electric field; loss, gain and/or nonlinearities can also be modeled. Based on this treatment, we investigate the criteria needed to achieve an enhancement in various nonlinear effects, and to produce efficient sources of terahertz radiation, in particular. Our results agree well with exact finite-difference time-domain (FDTD) results. Therefore, this approach can also in certain circumstances be used as a potential substitute for the more numerically intensive FDTD method.

[83]
Z. Xu, X. Jiang, J. D. Joannopoulos, L. Torner, and M. Soljačić, “Nonlinear photonic crystals near the supercollimation point,” Optics Letters, vol. 33, pp. 1762–1764, August 2008. [ bib | DOI | .pdf ]
We uncover a strong coupling between nonlinearity and diffraction in a photonic crystal at the supercollimation point. We show that this is modeled by a nonlinear diffraction term in a nonlinear-Schrödinger-type equation in which the properties of solitons are investigated. Linear stability analysis shows solitons are stable in an existence domain that obeys the Vakhitov–Kolokolov criterium. In addition, we investigate the influence of the nonlinear diffraction on soliton collision scenarios.

[84]
A. F. Oskooi, L. Zhang, Y. Avniel, and S. G. Johnson, “The failure of perfectly matched layers, and towards their redemption by adiabatic absorbers,” Optics Express, vol. 16, pp. 11376–11392, July 2008. [ bib | http ]
Although perfectly matched layers (PMLs) have been widely used to truncate numerical simulations of electromagnetism and other wave equations, we point out important cases in which a PML fails to be reflectionless even in the limit of infinite resolution. In particular, the underlying coordinate-stretching idea behind PML breaks down in photonic crystals and in other structures where the material is not an analytic function in the direction perpendicular to the boundary, leading to substantial reflections. The alternative is an adiabatic absorber, in which reflections are made negligible by gradually increasing the material absorption at the boundaries, similar to a common strategy to combat discretization reflections in PMLs. We demonstrate the fundamental connection between such reflections and the smoothness of the absorption profile via coupled-mode theory, and show how to obtain higher-order and even exponential vanishing of the reflection with absorber thickness (although further work remains in optimizing the constant factor).

[85]
K. K. Y. Lee, Y. Avniel, and S. G. Johnson, “Rigorous sufficient conditions for index-guided modes in microstructured dielectric waveguides,” Optics Express, vol. 16, pp. 9261–9275, June 2008. [ bib | DOI | http ]
We derive a sufficient condition for the existence of index-guided modes in a very general class of dielectric waveguides, including photonic-crystal fibers (arbitrary periodic claddings, such as “holey fibers”), anisotropic materials, and waveguides with periodicity along the propagation direction. This condition provides a rigorous guarantee of cutoff-free index-guided modes in any such structure where the core is formed by increasing the index of refraction (e.g. removing a hole). It also provides a weaker guarantee of guidance in cases where the refractive index is increased “on average” (precisely defined). The proof is based on a simple variational method, inspired by analogous proofs of localization for two-dimensional attractive potentials in quantum mechanics.

[86]
A. W. Rodriguez, J. D. Joannopoulos, and S. G. Johnson, “Repulsive and attractive Casimir forces in a glide-symmetric geometry,” Physical Review A, vol. 77, p. 062107, June 2008. [ bib | http ]
We describe a three-dimensional geometry in which both attractive and repulsive Casimir forces arise using ordinary metallic materials, as computed via an exact numerical method (no uncontrolled approximations). The geometry consists of a zipperlike, glide-symmetric structure formed of interleaved metal brackets attached to parallel platesâbecause of the interleaving pattern, a net repulsive force can arise from a combination of attractive interactions. Depending on the separation, the perpendicular force between the plates and brackets varies from attractive (large separations) to repulsive (intermediate distances) and back to attractive (close separations), with one point of stable equilibrium in the perpendicular direction. This geometry was motivated by a simple intuition of attractive interactions between surfaces, and so we also consider how a rough proximity-force approximation of pairwise attractions compares to the exact calculations.

[87]
Y. D. Chong, X.-G. Wen, and M. Soljačić, “Effective theory of quadratic degeneracies,” Physical Review B, vol. 77, p. 235125, June 2008. [ bib | http ]
We present an effective theory for the Bloch functions of a two-dimensional square lattice near a quadratic degeneracy point. The degeneracy is protected by the symmetries of the crystal, and breaking these symmetries can either open a band gap or split the degeneracy into a pair of linear degeneracies that are continuable to Dirac points. A degeneracy of this type occurs between the second and third transverse magnetic bands of a photonic crystal formed by a square lattice of dielectric rods. We show that the theory agrees with numerically computed photonic band structures and yields the correct Chern numbers induced by parity breaking.

[88]
A. W. Rodriguez, A. P. McCauley, Y. Avniel, and S. G. Johnson, “Computation and visualization of photonic quasicrystal spectra via Bloch's theorem,” Physical Review B, vol. 77, p. 104201, March 2008. [ bib | http | .pdf ]
Previous methods for determining photonic quasicrystal (PQC) spectra have relied on the use of large supercells to compute the eigenfrequencies and/or local density of states (LDOS). In this manuscript, we present a method by which the energy spectrum and the eigenstates of a PQC can be obtained by solving Maxwell's equations in higher dimensions for any PQC defined by the standard cut-and-project construction, to which a generalization of Bloch's theorem applies. In addition, we demonstrate how one can compute band structures with defect states in the higher-dimensional superspace with no additional computational cost. As a proof of concept, these general ideas are demonstrated for the simple case of one-dimensional quasicrystals, which can also be solved by simple transfer-matrix techniques.

[89]
S. J. Rahi, A. W. Rodriguez, T. Emig, R. L. Jaffe, S. G. Johnson, and M. Kardar, “Nonmonotonic effects of parallel sidewalls on Casimir forces between cylinders,” Physical Review A, vol. 77, p. 030101(R), March 2008. [ bib | http | .pdf ]
We analyze the Casimir force between two parallel infinite metal cylinders with nearby metal plates using two methods. Surprisingly, the attractive force between cylinders depends nonmonotonically on the separation from the plate(s), and the cylinder-plate force depends nonmonotonically on the separation of the cylinders. These multibody phenomenona do not follow from simple two-body force descriptions. We can explain the nonmonotonicity with the screening (enhancement) of the interactions by the fluctuating charges (currents) on the two cylinders and their images on the nearby plate(s).

[90]
C. Kottke, A. Farjadpour, and S. G. Johnson, “Perturbation theory for anisotropic dielectric interfaces, and application to sub-pixel smoothing of discretized numerical methods,” Physical Review E, vol. 77, p. 036611, March 2008. [ bib | http | .pdf ]
We derive a correct first-order perturbation theory in electromagnetism for cases where an interface between two anisotropic dielectric materials is slightly shifted. Most previous perturbative methods give incorrect results for this case, even to lowest order, because of the complicated discontinuous boundary conditions on the electric field at such an interface. Our final expression is simply a surface integral, over the material interface, of the continuous field components from the unperturbed structure. The derivation is based on a “localized” coordinate-transformation technique, which avoids both the problem of field discontinuities and the challenge of constructing an explicit coordinate transformation by taking a limit in which a coordinate perturbation is infinitesimally localized around the boundary. Not only is our result potentially useful in evaluating boundary perturbations, e.g. from fabrication imperfections, in highly anisotropic media such as many metamaterials, but it also has a direct application in numerical electromagnetism. In particular, we show how it leads to a sub-pixel smoothing scheme to ameliorate staircasing effects in discretized simulations of anisotropic media, in such a way as to greatly reduce the numerical errors compared to other proposed smoothing schemes.

[91]
J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light. Princeton University Press, second ed., February 2008. [ bib | http ]
Since it was first published in 1995, Photonic Crystals has remained the definitive text for both undergraduates and researchers on photonic band-gap materials and their use in controlling the propagation of light. This newly expanded and revised edition covers the latest developments in the field, providing the most up-to-date, concise, and comprehensive book available on these novel materials and their applications.

Starting from Maxwell's equations and Fourier analysis, the authors develop the theoretical tools of photonics using principles of linear algebra and symmetry, emphasizing analogies with traditional solid-state physics and quantum theory. They then investigate the unique phenomena that take place within photonic crystals at defect sites and surfaces, from one to three dimensions. This new edition includes entirely new chapters describing important hybrid structures that use band gaps or periodicity only in some directions: periodic waveguides, photonic-crystal slabs, and photonic-crystal fibers. The authors demonstrate how the capabilities of photonic crystals to localize light can be put to work in devices such as filters and splitters. A new appendix provides an overview of computational methods for electromagnetism. Existing chapters have been considerably updated and expanded to include many new three-dimensional photonic crystals, an extensive tutorial on device design using temporal coupled-mode theory, discussions of diffraction and refraction at crystal interfaces, and more. Richly illustrated and accessibly written, Photonic Crystals is an indispensable resource for students and researchers.

[92]
Z. Wang, Y. D. Chong, J. D. Joannopoulos, and M. Soljačić, “Reflection-free one-way edge modes in a gyromagnetic photonic crystal,” Physical Review Letters, vol. 100, p. 013905, January 2008. [ bib | http | .pdf ]
We point out that electromagnetic one-way edge modes analogous to quantum Hall edge states, originally predicted by Raghu and Haldane in 2D photonic crystals possessing Dirac point-derived band gaps, can appear in more general settings. We show that the TM modes in a gyromagnetic photonic crystal can be formally mapped to electronic wave functions in a periodic electromagnetic field, so that the only requirement for the existence of one-way edge modes is that the Chern number for all bands below a gap is nonzero. In a square-lattice yttrium-iron-garnet crystal operating at microwave frequencies, which lacks Dirac points, time-reversal breaking is strong enough that the effect should be easily observable. For realistic material parameters, the edge modes occupy a 10% band gap. Numerical simulations of a one-way waveguide incorporating this crystal show 100% transmission across strong defects.

[93]
A. Karalis, J. D. Joannopoulos, and M. Soljačić, “Efficient wireless non-radiative mid-range energy transfer,” Annals of Physics, vol. 323, pp. 34–48, January 2008. [ bib | DOI | .pdf ]
We investigate whether, and to what extent, the physical phenomenon of long-lifetime resonant electromagnetic states with localized slowly-evanescent field patterns can be used to transfer energy efficiently over non-negligible distances, even in the presence of extraneous environmental objects. Via detailed theoretical and numerical analyses of typical real-world model-situations and realistic material parameters, we establish that such a non-radiative scheme can strong coupling between two medium-range distant such states and thus could indeed be practical for efficient medium-range wireless energy transfer.

[94]
E. J. Reed, M. R. Manaa, L. E. Fried, K. R. Glaesemann, and J. D. Joannopoulos, “A transient semimetallic layer in detonating nitromethane,” Nature Physics, vol. 4, pp. 72–76, January 2008. [ bib | DOI ]
Despite decades of research, the microscopic details and extreme states of matter found within a detonating high explosive have yet to be elucidated. Here we present the first quantum molecular-dynamics simulation of a shocked explosive near detonation conditions. We discover that the wide-bandgap insulator nitromethane (CH3NO2) undergoes chemical decomposition and a transformation into a semimetallic state for a limited distance behind the detonation front. We find that this transformation is associated with the production of charged decomposition species and provides a mechanism to explain recent experimental observations.

[95]
S. Zaheer, A. W. Rodriguez, S. G. Johnson, and R. L. Jaffe, “Optical-approximation analysis of sidewall-spacing effects on the force between two squares with parallel sidewalls,” Physical Review A, vol. 76, p. 063816, December 2007. [ bib | .pdf ]
Using the ray-optics approximation, we analyze the Casimir force in a two-dimensional domain formed by two metallic blocks adjacent to parallel metallic sidewalls, which are separated from the blocks by a finite distance h. For h>0, the ray-optics approach is not exact because diffraction effects are neglected. Nevertheless, we show that ray optics is able to qualitatively reproduce a surprising effect recently identified in an exact numerical calculation: the force between the blocks varies nonmonotonically with h. In this sense, the ray-optics approach captures an essential part of the physics of multibody interactions in this system, unlike simpler pairwise-interaction approximations such as proximity force approximations (PFA). Furthermore, by comparison to the exact numerical results, we are able to quantify the impact of diffraction on Casimir forces in this geometry.

[96]
M. Ghebrebrhan, M. Ibanescu, S. G. Johnson, M. Soljačić, and J. D. Joannopoulos, “Distinguishing zero-group-velocity modes in photonic crystals,” Physical Review A, vol. 76, p. 063810, December 2007. [ bib | .pdf ]
We examine differences between various zero-group-velocity modes in photonic crystals, including those that arise from Bragg diffraction, anticrossings, and band repulsion. Zero-group velocity occurs at points where the group velocity changes sign, and therefore is conceptually related to “left-hande” media, in which the group velocity is opposite to the phase velocity. We consider this relationship more quantitatively in terms of the Fourier decomposition of the modes, by defining a measure of how much the “average” phase velocity is parallel to the group velocity—an anomalous region is one in which they are mostly antiparallel. We find that this quantity can be used to qualitatively distinguish different zero-group-velocity points. In one dimension, such anomalous regions are found never to occur. In higher dimensions, they are exhibited around certain zero-group-velocity points, and lead to unusual enhanced confinement behavior in microcavities.

[97]
P. Bermel, C. Luo, L. Zeng, L. C. Kimerling, and J. D. Joannopoulos, “Improving thin-film crystalline silicon solar cell efficiencies with photonic crystals,” Optics Express, vol. 15, pp. 16986–17000, December 2007. [ bib | http ]
Most photovoltaic (solar) cells are made from crystalline silicon (c-Si), which has an indirect band gap. This gives rise to weak absorption of one-third of usable solar photons. Therefore, improved light trapping schemes are needed, particularly for c-Si thin film solar cells. Here, a photonic crystal-based light-trapping approach is analyzed and compared to previous approaches. For a solar cell made of a 2 μm thin film of c-Si and a 6 bilayer distributed Bragg reflector (DBR) in the back, power generation can be enhanced by a relative amount of 24.0% by adding a 1D grating, 26.3% by replacing the DBR with a six-period triangular photonic crystal made of air holes in silicon, 31.3% by a DBR plus 2D grating, and 26.5% by replacing it with an eight-period inverse opal photonic crystal.

[98]
J. Bravo-Abad, A. Rodriguez, P. Bermel, S. G. Johnson, J. D. Joannopoulos, and M. Soljačić, “Enhanced nonlinear optics in photonic-crystal microcavities,” Optics Express, vol. 15, pp. 16161–16176, November 2007. [ bib | http | .pdf ]
Nonlinear photonic-crystal microresonators offer unique fundamental ways of enhancing a variety of nonlinear optical processes. This enhancement improves the performance of nonlinear optical devices to such an extent that their corresponding operation powers and switching times are suitable for their implementation in realistic ultrafast integrated optical devices. Here, we review three different nonlinear optical phenomena that can be strongly enhanced in photonic crystal microcavities. First, we discuss a system in which this enhancement has been successfully demonstrated both theoretically and experimentally, namely, a photonic crystal cavity showing optical bistability properties. In this part, we also present the physical basis for this dramatic improvement with respect to the case of traditional nonlinear devices based on nonlinear Fabry-Perot etalons. Secondly, we show how nonlinear photonic crystal cavities can be also used to obtain complete second-harmonic frequency conversion at very low input powers. Finally, we demonstrate that the nonlinear susceptibility of materials can be strongly modified via the so-called Purcell effect, present in the resonant cavities under study.

[99]
J. Bravo-Abad, S. Fan, S. G. Johnson, J. D. Joannopoulos, and M. Soljačić, “Modeling nonlinear optical phenomena in nanophotonics,” Journal of Lightwave Technology, vol. 25, pp. 2539–2546, September 2007. Invited paper. [ bib | .pdf ]
In this paper, we review various numerical methods currently used to model nonlinear optical processes in nanophotonics. Among the different theoretical frameworks that have been used to study nonlinear photonic structures, we particularly focus on the application of both perturbation theory and coupled-mode theory to the analysis of complex nonlinear nanophotonic devices. This description is illustrated on several examples of how these techniques can be used to design photonic-crystal-based nonlinear devices. In addition, in all these examples, we show that the predictions made by the two mentioned techniques are in a good agreement with the numerical results obtained from a nonlinear finite-difference-time-domain approach to these problems.

[100]
A. Rodriguez, M. Ibanescu, D. Iannuzzi, J. D. Joannopoulos, and S. G. Johnson, “Virtual photons in imaginary time: Computing exact Casimir forces via standard numerical-electromagnetism techniques,” Physical Review A, vol. 76, p. 032106, September 2007. [ bib | .pdf ]
We describe a numerical method to compute Casimir forces in arbitrary geometries, for arbitrary dielectric and metallic materials, with arbitrary accuracy (given sufficient computational resources). Our approach, based on well-established integration of the mean stress tensor evaluated via the fluctuation-dissipation theorem, is designed to directly exploit fast methods developed for classical computational electromagnetism, since it only involves repeated evaluation of the Green's function for imaginary frequencies (equivalently, real frequencies in imaginary time). We develop the approach by systematically examining various formulations of Casimir forces from the previous decades and evaluating them according to their suitability for numerical computation. We illustrate our approach with a simple finite-difference frequency-domain implementation, test it for known geometries such as a cylinder and a plate, and apply it to new geometries. In particular, we show that a pistonlike geometry of two squares sliding between metal walls, in both two and three dimensions with both perfect and realistic metallic materials, exhibits a surprising non-monotonic “lateral” force from the walls.

[101]
P. Bermel, A. Rodriguez, J. D. Joannopoulos, and M. Soljačić, “Tailoring optical nonlinearities via the Purcell effect,” Physical Review Letters, vol. 99, p. 053601, August 2007. [ bib | http | .pdf ]
We predict that the effective nonlinear optical susceptibility can be tailored using the Purcell effect. While this is a general physical principle that applies to a wide variety of nonlinearities, we specifically investigate the Kerr nonlinearity. We show theoretically that using the Purcell effect for frequencies close to an atomic resonance can substantially influence the resultant Kerr nonlinearity for light of all (even highly detuned) frequencies. For example, in realistic physical systems, enhancement of the Kerr coefficient by one to two orders of magnitude could be achieved.

[102]
A. Rodriguez, M. Ibanescu, D. Iannuzzi, F. Capasso, J. D. Joannopoulos, and S. G. Johnson, “Computation and visualization of Casimir forces in arbitrary geometries: Nonmonotonic lateral-wall forces and the failure of proximity-force approximations,” Physical Review Letters, vol. 99, p. 080401, August 2007. [ bib | .pdf ]
We present a method of computing Casimir forces for arbitrary geometries, with any desired accuracy, that can directly exploit the efficiency of standard numerical-electromagnetism techniques. Using the simplest possible finite-difference implementation of this approach, we obtain both agreement with past results for cylinder-plate geometries, and also present results for new geometries. In particular, we examine a pistonlike problem involving two dielectric and metallic squares sliding between two metallic walls, in two and three dimensions, respectively, and demonstrate nonadditive and nonmonotonic changes in the force due to these lateral walls.

[103]
E. J. Reed, M. R. Armstrong, K. Kim, M. Soljačić, R. Gee, J. H. Glownia, and J. D. Joannopoulos, “Terahertz radiation from shocked materials,” Materials Today, vol. 10, pp. 44–50, July 2007. [ bib | DOI | .pdf ]
Distinct physical mechanisms for the generation of temporally coherent, narrow bandwidth optical radiation are few and rare in nature. Such sources, including lasers, have widespread applications ranging from spectroscopy to interferometry. We review the recent theoretical prediction of a new type of temporally coherent optical radiation source in the 1–100 THz frequency range that can be realized when crystalline polarizable materials like NaCl are subject to a compressive shock wave.

[104]
X. Jiang, C. Zhou, X. Yu, S. Fan, M. Soljačić, and J. D. Joannopoulos, “The nonlinear effect from the interplay between the nonlinearity and the supercollimation of photonic crystal,” Applied Physics Letters, vol. 91, p. 031105, July 2007. [ bib | http | .pdf ]
The authors theoretically and numerically investigate the beam propagation near the supercollimation frequency ωn0 in a photonic crystal made of nonlinear material. Since the value and sign of the equal-frequency-contour curvature which dominates the beam behaviors can be nonlinearly tuned near ωn0, a kind of nonlinear effect is generated. The envelope equation with unique form is also obtained. Beam-control mechanisms are theoretically predicted and observed in numerical experiments, such as tunable collimation, tunable beam-divergence angle, and self-lock of collimation. These mechanisms can be utilized to function as fiber, lens and coupler, or to design photonic devices.

[105]
A. Kurs, A. Karalis, R. Moffat, J. D. Joannopoulos, P. Fisher, and M. Soljačić, “Wireless power transfer via strongly coupled magnetic resonances,” Science, vol. 317, pp. 83–86, July 2007. [ bib | DOI ]
Using self-resonant coils in a strongly coupled regime, we experimentally demonstrated efficient nonradiative power transfer over distances up to 8 times the radius of the coils. We were able to transfer 60 watts with  40% efficiency over distances in excess of 2 meters. We present a quantitative model describing the power transfer, which matches the experimental results to within 5%. We discuss the practical applicability of this system and suggest directions for further study.

[106]
R. E. Hamam, A. Karalis, J. D. Joannopoulos, and M. Soljačić, “Coupled-mode theory for general free-space resonant scattering of waves,” Physical Review A, vol. 75, p. 053801, May 2007. [ bib | http | .pdf ]
We present a universal coupled-mode-theory treatment of free-space scattering of waves from resonant objects. The range of applicability of the presented approach is fairly broad: it can be used for almost any linear wave system, as long as the resonant scatterer has either three-dimensional (3D) spherical or 2D cylindrical symmetry, or else is sufficiently smaller than the resonant wavelength of the incident wave. The presented framework, while being intuitive and analytically simple, can nevertheless provide quantitatively very accurate modeling of scattering cross sections, absorption cross sections, and many other quantities of interest. We illustrate this approach by showing how it applies to the particular examples of scattering of light from spherically symmetric resonant objects and atoms, and scattering of neutrons off nuclei.

[107]
E. J. Reed, M. Soljačić, and J. D. Joannopoulos, “Maxwell equation simulations of coherent optical photon emission from shock waves in crystals,” Physical Review E, vol. 75, p. 056611, May 2007. [ bib | http | .pdf ]
We have predicted that weak coherent radiation in the 12013100 THz frequency regime can be emitted under some circumstances when a shock wave propagates through a polarizable crystal, like NaCl [Reed et al., Phys. Rev. Lett. 96, 013904 (2006)]. In this work, we present and analyze a new model of a shocked polarizable crystal that is amenable to systematic analytical study and direct numerical solution of Maxwell's equations to predict emitted coherent field amplitudes and properties. Our simulations and analysis indicate that the field amplitude of the effect decreases rapidly with increasing shock front rise distance. These models establish a fundamental limit of the ratio of emitted terahertz amplitude to the static polarization of a material. While this effect is treated classically in our previous work, we present a quantum perturbation analysis showing that it can also occur in the low-amplitude emission quantum limit.

[108]
O. Shapira, A. Stolyarov, N. D. Orf, K. Kuriki, A. F. Abouraddy, J. D. Joannopoulos, and Y. Fink, “Towards dynamic surface-emitting fiber lasers,” Optics and Photonics News, vol. 18, pp. 26–31, May 2007. [ bib | http ]
The surface-emitting fiber laser combines characteristics of fiber lasers and VCSELs that could be translated into new and exciting applications in medicine, security and “smart” fabrics.

[109]
D.-Z. A. Chen, R. Hamam, M. Soljačić, J. D. Joannopoulos, and G. Chen, “Extraordinary optical transmission through subwavelength holes in a polaritonic silicon dioxide film,” Applied Physics Letters, vol. 90, p. 181921, May 2007. [ bib | http | .pdf ]
The authors present experimental data showing that extraordinary optical transmission occurs through subwavelength holes etched in an amorphous silicon dioxide film. The discrete frequency ranges of the enhanced transmission suggest the involvement of surface phonon-polaritons in mediating the transmission in a manner analogous to surface plasmons on metal films. Finite-difference time-domain simulations also predict the enhancement and correlate well with the experimental data. Both experimental and theoretical results show a fivefold increase in transmission through a perforated film versus a solid film.

[110]
E. J. Reed, M. Soljačić, R. Gee, and J. D. Joannopoulos, “Molecular dynamics simulations of coherent optical photon emission from shock waves in crystals,” Physical Review B, vol. 75, p. 174302, May 2007. [ bib | http | .pdf ]
We have previously predicted that coherent electromagnetic radiation in the 1–100 THz frequency range can be generated in crystalline polarizable materials when subject to a shock wave or solitonlike propagating excitation [E. J. Reed et al., Phys. Rev. Lett. 96, 013904 (2006)]. In this work, we present analysis and molecular dynamics simulations of shock waves in crystalline NaCl which expand upon this prediction. We demonstrate that the coherent polarization currents responsible for the effect are generated by a nonresonant, nonlinear effect that occurs at the shock front. We consider the effect of thermal noise and various shock pressures on the coherent polarization currents and find that the amplitude generally increases with increasing shock pressure and decreasing material temperature. Finally, we present calculations of the amplitude and distribution of emitted radiation showing that the radiation can be directed or undirected under various realistic conditions of the shape of the shock front.

[111]
A. Rodriguez, M. Soljačić, J. D. Joannopoulos, and S. G. Johnson, “χ(2) and χ(3) harmonic generation at a critical power in inhomogeneous doubly resonant cavities,” Optics Express, vol. 15, pp. 7303–7318, May 2007. [ bib | http | .pdf ]
We derive general conditions for 100% frequency conversion in any doubly resonant nonlinear cavity, for both second- and third-harmonic generation via χ(2) and χ(3) nonlinearities. We find that conversion efficiency is optimized for a certain “critical” power depending on the cavity parameters, and assuming reasonable parameters we predict 100% conversion using milliwatts of power or less. These results follow from a semi-analytical coupled-mode theory framework which is generalized from previous work to include both χ(2) and χ(3) media as well as inhomogeneous (fully vectorial) cavities, analyzed in the high-efficiency limit where down-conversion processes lead to a maximum efficiency at the critical power, and which is verified by direct finite-difference time-domain (FDTD) simulations of the nonlinear Maxwell equations. Explicit formulas for the nonlinear coupling coefficients are derived in terms of the linear cavity eigenmodes, which can be used to design and evaluate cavities in arbitrary geometries.

[112]
B. Maes, M. Ibanescu, J. D. Joannopoulos, P. Bienstman, and R. Baets, “Microcavities based on multimodal interference,” Optics Express, vol. 15, pp. 6268–6278, May 2007. [ bib | http ]
We describe intricate cavity mode structures, that are possible in waveguide devices with two or more guided modes. The main element is interference between the scattered fields of two modes at the facets, resulting in multipole or mode cancelations. Therefore, strong coupling between the modes, such as around zero group velocity points, is advantageous to obtain high quality factors. We discuss the mechanism in three different settings: a cylindrical structure with and without negative group velocity mode, and a surface plasmon device. A general semi-analytical expression for the cavity parameters describes the phenomenon, and it is validated with extensive numerical calculations.

[113]
E. Lidorikis, S. Egusa, and J. D. Joannopoulos, “Effective medium properties and photonic crystal superstructures of metallic nanoparticle arrays,” Journal of Applied Physics, vol. 101, p. 054304, March 2007. [ bib | http ]
Using the finite-difference time-domain method we extract the effective optical constants of metallic nanoparticle arrays. We explore their behavior in the full range of filling fractions and find excellent agreement with the Maxwell-Garnett [Philos. Trans. R. Soc. London 203, 385 (1904)] effective medium theory for the effective dielectric constant. We also find that the resonance response of such systems exhibits an effective magnetic component, typically overlooked in standard effective medium theories. We verify that the description of these nanoarrays as an effective bulk medium is exact within numerical precision, at least in one-dimensional arrangements, by comparing with full simulations of more complex superlayer configurations. Finally, using the effective constants we study photonic crystal superstructures consisting of these arrays, demonstrating an interesting optical response where resonant absorption and reflection bands are separated by extremely sharp edges of almost 100% relative change per nanometer wavelength.

[114]
D. L. Chan, I. Celanovic, J. D. Joannopoulos, and M. Soljačić, “Emulating one-dimensional resonant Q-matching behavior in a two-dimensional system via Fano resonances,” Physical Review A, vol. 74, p. 064901, December 2006. [ bib | http | .pdf ]
Through detailed numerical and analytical studies, we establish that the significant enhancement of thermal emission via Q matching, which has been possible in one-dimensional (1D) systems only, can be extended to two-dimensional (2D) systems by means of Fano resonances in the 2D system. In particular, we show the existence of essentially 1D behavior in a 2D system—a case of reduced dimensionality. Moreover, we show how properties of these spectra can be controlled by changing the geometrical parameters of the 2D system.

[115]
A. F. Abouraddy, O. Shapira, M. Bayindir, J. Arnold, J. D. Joannopoulos, and Y. Fink, “Fabrics that “see”: Photosensitive fibers,” Optics and Photonics News, vol. 17, p. 21, December 2006. [ bib | http ]
We can now construct conformal detectors that allow us to have optically functional clothing.

[116]
S. A. Jacobs, B. Temelkuran, O. Weisberg, M. Ibanescu, S. G. Johnson, and M. Soljačić, “Hollow core fibers,” in Specialty Optical Fibers Handbook (A. Mendez and T. Morse, eds.), ch. 11, New York: Elsevier, December 2006. [ bib ]
[117]
M. Bayindir, A. F. Abouraddy, O. Shapira, J. Viens, D. S. Saygin-Hinczewski, F. Sorin, J. Arnold, J. D. Joannopoulos, and Y. Fink, “Kilometer-long ordered nanophotonic devices by preform-to-fiber fabrication,” IEEE J. Selected Topics in Quantum Electronics, vol. 12, pp. 1202–1213, November 2006. [ bib | DOI ]
A preform-to-fiber approach to the fabrication of functional fiber-based devices by thermal drawing in the viscous state is presented. A macroscopic preform rod containing metallic, semiconducting, and insulating constituents in a variety of geometries and close contact produces kilometer-long novel nanostructured fibers and fiber devices. We first review the material selection criteria and then describe metal–semiconductor–metal photosensitive and thermally sensitive fibers. These flexible, lightweight, and low-cost functional fibers may pave the way for new types of fiber sensors, such as thermal sensing fabrics, artificial skin, and large-area optoelectronic screens. Next, the preform-to-fiber approach is used to fabricate spectrally tunable photodetectors that integrate a photosensitive core and a nanostructured photonic crystal structure containing a resonant cavity. An integrated, self-monitoring optical-transmission waveguide is then described that incorporates optical transport and thermal monitoring. This fiber allows one to predict power-transmission failure, which is of paramount importance if high-power optical transmission lines are to be operated safely and reliably in medical, industrial and defense applications. A hybrid electron–photon fiber consisting of a hollow core (for optical transport by means of a photonic bandgap) and metallic wires (for electron transport) is described that may be used for transporting atoms and molecules by radiation pressure. Finally, a solid microstructured fiber fabricated with a highly nonlinear chalcogenide glass enables the generation of supercontinuum light at near-infrared wavelengths.

[118]
J. Bravo-Abad, M. Ibanescu, J. D. Joannopoulos, and M. Soljačić, “Photonic crystal optical waveguides for on-chip Bose-Einstein condensates,” Physical Review A, vol. 74, p. 053619, November 2006. [ bib | http | .pdf ]
We propose an on-chip optical waveguide for Bose-Einstein condensates based on the evanescent light fields created by surface states of a photonic crystal. It is shown that the modal properties of these surface states can be tailored to confine the condensate at distances from the chip surface significantly longer that those that can be reached by using conventional index-contrast guidance. We numerically demonstrate that by index-guiding the surface states through two parallel waveguides, the atomic cloud can be confined in a two-dimensional trap at about 1 μm above the structure using a power of 0.1 mW.

[119]
Y. Yi, S. Akiyama, P. Bermel, X. Duan, and L. C. Kimerling, “Sharp bending of on-chip silicon Bragg cladding waveguide with light guiding in low index core materials,” IEEE J. Selected Topics in Quantum Electronics, vol. 12, pp. 1345–1348, November 2006. [ bib | DOI | .pdf ]
A novel on-chip Bragg cladding waveguide is designed and fabricated using conventional CMOS techniques. This optical waveguide has a low refractive index core surrounded by high index-contrast cladding bilayers. Polysilicon (n = 3.5) and silicon nitride (n=2.0) are used for high index-contrast Bragg layers, where index difference is as high as 1.5. Our simulation shows that sharp bending in low index core materials can be achieved, which is not possible using index guiding mechanism. Within our approach, various on-chip applications are expected such as optical integration, high power transmission, biosensor/microelectromechanical system and so on.

[120]
B. Maes, M. Soljačić, J. D. Joannopoulos, P. Bienstman, R. Baets, S.-P. Gorza, and M. Haelterman, “Switching through symmetry breaking in coupled nonlienar micro-cavities,” Optics Express, vol. 14, pp. 10678–10683, October 2006. [ bib | http | .pdf ]
We describe stable symmetry-breaking states in systems with two coupled nonlinear cavities, using coupled-mode theory and rigorous simulations. Above a threshold input level the symmetric state of the passive Kerr system becomes unstable, and we show how this phenomenon can be employed for switching and flip-flop purposes, using positive pulses only. A device with compact photonic crystal microcavities is proposed by which we numerically demonstrate the principle.

[121]
P. Bermel, A. Rodriguez, S. G. Johnson, J. D. Joannopoulos, and M. Soljačić, “Single-photon all-optical switching using waveguide-cavity quantum electrodynamics,” Physical Review A, vol. 74, p. 043818, October 2006. [ bib | http | .pdf ]
This paper demonstrates switching of a single signal photon by a single gating photon of a different frequency, via a cross-phase-modulation. This effect is mediated by materials exhibiting electromagnetically induced transparency (EIT), which are embedded in photonic crystals (PhCs). An analytical model based on waveguide-cavity QED is constructed for our system, which consists of a PhC waveguide and a PhC microcavity containing a four-level EIT atom. It is solved exactly and analyzed using experimentally accessible parameters. It is found that the strong coupling regime is required for lossless two-photon quantum entanglement.

[122]
A. Farjadpour, D. Roundy, A. Rodriguez, M. Ibanescu, P. Bermel, J. D. Joannopoulos, S. G. Johnson, and G. Burr, “Improving accuracy by subpixel smoothing in FDTD,” Optics Letters, vol. 31, pp. 2972–2974, October 2006. [ bib | .pdf ]
Finite-difference time-domain (FDTD) methods suffer from reduced accuracy when modeling discontinuous dielectric materials, due to the inhererent discretization (pixelization). We show that accuracy can be significantly improved by using a subpixel smoothing of the dielectric function, but only if the smoothing scheme is properly designed. We develop such a scheme based on a simple criterion taken from perturbation theory and compare it with other published FDTD smoothing methods. In addition to consistently achieving the smallest errors, our scheme is the only one that attains quadratic convergence with resolution for arbitrarily sloped interfaces. Finally, we discuss additional difficulties that arise for sharp dielectric corners.

[123]
D. L. Chan, M. Soljačić, and J. D. Joannopoulos, “Direct calculation of thermal emission for three-dimensionally periodic photonic-crystal slabs,” Physical Review E, vol. 74, p. 036615, September 2006. [ bib | http | .pdf ]
We perform direct thermal emission calculations for three-dimensionally periodic photonic crystal slabs using stochastic electrodynamics following the Langevin approach, implemented via a finite-difference time-domain algorithm. We demonstrate that emissivity and absorptivity are equal, by showing that such photonic crystal systems emit as much radiation as they absorb, for every frequency, up to statistical fluctuations. We also study the effect of surface termination on absorption and emission spectra from these systems.

[124]
D. L. C. Chan and M. Soljačić, “Thermal emission and design in 2d-periodic metallic photonic crystal slabs,” Optics Express, vol. 14, pp. 8785–8796, September 2006. [ bib | http ]
We present a useful framework within which we can understand some of the physical phenomena that drive thermal emission in 2D-periodic metallic photonic crystal slabs, emphasizing phenomenology and physical intuition. Through detailed numerical calculations for these systems, we find that periodicity plays a key role in determining the types of physical phenomena that can be excited. We identify two structures as good candidates for thermal design, and conclude with a discussion of how the emissive properties of these systems can be tailored to our needs.

[125]
D. L. Chan, M. Soljačić, and J. D. Joannopoulos, “Thermal emission and design in one-dimensional periodic metallic photonic crystal slabs,” Physical Review E, vol. 74, p. 016609, July 2006. [ bib | http | .pdf ]
We present a useful framework within which we can understand some of the physical phenomena that drive thermal emission in one-dimensional periodic metallic photonic crystals, emphasizing phenomenology and physical intuition. We perform detailed numerical calculations for these systems and find that polarization and periodicity play key roles in determining the types of physical phenomena that can arise. Two promising structures are identified as good candidates for thermal design. We conclude with a discussion of how the emissive properties of these systems can be tailored to our needs.

[126]
T. T. Ngo, C. M. Liddell, M. Ghebrebrhan, and J. D. Joannopoulos, “Tetrastack: Colloidal diamond-inspired structure with omnidirectional photonic band gap for low refractive index contrast,” Applied Physics Letters, vol. 88, p. 241920, June 2006. [ bib | http ]
Omnidirectional photonic band gaps opening at low values of refractive index contrast have been found for a nonspherical colloid-based photonic crystal structure. A mechanically stable design is described for the diamondlike photonic crystal composed of colloidal tetrahedra. The proposed tetrastack structure displays omnidirectional 2–3 band gap over a large range of filling fractions, refractive index contrasts, and building block orientations. The threshold refractive index for the inverted tetrastack structure was 1.94. A gap width of 25.3% relative to the center frequency was obtained for an inverted tetrastack with a 0.21 filling fraction of silicon.

[127]
A. F. Abouraddy, O. Shapira, M. Bayindir, J. Arnold, F. Sorin, D. S. Hinczewski, J. D. Joannopoulos, and Y. Fink, “Large-scale optical-field measurements with geometric fibre constructs,” Nature Materials, vol. 5, pp. 532–536, June 2006. [ bib | DOI ]
Optical fields are measured using sequential arrangements of optical components such as lenses, filters, and beam splitters in conjunction with planar arrays of point detectors placed on a common axis. All such systems are constrained in terms of size, weight, durability and field of view. Here a new, geometric approach to optical-field measurements is presented that lifts some of the aforementioned limitations and, moreover, enables access to optical information on unprecedented length and volume scales. Tough polymeric photodetecting fibres drawn from a preform are woven into light-weight, low-optical-density, two- and three-dimensional constructs that measure the amplitude and phase of an electromagnetic field on very large areas. First, a three-dimensional spherical construct is used to measure the direction of illumination over 4π steradians. Second, an intensity distribution is measured by a planar array using a tomographic algorithm. Finally, both the amplitude and phase of an optical wave front are acquired with a dual-plane construct. Hence, the problem of optical-field measurement is transformed from one involving the choice and placement of lenses and detector arrays to that of designing geometrical constructions of polymeric, light-sensitive fibres.

[128]
O. Shapira, K. Kuriki, N. D. Orf, A. F. Abouraddy, G. Benoit, J. F. Viens, A. Rodriguez, M. Ibanescu, J. D. Joannopoulos, Y. Fink, and M. M. Brewster, “Surface-emitting fiber lasers,” Optics Express, vol. 14, pp. 3929–3935, May 2006. [ bib | http ]
All fiber lasers to date emit radiation only along the fiber axis. Here a fiber that exhibits laser emission that is radially directed from its circumferential surface is demonstrated. A unique and controlled azimuthally anisotropic optical wave front results from the interplay between a cylindrical photonic bandgap fiber resonator, anisotropic organic dye gain, and a linearly polarized axial pump. Low threshold (86nJ) lasing at nine different wavelengths is demonstrated throughout the visible and near-infrared spectra. We also report the experimental realization of unprecedented layer thicknesses of 29.5 nm maintained throughout meter-long fibers. Such a device may have interesting medical applications ranging from photodynamic therapy to in vivo molecular imaging, as well as textile fabric displays.

[129]
P. Bermel, E. Lidorikis, Y. Fink, and J. D. Joannopoulos, “Active materials embedded in photonic crystals and coupled to electromagnetic radiation,” Physical Review B, vol. 73, p. 165125, April 2006. [ bib | http ]
A calculational scheme is presented to model the interaction of light with active dielectric media, represented by four-level atomic materials, surrounded by photonic crystals. Optically pumped lasing is studied in three model systems: a Fabry-Perot cavity, a line of defects in a two-dimensional square lattice of rods, and a cylindrical photonic crystal. Field profiles and conversion efficiencies are calculated for these systems. It is shown that high conversion efficiency can be achieved for large regions of active material in the cavity, as well as for a single fluorescent atom in a hollow-core cylindrical photonic crystal, suggesting designs for ultralow-threshold lasers and ultrasensitive biological sensors.

[130]
E. J. Reed, M. Soljačić, and J. D. Joannopoulos, “Comment on “explanation of the inverse Doppler effect observed in nonlinear transmission lines”,” Physical Review Letters, vol. 96, p. 069402, February 2006. [ bib | http | .pdf ]
A Comment on the Letter by Alexander B. Kozyrev and Daniel W. van der Weide, Phys. Rev. Lett. 94, 203902 (2005). The authors of the Letter offer a Reply.

[131]
C. Luo, M. Ibanescu, E. J. Reed, S. G. Johnson, and J. D. Joannopoulos, “Doppler radiation emitted by an oscillating dipole moving inside a photonic band-gap crystal,” Physical Review Letters, vol. 96, p. 043903, February 2006. [ bib | .pdf ]
We study the radiation emitted by an oscillating dipole moving with a constant velocity in a photonic crystal, and analyze the effects that arise in the presence of a photonic band gap. It is demonstrated through numerical simulations that the radiation strength may be enhanced or inhibited according to the photonic band structure, and anomalous effects in the sign and magnitude of the Doppler shifts are possible, both outside and inside the gap. We suggest that this effect could be used to identify the physical origin of the backward waves in recent metamaterials.

[132]
P. T. Rakich, M. S. Dahlem, S. Tandon, M. Ibanescu, M. Soljačić, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, and E. P. Ippen, “Achieving centimetre scale supercollimation in a large area 2d photonic crystal,” Nature Materials, vol. 5, pp. 93–96, February 2006. [ bib | .pdf ]
Diffraction, a fundamental process in wave physics, leads to spreading of the optical beams as they propagate. However, new photonic crystal (PhC) meta-materials can be nano-engineered to generate extreme anisotropy, resulting in apparent propagation of light without diffraction. This surprising phenomenon, called supercollimation, effectively freezes the spatial width of a light beam inside a PhC, observed over a few isotropic diffraction-lengths. However, using such experiments to predict the behaviour for longer propagation lengths is difficult, as a tiny error in a measured width can extrapolate to order unity uncertainty in the width at distances over hundreds of diffraction-lengths. Here, supercollimation is demonstrated in a macroscopic PhC system over centimetre-scale distances, retaining spatial width confinement without the need for waveguides or nonlinearities. Through quantitative studies of the beam evolution in a two-dimensional PhC, we find that supercollimation possesses unexpected but inherent robustness with respect to short-scale disorder such as fabrication roughness, enabling supercollimation over 600 isotropic diffraction-lengths. The effects of disorder are identified through experiments and understood through rigorous simulations. In addition, a supercollimation steering capability is proposed.

[133]
E. J. Reed, M. Soljačić, R. Gee, and J. D. Joannopoulos, “Coherent optical photons from shock waves in crystals,” Physical Review Letters, vol. 96, p. 013904, January 2006. [ bib | http | .pdf ]
We predict that coherent electromagnetic radiation in the 12013100 THz frequency range can be generated in crystalline materials when subject to a shock wave or solitonlike propagating excitation. To our knowledge, this phenomenon represents a fundamentally new form of coherent optical radiation source that is distinct from lasers and free-electron lasers. The radiation is generated by the synchronized motion of large numbers of atoms when a shock wave propagates through a crystal. General analytical theory and NaCl molecular dynamics simulations demonstrate coherence lengths on the order of mm (around 20 THz) and potentially greater. The emission frequencies are determined by the shock speed and the lattice constants of the crystal and can potentially be used to determine atomic-scale properties of the shocked material.

[134]
M. Ibanescu, E. J. Reed, and J. D. Joannopoulos, “Enhanced photonic band-gap confinement via Van Hove saddle point singularities,” Physical Review Letters, vol. 96, p. 033904, January 2006. [ bib | http ]
We show that a saddle point Van Hove singularity in a band adjacent to a photonic crystal band gap can lead to situations which defy the conventional wisdom that the strongest band-gap confinement is found at frequencies near the midgap. As an example, we present a two-dimensional square photonic crystal waveguide where the strongest confinement is close to the band edge. The underlying mechanism can also apply to any system that is described by a band structure with a gap. In general, the saddle point favors the appearance of a very flat band, which in turn results in an enhanced confinement at band-gap frequencies immediately above or below the flat band.

[135]
M. L. Povinelli, M. Lončar, E. J. Smythe, M. Ibanescu, S. G. Johnson, F. Capasso, and J. D. Joannopoulos, “Enhancement mechanisms for optical forces in integrated optics,” Proc. SPIE, vol. 6326, p. 632609, 2006. [ bib | .pdf ]
We investigate the extension of optical micromanipulation to integrated optics. In particular, we consider whether propagating light signals can cause mechanical reconfiguration of a device. While such forces are intrinsically weak, we predict theoretically that significant displacements can be achieved using various enhancement mechanisms. These include the use of high-index materials, high-Q (cavity quality factor) enhancement, and slow light in photonic crystals. Silicon optical waveguides have a considerable refractive index contrast with the surrounding air, with a ratio of roughly 3.45/1 at optical communications wavelengths. We show that the strong confinement of light to silicon magnifies optical forces arising from overlap in the guided modes of neighboring waveguides. Silica microsphere resonators are known to have extremely high cavity quality factors, in excess of 108. We show that the quality factor of the resonator magnifies the optical force due to modal overlap between two neighboring spheres. Thirdly, we investigate slow-light enhancement of optical forces using photonic-crystal devices. We show that slow-light velocities give rise to larger forces for the same amount of signal power, enhancing optomechanical coupling effects. In addition to being of fundamental interest, our work suggests that optical manipulation may ultimately provide a route to all-optical conformational control and switching.

[136]
A. Farjadpour, D. Roundy, A. Rodriguez, M. Ibanescu, P. Bermel, J. D. Joannopoulos, S. G. Johnson, and G. W. Burr, “Improving accuracy by sub-pixel smoothing in FDTD,” Proc. SPIE, vol. 6322, p. 63220G, 2006. [ bib | .pdf ]
Finite-difference time-domain (FDTD) methods suffer from reduced accuracy when modeling discontinuous dielectric materials, due to the inhererent discretization (“pixellization”). We show that accuracy can be significantly improved by using a sub-pixel smoothing of the dielectric function, but only if the smoothing scheme is properly designed. We develop such a scheme based on a simple criterion taken from perturbation theory, and compare it to other published FDTD smoothing methods. In addition to consistently achieving the smallest errors, our scheme is the only one that attains quadratic convergence with resolution for arbitrarily sloped interfaces. Finally, we discuss additional difficulties that arise for sharp dielectric corners.

[137]
M. L. Povinelli, S. G. Johnson, and J. D. Joannopoulos, “Tunable time delays in photonic-crystal waveguides,” Proc. SPIE, vol. 6128, p. 61280R, 2006. [ bib | .pdf ]
We study tunable time-delay devices in which the time delay is tuned by changing the group velocity of the propagating signal. The device is designed to place the operating frequency near a photonic band edge. This enhances the change in delay for a given tuning range of the device refractive index. Here we provide an extended explanation of mode symmetry, nomenclature, and the complete band structure of a sample, integrated device to aid the understanding of our previously published work.

[138]
M. Ibanescu, M. Soljačić, S. G. Johnson, and J. D. Joannopoulos, “Ultra-flat bands in two-dimensional photonic crystals,” Proc. SPIE, vol. 6128, p. 612808, 2006. Invited paper. [ bib | .pdf ]
We show that two-dimensional photonic crystals can be designed to have dispersion relations with an extended ultraflat cross-section, meaning that for a fixed wave vector wave vector component kx the frequency of a band is almost constant when the other wave vector component ky takes all possible values. these ultra-flat are the result of a non-trivial saddle point in the dispersion relation located in the interior of the Brillouin zone. Interesting consequences include 1D-like behavior, improved super-collimation, and enhanced density of states.

[139]
A. Rodriguez, M. Ibanescu, J. D. Joannopoulos, and S. G. Johnson, “Disorder-immune confinement of light in photonic-crystal cavities,” Optics Letters, vol. 30, pp. 3192–3194, December 2005. [ bib | .pdf ]
We demonstrate by finite-difference time-domain simulations in 2D and 3D that optical cavities in realistic finite photonic crystals have lifetimes and modal volumes that are essentially insensitive to disorder (of various types, including surface disorder and randomized positions), even with unphysically large disorder. A lifetime Q=108 is demonstrated in a 3D single-mode cavity with a half-wavelength mode diameter using only eight vertical periods of a disordered crystal.

[140]
M. L. Povinelli, M. Loncar, M. Ibanescu, E. J. Smythe, S. G. Johnson, F. Capasso, and J. D. Joannopoulos, “Evanescent-wave bonding between optical waveguides,” Optics Letters, vol. 30, pp. 3042–3044, November 2005. [ bib | .pdf ]
Forces arising from overlap between the guided waves of parallel, microphotonic waveguides are calculated. Both attractive and repulsive forces, determined by the choice of relative input phase, are found. Using realistic parameters for a silicon-on-insulator material system, we estimate that the forces are large enough to cause observable displacements. Our results illustrate the potential for a broader class of optically tunable microphotonic devices and microstructured artificial materials.

[141]
M. Skorobogatiy, S. A. Jacobs, S. G. Johnson, C. Anastassiou, and B. Temelkuran, “Heating of hollow photonic Bragg fibers from field propagation, coupling, and bending,” Journal of Lightwave Technology, vol. 23, pp. 3517–3525, November 2005. [ bib | .pdf ]
We investigate heating from field propagation, coupling, and bending, which are the potential failure mechanisms for an emerging new type of high-power radiation guides-hollow photonic Bragg fibers. Continuous wave (CW) and pulsed radiation sources are considered, assuming continuous operation of the laser source.

[142]
M. Bayindir, O. Shapira, D. Saygin-Hinczewski, J. Viens, A. F. Abouraddy, J. D. Joannopoulos, and Y. Fink, “Integrated fibres for self-monitored optical transport,” Nature Materials, vol. 4, pp. 820–825, November 2005. [ bib | DOI ]
The ability to integrate distinct functional elements into a single device structure enables the realization of systems with higher-level functionality. Here we report on the design and fabrication of a fibre device structure that contains integrated optical, electrical and thermal elements for self-monitored optical transport. The fibre transmission element uses a hollow-core multilayer cylindrical photonic bandgap structure designed to guide high-power radiation at 10.6 μm along the fibre axis. Multiple thermal-detection elements are placed in the vicinity of the hollow core for the purpose of temperature monitoring along the entire fibre length. Metal wires bridged by a semiconductor layer extend along the length of the fibre and deliver an electrical response to the fibre ends on change in the fibre temperature. The multimaterial fibre is drawn at high speeds from a single preform to produce extended lengths of optically and thermally functional fibres. The exponential dependence on temperature of the electrical conductivity of the semiconducting material allows for the discrimination, in real time, between normal transmission conditions and those that are indicative of localized defect formation, thus enabling a self-monitoring high-power optical transmission line for failure prediction and prevention.

[143]
M. Povinelli, S. G. Johnson, M. Loncar, M. Ibanescu, E. Smythe, F. Capasso, and J. D. Joannopoulos, “High-Q enhancement of attractive and repulsive optical forces between coupled whispering-gallery-mode resonators,” Optics Express, vol. 13, pp. 8286–8295, October 2005. [ bib | http | .pdf ]
We have calculated the optically-induced force between coupled high-Q whispering gallery modes of microsphere resonators. Attractive and repulsive forces are found, depending whether the bi-sphere mode is symmetric or antisymmetric. The magnitude of the force is linearly proportional to the total power in the spheres and consequently linearly enhanced by Q. Forces on the order of 100 nN are found for Q=108, large enough to cause displacements in the range of 1μm when the sphere is attached to a fiber stem with spring constant 0.004 N/m.

[144]
M. Povinelli, S. G. Johnson, and J. D. Joannopoulos, “Slow-light, band-edge waveguides for tunable time delays,” Optics Express, vol. 13, pp. 7145–7159, September 2005. [ bib | http | .pdf ]
We propose the use of slow-light, band-edge waveguides for compact, integrated, tunable optical time delays. We show that slow group velocities at the photonic band edge give rise to large changes in time delay for small changes in refractive index, thereby shrinking device size. Figures of merit are introduced to quantify the sensitivity, as well as the accompanying signal degradation due to dispersion. It is shown that exact calculations of the figures of merit for a realistic, three-dimensional grating structure are well predicted by a simple quadratic-band model, simplifying device design. We present adiabatic taper designs that attain <0.1% reflection in short lengths of 10 to 20 times the grating period. We show further that cascading two gratings compensates for signal dispersion and gives rise to a constant tunable time delay across bandwidths greater than 100GHz. Given typical loss values for silicon-on-insulator waveguides, we estimate that gratings can be designed to exhibit tunable delays in the picosecond range using current fabrication technology.

[145]
S. N. Tandon, M. Soljačić, G. S. Petrich, J. D. Joannopoulos, and L. A. Kolodziejski, “The superprism effect using large area 2d-periodic photonic crystal slabs,” Photonics and Nanostructures, vol. 3, pp. 10–18, August 2005. [ bib | DOI | .pdf ]
The “superprism effect” is an effect observed in photonic crystal structures whereby the direction of light propagation is extremely sensitive to the wavelength and angle of incidence. To realize the superprism effect, new structures are presented which rely on the sensitivity of the phase velocity in a two-dimensional (2D) photonic crystal slab to observe angular magnification outside the photonic crystal medium. Constant frequency contour calculations for a photonic crystal slab of finite thickness are used to predict the phase velocity superprism effect. Further analysis using 2D finite-difference time-domain simulations indicate that a large area photonic crystal and wide excitation beam are necessary for clear observation of the superprism effect. A fabrication technique is demonstrated to achieve the structure's required nanometer-sized features over centimeter-scale areas.

[146]
A. Karalis, E. Lidorikis, M. Ibanescu, J. D. Joannopoulos, and M. Soljačić, “Surface-plasmon-assisted guiding of broadband slow and subwavelength light in air,” Physical Review Letters, vol. 95, p. 063901, August 2005. [ bib | http | .pdf ]
A class of axially uniform waveguides is introduced, employing a new mechanism to guide light inside a low-index dielectric material without the use of photonic band gap, and simultaneously exhibiting subwavelength modal size and very slow group velocity over an unusually large frequency bandwidth. Their basis is the presence of plasmonic modes on the interfaces between dielectric regions and the flat unpatterned surface of a bulk metallic substrate. These novel waveguides allow for easy broadband coupling and exhibit absorption losses limited only by the intrinsic loss of the metal.

[147]
S. G. Johnson, M. L. Povinelli, M. Soljačić, A. Karalis, S. Jacobs, and J. D. Joannopoulos, “Roughness losses and volume-current methods in photonic-crystal waveguides,” Applied Physics B, vol. 81, pp. 283–293, July 2005. Invited paper, special issue on photonic crystals. [ bib | .pdf ]
We present predicted relative scattering losses from sidewall roughness in a strip waveguide compared to an identical waveguide surrounded by a photonic crystal with a complete or incomplete gap in both 2d and 3d. To do so, we develop a new semi-analytical extension of the classic “volume-current method” (Green's functions with a Born approximation), correcting a longstanding limitation of such methods to low-index contrast systems (the classic method may be off by an order of magnitude in high-contrast systems). The resulting loss predictions show that even incomplete gap structures such as photonic-crystal slabs should, with proper design, be able to reduce losses by a factor of two compared to an identical strip waveguide; however, incautious design can lead to increased losses in the photonic-crystal system, a phenomena that we explain in terms of the band structure of the unperturbed crystal.

[148]
G. Benoit, K. Kuriki, J.-F. Viens, J. D. Joannopoulos, and Y. Fink, “Dynamic all-optical tuning of transverse resonant cavity modes in photonic bandgap fibers,” Optics Letters, vol. 30, pp. 1620–1622, July 2005. [ bib | http ]
Photonic bandgap fibers for transverse illumination containing half-wavelength microcavities have recently been designed and fabricated. We report on the fabrication and characterization of an all-optical tunable microcavity fiber. The fiber is made by incorporating a photorefractive material inside a Fabry-Perot cavity structure with a quality factor Q>200 operating at 1.5 μm. Under short-wavelength transverse external illumination, a 2 nm reversible shift of the cavity resonant mode is achieved. Dynamic all-optical tuning is reported at frequencies up to 400 Hz. Experimental results are compared with simulations based on the amplitude and kinetics of the transient photodarkening effect measured in situ in thin films.

[149]
S. G. Johnson, M. Soljačić, and J. D. Joannopoulos, “Photonic crystals,” in Encyclopedia of Nonlinear Science (A. Scott, ed.), New York: Routledge, Taylor and Francis Group, July 2005. [ bib ]
[150]
D. L. Chan, E. Lidorikis, and J. D. Joannopoulos, “Point defect geometries in inverted opal photonic crystals,” Physical Review E, vol. 71, pp. 056602–056607, May 2005. [ bib | http ]
We study point defect geometries in inverted opal photonic crystals that can be easily fabricated by means of colloidal self-assembly. Two broad classes of defects are considered: substitutional and interstitial. Substitutional point defects are found to introduce a usable defect band into the photonic band gap. This can be done by using a silica sphere of radius between 0.33a and 0.35a (where a is the lattice constant). The state is triply degenerate. Reflectance and local density of states calculations are performed to verify the existence and frequency of this defect. The point defect can be made by precoating shrunk silica spheres with a thin layer of silicon. Such a defect can be used as a microcavity for localizing light at a point, with a quality factor Q that is limited primarily by the proximity of the defect to the surface of the photonic crystal and other such defects.

[151]
X. Jiang, Y. Zhang, S. Feng, K. C. Huang, Y. Yi, and J. D. Joannopoulos, “Photonic band gaps and localization in the Thue–Morse structures,” Applied Physics Letters, vol. 86, p. 201110, May 2005. [ bib | http ]
Both theoretically and experimentally, we demonstrate that the photonic band gaps in Thue–Morse aperiodic systems can be separated into two flavors, the fractal gaps and the traditional gaps, distinguished by the presence or absence of fractal structure, respectively. The origin of two kind gaps is explained by the different interface correlations. This explanation is confirmed by the gap width behaviors. In addition, the eigenstates near the fractal gaps have a cluster-periodic form, while those near the traditional gaps have the Bloch wavelike form. Our detailed study of these differences is essential for understanding the spectra and light localization in aperiodic systems.

[152]
O. Shapira, A. F. Abouraddy, J. D. Joannopoulos, and Y. Fink, “Complete modal decomposition for optical waveguides,” Physical Review Letters, vol. 94, pp. 143902–143905, April 2005. [ bib | http ]
Virtually all electromagnetic waveguiding structures support a multiplicity of modes. Nevertheless, to date, an experimental method for unique decomposition of the fields in terms of the component eigenmodes has not been realized. The fundamental problem is that all current attempts of modal decomposition do not yield phase information. Here we introduce a noninterferometric approach to achieve modal decomposition of the fields at the output of a general waveguiding structure. The technique utilizes a mapping of the two-dimensional field distribution onto the one-dimensional space of waveguide eigenmodes, together with a phase-retrieval algorithm to extract the amplitudes and phases of all the guided vectorial modes. Experimental validation is provided by using this approach to examine the interactions of 16 modes in a hollow-core photonic-band gap fiber.

[153]
M. Soljačić, E. Lidorikis, J. D. Joannopoulos, and L. V. Hau, “Ultralow-power all-optical switching,” Applied Physics Letters, vol. 86, p. 171101, April 2005. [ bib | http | .pdf ]
Using analytical modeling and detailed numerical simulations, we investigate properties of hybrid systems of photonic crystal microcavities which incorporate a highly nonlinear ultraslow light medium. We demonstrate that such systems, while being miniature in size (order wavelength), and integrable, could enable ultrafast nonlinear all-optical switching at ultralow (even single photon) energy levels.

[154]
M. Ibanescu, S. G. Johnson, D. Roundy, Y. Fink, and J. D. Joannopoulos, “Microcavity confinement based on an anomalous zero group-velocity waveguide mode,” Optics Letters, vol. 30, pp. 552–554, March 2005. [ bib | .pdf ]
We propose and demonstrate a mechanism for small-modal-volume high-Q cavities based on an anomalous uniform waveguide mode that has zero group velocity at a nonzero wave vector. In a short piece of a uniform waveguide with a specially designed cross section, light is confined longitudinally by small group-velocity propagation and transversely by a reflective cladding. The quality factor Q is greatly enhanced by the small group velocity for a set of cavity lengths that are separated by approximately π/k0, where k0 is the longitudinal wave vector for which the group velocity is zero.

[155]
M. Soljačić, E. Lidorikis, L. V. Hau, and J. D. Joannopoulos, “Enhancement of microcavity lifetimes using highly dispersive materials,” Physical Review E, vol. 71, pp. 026602–026606, February 2005. [ bib | http | .pdf ]
We show analytically and numerically that highly dispersive media can be used to drastically increase lifetimes of high-Q microresonators. In such a resonator, lifetime is limited either by undesired coupling to radiation, or by intrinsic absorption of the constituent materials. The presence of dispersion weakens coupling to the undesired radiation modes and also effectively reduces the material absorption.

[156]
E. J. Reed, M. Soljačić, M. Ibanescu, and J. D. Joannopoulos, “Reversed and anomalous Doppler effects in photonic crystals and other time-dependent periodic media,” Journal of Computer-Aided Materials Design, vol. 12, pp. 1–15, January 2005. [ bib | DOI | .pdf ]
We predict that reversed and anomalous non-relativistic Doppler shifts can be observed under some circumstances when light reflects from a shock wave front propagating through a photonic crystal, or material with a periodic modulation of the dielectric. This theoretical prediction is generalizable and applies to wave-like excitations in a variety of periodic media. An experimental observation of this effect has recently been made (Seddon, N. and Bearpark, T. Science, 302 (2003) 1537) and we provide a brief discussion of this experiment.

[157]
P. T. Rakich, H. Sotobayashi, J. T. Gopinath, S. G. Johnson, J. W. Sickler, C. W. Wong, J. D. Joannopoulos, and E. P. Ippen, “Nano-scale photonic crystal microcavity characterization with an all-fiber based 1.2–2.0 μm supercontinuum,” Optics Express, vol. 13, pp. 821–825, January 2005. [ bib | http | .pdf ]
The use of ultra-broadband supercontinuum generated by an all-fiber system to characterize high-index contrast photonic circuits over the wavelength range 1.2–2.0 μm is demonstrated. Efficient, broadband waveguide coupling techniques and sensitive normalized detection enable rapid and high-resolution measurements of nano-scale one-dimensional photonic crystal microcavities. Experimental mappings of bandgaps and cavity mode resonances with a wavelength resolution of 0.1 nm compare well with computer simulations.

[158]
P. T. Rakich, H. Sotobayashi, J. T. Gopinath, J. W. Sickler, C. W. Wong, S. G. Johnson, M. Qi, E. Lidorikis, H. I. Smith, J. D. Joannopoulos, and E. P. Ippen, “Broadband optical studies of 1-D and 3-D photonic crystals,” Proc. SPIE, vol. 6017, p. 601702, 2005. Invited paper. [ bib | .pdf ]
Supercontinuum based sources and measurement techniques are developed, enabling optical ultra-broadband studies of nano-scale photonic crystal devices and integrated photonic circuits over 1.2–2.0 μm wavelength range. Experiments involving 1-D periodic photonic crystal microcavity waveguides and 3-D periodic photonic crystals with embedded point defects are described. Experimental findings are compared with rigorous electromagnetic simulations.

[159]
M. L. Povinelli, S. G. Johnson, and J. D. Joannopoulos, “High-index-contrast, photonic-band-edge waveguides for tunable time delays,” Proc. SPIE, vol. 5926, p. 59260D, 2005. [ bib | .pdf ]
We describe the use of high-index-contrast, photonic-crystal wavegides for tunable time delays. The waveguide is designed such that the operating frequency is near a photonic band edge. In this slow light region, a small change in index yields a large change in group velocity, and consequently in time delay. Figures of merit for tunable time delay devices are introduced, including sensitivity, length, and dispersion. We show that a simple quadratic band model is a good predictor of the figures of merit for realistic, 3D, high-index-contrast structures. By cascading two grated waveguides, we can obtain a flat tunable time delay across the operating bandwidth.

[160]
C. Luo, A. Narayanaswamy, G. Chen, and J. D. Joannopoulos, “Thermal radiation from photonic crystals: A direct calculation,” Physical Review Letters, vol. 93, pp. 213905–213908, November 2004. [ bib | http ]
A classical simulation of equilibrium thermal emissivity from dispersive, lossy photonic crystals is presented. Normal emission results consistent with those assuming Kirchoff's law are obtained; i.e., a photonic crystal does not emit more than what a blackbody does. Significant enhancement, however, can be achieved over the radiation intensity from a uniform slab, indicating the potential usefulness of photonic crystals in incandescent lighting and thermal photovoltaic applications.

[161]
S. G. Johnson and J. D. Joannopoulos, “Photonic crystals: Electromagnetic theory,” in Encyclopedia of Modern Optics (B. D. Guenther, D. G. Steel, and L. Bayvel, eds.), pp. 120–127, Oxford: Elsevier, November 2004. [ bib | DOI ]
[162]
M. Bayindir, F. Sorin, A. F. Abouraddy, J. Viens, S. D. Hart, J. D. Joannopoulos, and Y. Fink, “Metal–insulator–semiconductor optoelectronic fibres,” Nature, vol. 431, pp. 826–829, October 2004. [ bib | DOI ]
The combination of conductors, semiconductors and insulators with well-defined geometries and at prescribed length scales, while forming intimate interfaces, is essential in most functional electronic and optoelectronic devices. These are typically produced using a variety of elaborate wafer-based processes, which allow for small features, but are restricted to planar geometries and limited coverage area. In contrast, the technique of fibre drawing from a preformed reel or tube is simpler and yields extended lengths of highly uniform fibres with well-controlled geometries and good optical transport characteristics. So far, this technique has been restricted to particular materials and larger features. Here we report on the design, fabrication and characterization of fibres made of conducting, semiconducting and insulating materials in intimate contact and in a variety of geometries. We demonstrate that this approach can be used to construct a tunable fibre photodetector comprising an amorphous semiconductor core contacted by metallic microwires, and surrounded by a cylindrical-shell resonant optical cavity. Such a fibre is sensitive to illumination along its entire length (tens of meters), thus forming a photodetecting element of dimensionality one. We also construct a grid of such fibres that can identify the location of an illumination point. The advantage of this type of photodetector array is that it needs a number of elements of only order N, in contrast to the conventional order N2 for detector arrays made of photodetecting elements of dimensionality zero.

[163]
Y. Yi, S. Akiyama, P. Bermel, X. Duan, and L. C. Kimerling, “On-chip Si-based Bragg cladding waveguide with high index contrast bilayers,” Optics Express, vol. 12, pp. 4775–4780, October 2004. [ bib | http ]
A new silicon based waveguide with full CMOS compatibility is developed to fabricate an on-chip Bragg cladding waveguide that has an oxide core surrounded by a high index contrast cladding layers. The cladding consists of several dielectric bilayers, where each bilayer consists of a high index-contrast pair of layers of Si and Si3N4. This new waveguide guides light based on omnidirectional reflection, reflecting light at any angle or polarization back into the core. Its fabrication is fully compatible with current microelectronics processes. In principle, a core of any low-index material can be realized with our novel structure, including air. Potential applications include tight turning radii, high power transmission, and dispersion compensation.

[164]
K. C. Huang, M. L. Povinelli, and J. D. Joannopoulos, “Negative effective permeability in polaritonic photonic crystals,” Applied Physics Letters, vol. 85, pp. 543–545, July 2004. [ bib | http ]
We find that a two-dimensional photonic crystal composed of polaritonic materials behaves as an effective medium with negative permeability in the micron wavelength range. The resonance in μeff is due to the large values of ε(ω) attained near the transverse phonon frequency ωT. The minimal wavelength for achieving an effective permeability less than -1 in a LiTaO3 crystal, obtained by optimizing the rod size and the lattice constant, is around 12 μm, a range previously inaccessible using dielectric metamaterials. For certain dissipation levels, we find that other polaritonic media also exhibit a resonant effect with μeff < -1 for wavelengths ranging from 2 to ∼100 μm.

[165]
K. C. Huang, E. Lidorikis, X. Jiang, J. D. Joannopoulos, K. A. Nelson, P. Bienstman, and S. Fan, “Nature of lossy Bloch states in polaritonic photonic crystals,” Physical Review B, vol. 69, pp. 195111–195120, May 2004. [ bib | http ]
We examine the effects of absorption losses in photonic crystal structures composed of polar materials which exhibit transverse phonon-polariton excitations. In order to explore the Bloch states of such a system, we study the two subspaces of the complete set of complex (k,ω)states consisting of either real frequency, accessible through a frequency-domain method, or real-wave vector, which we determine using a frequency-dependent time-domain method. We describe analytically the conditions under which the imaginary frequency component of a real-wave-vector state is related to the imaginary-wave-vector component of a real-frequency state through a factor of the group velocity, and we present a one-dimensional lossy crystal as an example that satisfies these constraints. We also discover that the real-frequency states of a two-dimensional crystal bear little resemblance to the class of real-wave-vector states, due to interplay between the prohibitively large spatial decay of the states near the edge of the Brillouin zone and the existence of metalliclike states localized to the surrounding ambient dielectric region with much lower levels of loss. We then put these results in the context of possible experiments, including reflection of a plane-wave from a slab structure, and discuss the viability for observing the node switching and flux expulsion phenomena previously discovered in lossless crystals.

[166]
K. Kuriki, O. Shapira, S. Hart, G. Benoit, Y. Kuriki, J. Viens, M. Bayindir, J. D. Joannopoulos, and Y. Fink, “Hollow multilayer photonic bandgap fibers for NIR applications,” Optics Express, vol. 12, pp. 1510–1517, April 2004. [ bib | http ]
Here we report the fabrication of hollow-core cylindrical photonic bandgap fibers with fundamental photonic bandgaps at near-infrared wavelengths, from 0.85 to 2.28 μm. In these fibers the photonic bandgaps are created by an all-solid multilayer composite meso-structure having a photonic crystal lattice period as small as 260 nm, individual layers below 75 nm and as many as 35 periods. These represent, to the best of our knowledge, the smallest period lengths and highest period counts reported to date for hollow PBG fibers. The fibers are drawn from a multilayer preform into extended lengths of fiber. Light is guided in the fibers through a large hollow core that is lined with an interior omnidirectional dielectric mirror. We extend the range of materials that can be used in these fibers to include poly(ether imide) (PEI) in addition to the arsenic triselenide (As2Se3) glass and poly(ether sulfone) (PES) that have been used previously. Further, we characterize the refractive indices of these materials over a broad wavelength range (0.25 – 15 μm) and incorporated the measured optical properties into calculations of the fiber photonic band structure and a preliminary loss analysis.

[167]
C. Luo, M. Soljačić, and J. D. Joannopoulos, “Superprism effect based on phase velocities,” Optics Letters, vol. 29, pp. 745–747, April 2004. [ bib | http | .pdf ]
The superprism effect has been studied in the past by use of the anomalous group velocities of optical waves in photonic crystals. We suggest the possibility of realizing agile beam steering based on purely phase-velocity effects. We present designs of photonic crystal prisms that might make experimental observation of this effect possible.

[168]
E. Lidorikis, M. Soljačić, M. I. Y. Fink, and J. D. Joannopoulos, “Cutoff solitons in axially uniform systems,” Optics Letters, vol. 29, pp. 851–853, April 2004. [ bib | http | .pdf ]
The optical response of axially uniform nonlinear photonic bandgap fibers is studied theoretically. We observe gap-soliton-like generation and associated bistability, similar to what is typically found in periodically modulated nonlinear structures. This response stems from the nature of the guided-mode dispersion relations, which involve a frequency cutoff at zero wave vector. In such systems, solutions with zero group velocities and minimal coupling to radiation modes come in naturally. We term such solitons “cutoff solitons”; they provide an interesting alternative to gap solitons in periodically index-modulated fibers for in-fiber all-optical signal processing.

[169]
M. Soljačić and J. D. Joannopoulos, “Enhancement of nonlinear effects using photonic crystals,” Nature Materials, vol. 3, pp. 211–219, April 2004. [ bib | DOI | .pdf ]
The quest for all-optical signal processing is generally deemed to be impractical because optical nonlinearities are usually weak. The emerging field of nonlinear photonic crystals seems destined to change this view dramatically. Theoretical considerations show that all-optical devices using photonic crystal designs promise to be smaller than the wavelength of light, and to operate with bandwidths that are very difficult to achieve electronically. When created in commonly used materials, these devices could operate at powers of only a few milliwatts. Moreover, if these designs are combined with materials and systems that support electromagnetically induced transparency, operation at single-photon power levels could be feasible.

[170]
X. Jiang, S. Feng, C. M. Soukoulis, J. Zi, J. D. Joannopoulos, and H. Cao, “Coupling, competition, and stability of modes in random lasers,” Physical Review B, vol. 69, pp. 104202–104208, March 2004. [ bib | http ]
We studied analytically and numerically the complex properties of random lasing modes. Mode repulsion in frequency domain for inhomogeneously broadened gain media was confirmed by our numerical results. We constructed a coupled-mode model to explain the synchronized lasing behavior for modes whose frequency difference is less than the homogeneous gain width. The stability of coupled modes was investigated. The effective competition coefficient Ce for two modes with both gain competition and field coupling is obtained analytically. In our numerical experiments, we also found the coupled oscillations of two lasing modes. From the analytical derivation, we demonstrated that such oscillations could reveal the field-coupling strength between the random modes.

[171]
P. Bermel, J. D. Joannopoulos, Y. Fink, P. A. Lane, and C. Tapalian, “Properties of radiating pointlike sources in cylindrical omnidirectionally reflecting waveguides,” Physical Review B, vol. 69, pp. 035316–035322, January 2004. [ bib | http ]
The behavior of pointlike electric dipole sources enclosed by an axially uniform, cylindrically symmetric waveguide of omnidirectionally reflecting material is analyzed. It is found that the emission spectrum of a source inside the waveguide is strongly modified by features resembling one-dimensional Van Hove singularities in the local density of states (LDOS). Additionally, more than 100% of the power radiated by a dipole in vacuum can be captured at the end of the waveguide, owing to the overall enhancement of the LDOS (the Purcell effect). The effect of varying the positions and orientations of electric dipole sources is also studied.

[172]
D. Roundy, E. Lidorikis, and J. D. Joannopoulos, “Polarization-selective waveguide bends in a photonic crystal structure with layered square symmetry,” Journal of Applied Physics, vol. 96, pp. 7750–7752, 2004. [ bib | http ]
We demonstrate single-mode horizontal and vertical waveguides in a recently proposed photonic crystal having layered square symmetry. The vertical waveguide supports two degenerate polarizations, and thus light can be selectively steered into horizontal waveguides oriented at 90o based on its polarization. We calculate the transmission of 90o bends, both from horizontal waveguide to horizontal waveguide and from horizontal waveguide to vertical waveguide. In the case of the horizontal-horizontal bend, we show a transmission of 83% for a simple (“zero” radius of curvature) bend, and a peak transmission of 100% for a bend which has been optimized by moving one rod from the inner corner to the outer corner of the bend. For the vertical to horizontal bend, we find a transmission of 95% for the allowed polarization, but with a much smaller bandwidth than in the case of the optimized horizontal bend.

[173]
A. Karalis, S. G. Johnson, and J. D. Joannopoulos, “Discrete-mode cancellation mechanism for high-Q integrated optical cavities with small modal volume,” Optics Letters, vol. 29, pp. 2309–2311, 2004. [ bib | .pdf ]
A mechanism to reduce radiation loss from integrated optical cavities without a complete photonic bandgap is introduced and demonstrated. It is applicable to any device with a patterned substrate (including both low and high index-contrast systems), when it supports discrete guided or leaky modes through which power escaping the cavity can be channeled into radiation. One then achieves the associated increase in Q by designing the cavity such that the near-field pattern becomes orthogonal to these discrete modes, therefore canceling the coupling of power into them and thus reducing the total radiation loss. The method is independent of any delocalization mechanism and can be used to create high-Q cavities with small modal volume.

[174]
M. L. Povinelli, M. Ibanescu, S. G. Johnson, and J. D. Joannopoulos, “Slow-light enhancement of radiation pressure in an omnidirectional-reflector waveguide,” Applied Physics Letters, vol. 85, pp. 1466–1468, 2004. [ bib | .pdf ]
We study the radiation pressure on the surface of a waveguide formed by omnidirectionally reflecting mirrors. In the absence of losses, the pressure goes to infinity as the distance between the mirrors is reduced to the cutoff separation of the waveguide mode. This divergence at constant power input is due to the reduction of the modal group velocity to zero, which results in the magnification of the electromagnetic field. Our structure suggests a promising alternative, microscale system for observing the variety of classical and quantum-optical effects associated with radiation pressure in Fabry–Perot cavities.

[175]
M. L. Povinelli, S. G. Johnson, E. Lidorikis, J. D. Joannopoulos, and M. Soljačić, “Effect of a photonic band gap on scattering from waveguide disorder,” Applied Physics Letters, vol. 84, pp. 3639–3641, 2004. [ bib | .pdf ]
We derive a general, analytical, coupled-mode theory for disorder-induced scattering in periodic systems that shows that in the experimentally relevant limit of weak disorder, the reflection in a photonic-crystal waveguide is just as low as in a comparable index-guided waveguide. Moreover, since the photonic band gap also blocks radiative loss, the total scattering loss is reduced, and the total transmission is higher. These general results are verified by direct numerical simulations in an example system.

[176]
M. Qi, E. Lidorikis, P. T. Rakich, S. G. Johnson, J. D. Joannopoulos, E. P. Ippen, and H. I. Smith, “A three-dimensional optical photonic crystal with designed point defects,” Nature, vol. 429, pp. 538–542, 2004. [ bib | .pdf ]
Photonic crystals offer unprecedented opportunities for miniaturization and integration of optical devices. They also exhibit a variety of new physical phenomena, including suppression or enhancement of spontaneous emission, low-threshold lasing, and quantum information processing. Various techniques for the fabrication of three-dimensional (3D) crystals photonicsuch as silicon micromachining, wafer fusion bonding, holographic lithography, self-assembly, angled-etching, micromanipulation, glancing-angle deposition, auto-cloning, have been proposed and demonstrated with different levels of success. However, a critical step towards the fabrication of functional 3D devices, that is, the incorporation of microcavities or waveguides in a controllable way, has not been achieved at optical wavelengths. Here we present the fabrication of 3D photonic crystals that are particularly suited for optical device integration using a lithographic layer-by-layer approach. Point-defect microcavities are introduced during the fabrication process and optical measurements show they have resonant signatures around telecommunications wavelengths (1.3–1.5μm). Measurements of reflectance and transmittance at near-infrared are in good agreement with numerical simulations.

[177]
C. W. Wong, P. T. Rakich, S. G. Johnson, M. Qi, H. I. Smith, E. P. Ippen, L. C. Kimerling, Y. Jeon, G. Barbastathis, and S.-G. Kim, “Strain-tunable silicon photonic band gap microcavities in optical waveguides,” Applied Physics Letters, vol. 84, pp. 1242–1244, 2004. [ bib | .pdf ]
We report the design, device fabrication, and measurements of tunable silicon photonic band gap microcavities in optical waveguides, using direct application of piezoelectric-induced strain to the photonic crystal. We show, through first-order perturbation computations and experimental measurements, a 1.54 nm shift in cavity resonances at 1.56 μm wavelengths for an applied strain of 0.04%. The strain is applied through integrated piezoelectric microactuators. For operation at infrared wavelengths, we combine x-ray and electron-beam lithography with thin-film piezoelectric processing. This level of integration permits realizable silicon-based photonic chip devices, such as high-density optical filters, with active reconfiguration.

[178]
S. Assefa, P. T. Rakich, P. Bienstman, S. G. Johnson, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, E. P. Ippen, and H. I. Smith, “Guiding 1.5μm light in photonic crystals based on dielectric rods,” Applied Physics Letters, vol. 85, pp. 6110–6112, 2004. [ bib | .pdf ]
Photonic-crystal structures consisting of dielectric rods were designed, fabricated, and optically characterized. The combination of the high refractive-index-contrast GaAs/AlxOy material system with electron-beam lithography enabled the fabrication of structures suitable for the optical propagation of 1.5 μm light. Experimental transmission spectra were obtained for structures consisting of a two-dimensional array of rods and line-defect waveguides. Optical measurements confirmed the presence of a photonic band gap, as well as band gap guidance in the line-defect waveguide. A two-stage coupling scheme facilitated efficient optical coupling into the line-defect waveguide.

[179]
M. Soljačić, E. Lidorikis, M. Ibanescu, S. G. Johnson, J. D. Joannopoulos, and Y. Fink, “Optical bistability and cutoff solitons in photonic bandgap fibers,” Optics Express, vol. 12, pp. 1518–1527, 2004. [ bib | http | .pdf ]
We present detailed theoretical and numerical analysis of certain novel non-linear optical phenomena enabled by photonic bandgap fibers. In particular, we demonstrate the feasibility of optical bistability in an axially modulated nonlinear photonic bandgap fiber through analytical theory and detailed numerical experiments. At 1.55μm carrier wavelength, the in-fiber devices we propose can operate with only a few tens of mW of power, have a nearly instantaneous response and recovery time, and be shorter than 100μm. Furthermore, we predict existence of gap-like solitons (which have thus-far been described only in axially periodic systems) in axially uniform photonic bandgap fibers.

[180]
M. Ibanescu, S. G. Johnson, D. Roundy, C. Luo, Y. Fink, and J. D. Joannopoulos, “Anomalous dispersion relations by symmetry breaking in axially uniform waveguides,” Physical Review Letters, vol. 92, p. 063903, 2004. [ bib | .pdf ]
We show that modes of axially uniform waveguides of arbitrary cross section can be made to have anomalous dispersion relations resulting from strong repulsion between two modes. When the axial wave vector k is 0, the two modes have different TE/TM symmetry and thus can be brought arbitrarily close to an accidental frequency degeneracy. For nonzero k, the symmetry is broken causing the modes to repel. When the modes are sufficiently close together this repulsion leads to unusual features such as extremely flattened dispersion relations, backward waves, zero group velocity for nonzero k, atypical divergence of the density of states, and nonzero group velocity at k = 0.

[181]
Y. Sasaki, Y. Ohtera, S. G. Johnson, and S. Kawakami, “A reference analytical model of three-dimensional photonic crystal waveguides and their mode spectrum,” Trans. Inst. Elect. Info. Comm. Eng. C, vol. J87-C, no. 3, pp. 328–334, 2004. [ bib ]
[182]
Y. Tanaka, Y. Sugimoto, N. Ikeda, H. Nakamura, K. Asakawa, K. Inoue, and S. G. Johnson, “Group velocity dependence of propagation losses in single-line-defect photonic crystal waveguides on gaas membranes,” Electronics Letters, vol. 40, no. 3, pp. 174–176, 2004. [ bib | .pdf ]
Group velocity, vg, dependence of propagation loss in single-line-defect photonic crystal waveguides on GaAs membranes, and minimum loss as low as 2.5 dB/mm, are presented. When vg is reduced by a factor of 7, an additional loss is found to be only 5 dB/mm, thus proving a feasible usage of low vg.

[183]
C. W. Wong, X. Yang, P. T. Rakich, S. G. Johnson, M. Qi, Y. Jeon, G. Barbastathis, and S.-G. Kim, “Strain-tunable photonic bandgap microcavity waveguides in silicon at 1.55 μm,” Proc. SPIE, vol. 5511, pp. 156–164, 2004. [ bib | .pdf ]
The majority of photonic crystals developed till-date are not dynamically tunable, especially in silicon-based structures. Dynamic tunability is required not only for reconfiguration of the optical characteristics based on user-demand, but also for compensation against external disturbances and relaxation of tight device fabrication tolerances. Recent developments in photonic crystals have suggested interesting possibilities for static small-strain modulations to affect the optical characteristics1-3, including a proposal for dynamic strain-tunability4. Here we report the theoretical analysis, device fabrication, and experimental measurements of tunable silicon photonic band gap microcavities in optical waveguides, through direct application of dynamic strain to the periodic structures5. The device concept consists of embedding the microcavity waveguide6 on a deformable SiO2 membrane. The membrane is strained through integrated thin-film piezoelectric microactuators. We show a 1.54 nm shift in cavity resonances at 1.56 μm wavelengths for an applied piezoelectric strain of 0.04%. This is in excellent agreement with our modeling, predicted through first-order semi-analytical perturbation theory7 and finite-difference time-domain calculations. The measured microcavity transmission shows resonances between 1.55 to 1.57 μm, with Q factors ranging from 159 to 280. For operation at infrared wavelengths, we integrate X-ray and electron-beam lithography (for critical 100 nm feature sizes) with thin-film piezoelectric surface micromachining. This level of integration permits realizable silicon-based photonic chip devices, such as high-density optical filters and spontaneous-emission enhancement devices with tunable configurations.

[184]
M. Skorobogatiy, S. A. Jacobs, S. G. Johnson, M. Meunier, and Y. Fink, “Modeling the impact of manufacturing imperfections on photonic crystal device performance: design of perturbation-tolerant PBG components,” Proc. SPIE, vol. 5450, pp. 161–172, 2004. [ bib | .pdf ]
Standard perturbation theory (PT) and coupled mode theory (CMT) formulations fail or exhibit very slow convergence when applied to the analysis of geometrical variations in high index-contrast optical components such as Bragg fibers and photonic crystals waveguides. By formulating Maxwell's equations in perturbation matched curvilinear coordinates, we have derived several rigorous PT and CMT expansions that are applicable in the case of generic non-uniform dielectric profile perturbations in high index-contrast waveguides. In strong fiber tapers and fiber Bragg gratings we demonstrate that our formulation is accurate and rapidly converges to an exact result when used in a CMT framework even in the high index-contrast regime. We then apply our method to investigate the impact of hollow Bragg fiber ellipticity on its Polarization Mode Dispersion (PMD) characteristics for telecom applications. Correct PT expansions allowed us to design an efficient optimization code which we successfully applied to the design of dispersion compensating hollow Bragg fiber with optimized low PMD and very large dispersion parameter. We have also successfully extended this methodology to treat radiation scattering due to common geometric variations in generic photonic crystals. As an example, scattering analysis in strong 2D photonic crystal tapers is demonstrated.

[185]
C. Luo, S. G. Johnson, M. Soljačić, J. D. Joannopoulos, and J. B. Pendry, “Novel optical phenomena with photonic crystals,” Proc. SPIE, vol. 5166, pp. 207–219, 2004. [ bib | .pdf ]
In this work we present an introduction to photonic crystals by discussing the basic concepts and principles behind these artificial materials, as well as their abilities to control light and enable unusual optical phenomena. We will focus on specific examples including (1) negative refraction of light, (2) the superprism effect (anomalous electromagnetic dispersion), and (3) the possibility of superlensing (subwavelength focusing). These are very general results based on direct solutions of Maxwell's equations, and can consequently be of relevance to many areas of science and technology.

[186]
M. F. Yanik, S. Fan, M. Soljačić, and J. D. Joannopoulos, “All-optical transistor action with bistable switching in a photonic crystal cross-waveguide geometry,” Optics Letters, vol. 28, pp. 2506–2508, December 2003. [ bib | .pdf ]
We demonstrate all-optical switching action in a nonlinear photonic crystal cross-waveguide geometry with instantaneous Kerr nonlinearity, in which the transmission of a signal can be reversibly switched on and off by a control input. Our geometry accomplishes both spatial and spectral separation between the signal and the control in the nonlinear regime. The device occupies a small footprint of a few micrometers squared and requires only a few milliwatts of power at a 10-Gbit s switching rate by use of Kerr nonlinearity in AlGaAs below half the electronic bandgap. We also show that the switching dynamics, as revealed by both coupled-mode theory and finite-difference time domain simulations, exhibits collective behavior that can be exploited to generate high-contrast logic levels and all-optical memory.

[187]
E. J. Reed, M. Soljačić, and J. D. Joannopoulos, “Reversed Doppler effect in photonic crystals,” Physical Review Letters, vol. Physical Review Letters, pp. 133901–133904, September 2003. [ bib | http | .pdf ]
Nonrelativistic reversed Doppler shifts have never been observed in nature and have only been speculated to occur in pathological systems with simultaneously negative effective permittivity and permeability. This Letter presents a different, new physical phenomenon that leads to a nonrelativistic reversed Doppler shift in light. It arises when light is reflected from a moving shock wave propagating through a photonic crystal. In addition to reflection of a single frequency, multiple discrete reflected frequencies or a 10 GHz periodic modulation can also be observed when a single carrier frequency of wavelength 1 μm is incident.

[188]
K. C. Huang, P. Bienstman, J. D. Joannopoulos, K. A. Nelson, and S. Fan, “Phonon-polariton excitations in photonic crystals,” Physical Review B, vol. 68, pp. 075209–075220, August 2003. Erratum: ibid., vol. 68, p. 159903 (2004). [ bib | http ]
The incorporation of materials which exhibit transverse phonon-polariton excitations into a photonic crystal produces an intricate optical system possessing unique and varied photon phenomena. In particular, we demonstrate theoretically that such a system will exhibit both near-dispersionless bands with field localization in the polaritonic material and metalliclike bands with complete flux expulsion in an extremely small frequency interval around the characteristic phonon frequency. Moreover, when the fundamental resonances of the polaritonic rods overlap with the bands of a geometrically identical metallodielectric crystal, nearby states will couple to produce a band in which the localized field varies continuously between two distinct nodal patterns, in an exceedingly small frequency range. We also discuss the implications of losses on these phenomena and verify that our results can be realized experimentally.

[189]
D. Roundy and J. D. Joannopoulos, “Photonic crystal structure with square symmetry within each layer and a three-dimensional band gap,” Applied Physics Letters, vol. 82, pp. 3835–3837, June 2003. [ bib | http ]
We present a layered photonic crystal structure having a connectivity that is different from diamond which possesses square symmetry within each layer. This structure has a complete photonic band gap of 18% of the midgap frequency with a dielectric contrast of 12:1, and is a structure with layered square symmetry having a gap greater than 10%. We demonstrate a waveguide in this crystal created by removing a row of rods from a single layer.

[190]
K. C. Huang, P. Bienstman, J. D. Joannopoulos, K. A. Nelson, and S. Fan, “Field expulsion and reconfiguration in polaritonic photonic crystals,” Physical Review Letters, vol. 90, pp. 196402–196405, May 2003. Erratum: ibid., vol. 92, p. 169901 (2004). [ bib | http ]
We uncover a rich set of optical phenomena stemming from the incorporation of polar materials exhibiting transverse phonon polariton excitations into a photonic crystal structure. We identify in the frequency spectrum two regimes in which the dielectric response of the polaritonic medium can induce extreme localization of the electromagnetic energy. Our analysis of the effect of polarization and the interaction between the polariton and photonic band gaps on the Bloch states leads to a pair of mechanisms for sensitive frequency-controlled relocation and/or reconfiguration of the fields.

[191]
E. J. Reed, M. Soljačić, and J. D. Joannopoulos, “Color of shock waves in photonic crystals,” Physical Review Letters, vol. 90, pp. 203904–203907, May 2003. [ bib | http | .pdf ]
Unexpected and stunning new physical phenomena result when light interacts with a shock wave or shocklike dielectric modulation propagating through a photonic crystal. These new phenomena include the capture of light at the shock wave front and reemission at a tunable pulse rate and carrier frequency across the band gap, and bandwidth narrowing as opposed to the ubiquitous bandwidth broadening. To our knowledge, these effects do not occur in any other physical system and are all realizable under experimentally accessible conditions. Furthermore, their generality make them amenable to observation in a variety of time-dependent photonic crystal systems, which has significant technological implications.

[192]
C. Luo, M. Ibanescu, S. G. Johnson, and J. D. Joannopoulos, “Cerenkov radiation in photonic crystals,” Science, vol. 299, pp. 368–371, 2003. [ bib | .pdf ]
In a conventional material, the coherent Cerenkov radiation due to a moving charged particle is associated with a velocity threshold, a forward-pointing radiation cone, and a forward direction of emission. We describe different behavior for the Cerenkov radiation in a photonic crystal. In particular, this radiation is intrinsically coupled with transition radiation and is observable without any threshold. Within one particle-velocity range, we found a radiation pattern with a backward-pointing radiation cone. In another velocity range, backward-propagating Cerenkov radiation can be expected. Potential applications include velocity-sensitive particle detection and radiation generation at selectable frequencies.

[193]
M. Soljačić, M. Ibanescu, S. G. Johnson, J. D. Joannopoulos, and Y. Fink, “Optical bistability in axially modulated OmniGuide fibers,” Optics Letters, vol. 28, pp. 516–518, 2003. [ bib | .pdf ]
We demonstrate the feasibility of optical bistability in an axially modulated nonlinear OmniGuide fiber through analytical theory and detailed numerical experiments. At 1.55-μm carrier wavelength, the in-fiber devices that we propose can operate with only a few tens of milliwatts of power, can have a nearly instantaneous response and recovery time, and can be shorter than 100 μm .

[194]
C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. Pendry, “Negative refraction without negative index in metallic photonic crystals,” Optics Express, vol. 11, pp. 746–754, 2003. [ bib | http | .pdf ]
It is shown that certain metallic photonic crystals can enable negative refraction and subwavelength imaging without relying on a negative effective index. These metallic structures are very simple in design and appear straightforward for fabrication. Their unusual electromagnetic response should provide an interesting comparison with the metallic left-handed materials.

[195]
T. Engeness, M. Ibanescu, S. G. Johnson, O. Weisberg, M. Skorobogatiy, S. Jacobs, and Y. Fink, “Dispersion tailoring and compensation by modal interactions in OmniGuide fibers,” Optics Express, vol. 11, pp. 1175–1196, 2003. [ bib | http | .pdf ]
We present a method for dispersion-tailoring of OmniGuide and other photonic band-gap guided fibers based on weak interactions (“anticrossings”) between the core-guided mode and a mode localized in an intentionally introduced defect of the crystal. Because the core mode can be guided in air and the defect mode in a much higher-index material, we are able to obtain dispersion parameters in excess of 500,000 ps/nm-km. Furthermore, because the dispersion is controlled entirely by geometric parameters and not by material dispersion, it is easily tunable by structural choices and fiber-drawing speed. So, for example, we demonstrate how the large dispersion can be made to coincide with a dispersion slope that matches commercial silica fibers to better than 1%, promising efficient compensation. Other parameters are shown to yield dispersion-free transmission in a hollow OmniGuide fiber that also maintains low losses and negligible nonlinearities, with a nondegenerate TE01 mode immune to polarization-mode dispersion (PMD). We present theoretical calculations for a chalcogenide-based material system that has recently been experimentally drawn.

[196]
M. Skorobogatiy, C. Anastassiou, S. G. Johnson, O. Weisberg, T. Engeness, S. Jacobs, R. Ahmad, and Y. Fink, “Quantitative characterization of higher-order mode converters in weakly multimoded fibers,” Optics Express, vol. 11, pp. 2838–2847, 2003. [ bib | http | .pdf ]
We present a rigorous analysis methodology of fundamental to higher order mode converters in step index few mode optical fibers. We demonstrate experimental conversion from a fundamental LP01 mode to the higher order LP11 mode utilizing a multiple mechanical bend mode converter. We perform a quantitative analysis of the measured light intensity, and demonstrate a modal decomposition algorithm to characterize the modal content excited in the fiber. Theoretical modelling of the current mode converter is then performed and compared with experimental findings.

[197]
M. Ibanescu, S. G. Johnson, M. Soljačić, J. D. Joannopoulos, Y. Fink, O. Weisberg, T. D. Engeness, S. A. Jacobs, and M. Skorobogatiy, “Analysis of mode structure in hollow dielectric waveguide fibers,” Physical Review E, vol. 67, p. 046608, 2003. [ bib | .pdf ]
In this paper, we analyze the electromagnetic mode structure of an OmniGuide fiber—hollow dielectric waveguide in which light is confined by a large index-contrast omnidirectional dielectric mirror. In particular, we find that the modes in an OmniGuide fiber are similar to those in a hollow metallic waveguide in their symmetries, cutoff frequencies, and dispersion relations. We show that the differences can be predicted by a model based on a single parameter—the phase shift upon reflection from the dielectric mirror. The analogy to the metal waveguide extends to the transmission properties, resulting in the identification of the TE01 mode as the lowest-loss mode of the OmniGuide fiber.

[198]
E. Lidorikis, M. L. Povinelli, S. G. Johnson, and J. D. Joannopoulos, “Polarization-independent linear waveguides in 3d photonic crystals,” Physical Review Letters, vol. 91, p. 023902, 2003. [ bib | .pdf ]
Using a symmetry-based approach, we have designed polarization-independent waveguides in a 3D photonic crystal. A comprehensive series of numerical experiments, involving the propagation of pulsed signals through long straight waveguide sections and sharp bends, quantitatively evaluates the bend-transmission coefficient over the entire bandwidth of the corresponding guided modes. High (∼95%) polarization-independent bend transmission is achieved within a certain frequency range.

[199]
C. Luo, S. G. Johnson, and J. D. Joannopoulos, “Subwavelength imaging in photonic crystals,” Physical Review B, vol. 68, p. 045115, 2003. [ bib | .pdf ]
We investigate the transmission of evanescent waves through a slab of photonic crystal and explore the recently suggested possibility of focusing light with subwavelength resolution. The amplification of near-field waves is shown to rely on resonant coupling mechanisms to surface photon bound states, and the negative refractive index is only one way of realizing this effect. It is found that the periodicity of the photonic crystal imposes an upper cutoff to the transverse wave vector of evanescent waves that can be amplified, and thus a photonic-crystal superlens is free of divergences even in the lossless case. A detailed numerical study of the optical image of such a superlens in two dimensions reveals a subtle and very important interplay between propagating waves and evanescent waves on the final image formation. Particular features that arise due to the presence of near-field light are discussed.

[200]
M. L. Povinelli, R. E. Bryant, S. Assefa, S. G. Johnson, S. Fan, A. A. Erchak, G. S. Petrich, E. Lidorikis, J. D. Joannopoulos, L. A. Kolodziejski, and E. P. Ippen, “Design of a nanoelectromechanical high-index-contrast guided-wave optical switch for single-mode operation at 1.55 μm,” IEEE Photonics Technology Letters, vol. 15, no. 9, pp. 1207–1209, 2003. [ bib | DOI | .pdf ]
A design is presented for a nanoelectromechanical optical switch based on the horizontal deflection of an input waveguide to align with one of two output waveguides. The use of high-index (GaAs) strip waveguides surrounded by air, designed to be single-mode at 1.55 μm, significantly decreases device dimensions as compared to previous designs. Design tradeoffs between optical and mechanical properties of the device are discussed. By means of three-dimensional numerical simulations, optical transmission is optimized for two different design strategies: butt and parallel coupling. High polarization-independent transmission (over 90%) is predicted for realistic design parameters.

[201]
S. G. Johnson and J. D. Joannopoulos, “Designing synthetic optical media: Photonic crystals,” Acta Materialia, vol. 51, pp. 5823–5835, 2003. [ bib | DOI | .pdf ]
A new class of materials, called photonic crystals, affect a photon's properties in much the same way that a semiconductor affects an electron's properties. This represents an ability to mold and guide light that leads naturally to novel applications in several fields, including optoelectronics and telecommunications. We present an introductory survey of the basic concepts and ideas that underlie photonic crystals, and present results and devices that illustrate their potential to circumvent limits of traditional optical systems.

[202]
E. Lidorikis, M. L. Povinelli, S. G. Johnson, M. Soljačić, M. Ibanescu, Y. Fink, and J. D. Joannopoulos, “Modeling of nanophotonics,” Proc. SPIE, vol. 5225, pp. 7–19, 2003. Invited paper. [ bib | .pdf ]
The ability of photonic crystals to mold the flow of light in new ways can lead to a variety of novel and improved designs of optical nanocomponents and nanodevices in photonics. Two examples will be presented: a) Using linear materials, a polarization independent waveguide is designed in a 3D photonic crystal. It is demonstrated that this system provides lossless guiding of light at length-scales approaching the wavelength of the light itself, offering a promising platform for the design of integrated high performance polarization-insensitive waveguide networks. b) Using nonlinear materials, a cylindrical photonic crystal fiber is designed that can exhibit all-optical switching without the need for an axial periodicity. It is shown that this property stems from the unique structure of the cylindrical photonic crystal guidedmode dispersion relation, and can lead to significant improvements in manufacturing ease, operating power usage, and device size requirements, making such a system ideal for integrated all-optical signal processing.

[203]
M. Soljačić, M. Ibanescu, C. Luo, S. G. Johnson, S. Fan, Y. Fink, and J. D. Joannopoulos, “All-optical switching using optical bistability in nonlinear photonic crystals,” Proc. SPIE, vol. 5000, pp. 200–214, 2003. Invited paper. [ bib | .pdf ]
We demonstrate optical bistability in a class of non-linear photonic crystal devices, through the use of detailed numerical experiments, and analytical theory. Our devices are shorter than the wavelength of light in length, they can operate with only a few mW of power, and can be faster than 1ps.

[204]
M. Skorobogatiy, S. G. Johnson, S. A. Jacobs, and Y. Fink, “Dielectric profile variations in high-index-contrast waveguides, coupled mode theory, and perturbation expansions,” Physical Review E, vol. 67, p. 046613, 2003. [ bib | .pdf ]
Perturbation theory formulation of Maxwell's equations gives a theoretically elegant and computationally efficient way of describing small imperfections and weak interactions in electromagnetic systems. It is generally appreciated that due to the discontinuous field boundary conditions in the systems employing high dielectric contrast profiles standard perturbation formulations fails when applied to the problem of shifted material boundaries. In this paper we developed coupled mode and perturbation theory formulations for treating generic perturbations of a waveguide cross section based on Hamiltonian formulation of Maxwell equations in curvilinear coordinates. We show that our formulation is accurate beyond the first order and rapidly converges to an exact result when used in a coupled mode theory framework even for the high-index-contrast discontinuous dielectric profiles. Among others, our formulation allows for an efficient numerical evaluation of such quantities as deterministic PMD and change in the GV and GVD of a mode due to generic profile distortion in a waveguide of arbitrary cross section. To our knowledge, this is the first time perturbation and coupled mode theories are developed to deal with arbitrary profile variations in high-index-contrast waveguides.

[205]
M. L. Povinelli, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, “Toward photonic-crystal metamaterials: Creating magnetic emitters in photonic crystals,” Applied Physics Letters, vol. 82, pp. 1069–1071, 2003. [ bib | .pdf ]
In this work, we explore the possibility of designing photonic crystals to act as magnetic metamaterials: structures that exhibit magnetic properties despite the nonmagnetic character of their constituents. The building blocks of a magnetic material are microscopic magnetic dipoles, and to create a synthetic analog we employ point-defect modes in a photonic crystal. We begin by identifying a point defect mode in a three-dimensional crystal whose local field pattern resembles an oscillating magnetic moment. By analyzing the far-field pattern of the field radiated from the defect, we prove quantitatively that such modes can be designed with a primarily magnetic character: over 98% of the emitted power goes into magnetic multipole radiation. Unlike the constituents of natural para- and ferromagnetic materials, these synthetic magnetic emitters can be designed to operate without losses even at optical frequencies.

[206]
P. Bienstman, S. Assefa, S. G. Johnson, J. D. Joannopoulos, G. S. Petrich, and L. A. Kolodziejski, “Taper structures for coupling into photonic crystal slab waveguides,” Journal of the Optical Society of America B, vol. 20, pp. 1817–1821, 2003. [ bib | .pdf ]
We present an adiabatic taper design in three dimensions for coupling light into photonic crystal defect waveguides in a square lattice of circular dielectric rods. The taper is a two-stage structure in which the first stage makes the transition from a dielectric waveguide to a coupled-cavity waveguide. The second stage subsequently transforms the waveguide mode from an index-guided mode to a band-gap-guided mode. We discuss differences between the two-dimensional device and its three-dimensional slab version.

[207]
S. G. Johnson, M. L. Povinelli, P. Bienstman, M. Skorobogatiy, M. Soljačić, M. Ibanescu, E. Lidorikis, and J. D. Joannopoulos, “Coupling, scattering and perturbation theory: Semi-analytical analyses of photonic-crystal waveguides,” in Proc. 2003 5th Intl. Conf. on Transparent Optical Networks and 2nd European Symp. on Photonic Crystals, vol. 1, pp. 103–109, 2003. [ bib | .pdf ]
Although brute-force simulations of Maxwell's equations, such as FDTD methods, have enjoyed wide success in modeling photonic-crystal systems, they are not ideally suited for the study of weak perturbations, such as surface roughness or gradual waveguide transitions, where a high resolution and/or large computational cells are required. Instead, we suggest that these important problems are ideally suited for semi-analytical methods, which employ perturbative corrections (typically only needing the lowest order) to the exactly understood perfect waveguide. However, semi-analytical methods developed for the study of conventional waveguides require modification for high index-contrast, strongly periodic photonic crystals, and we have developed corrected forms of coupled-wave theory, perturbation theory, and the volume-current method for this situation. In this paper, we survey these new developments and describe the most significant results for adiabatic waveguide transitions and disorder losses. We present design rules and scaling laws for adiabatic transitions. In the case of disorder, we show both analytically and numerically that photonic crystals can suppress radiation loss without any corresponding increase in reflection, compared to a conventional strip waveguide with the same modal area, group velocity, and disorder strength.

[208]
B. Temelkuran, S. D. Hart, G. Benoit, J. D. Joannopoulos, and Y. Fink, “Wavelength-scalable hollow optical fibres with large photonic bandgaps for CO2 laser transmission,” Nature, vol. 420, pp. 650–653, December 2002. [ bib | DOI ]
Conventional solid-core optical fibres require highly transparent materials. Such materials have been difficult to identify owing to the fundamental limitations associated with the propagation of light through solids, such as absorption, scattering and nonlinear effects. Hollow optical fibres offer the potential to minimize the dependence of light transmission on fibre material transparency. Here we report on the design and drawing of a hollow optical fibre lined with an interior omnidirectional dielectric mirror. Confinement of light in the hollow core is provided by the large photonic bandgaps established by the multiple alternating submicrometre-thick layers of a high-refractive-index glass and a low-refractive-index polymer. The fundamental and high-order transmission windows are determined by the layer dimensions and can be scaled from 0.75 to 10.6 μm in wavelength. Tens of metres of hollow photonic bandgap fibres for transmission of carbon dioxide laser light at 10.6 μm wavelength were drawn. The transmission losses are found to be less than 1.0 dB m-1, orders of magnitude lower than those of the intrinsic fibre material, thus demonstrating that low attenuation can be achieved through structural design rather than high-transparency material selection.

[209]
P. A. Bermel and M. Warner, “Photonic band structure of highly deformable self-assembling systems,” Physical Review E, vol. 65, p. 010702(R), December 2002. [ bib | http ]
We calculate the photonic band structure at normal incidence of highly deformable, systems self-assembling cholesteric elastomers subjected to external stress. Cholesteric elastomers display brilliantly colored reflections and lasing owing to gaps in their photonic band structure. This band structure has been shown to vary sensitively with strain in both theory and experiment. New gaps open up and all gaps shift in frequency. We predict a different “total” band gap for all polarizations in the vicinity of the previously observed de Vries band gap, which is only for one polarization.

[210]
Y. Yi, P. Bermel, K. Wada, X. Duan, J. D. Joannopoulos, and L. C. Kimerling, “Tunable multichannel optical filter based on silicon photonic band gap materials actuation,” Applied Physics Letters, vol. 81, pp. 4112–4114, November 2002. [ bib | http ]
A Si-based tunable omnidirectional reflecting photonic band gap structure with a relatively large air gap defect is fabricated and measured. Using only one device, low-voltage tuning around two telecom wavelengths of 1.55 and 1.3 μm by electrostatic force is realized. Four widely spaced resonant modes within the photonic band gap are observed, which is in good agreement with numerical simulations. The whole process is at low temperature and can be compatible with current microelectronics process technology. There are several potential applications of this technology in wavelength division multiplexing devices.

[211]
S. Fan and J. D. Joannopoulos, “Analysis of guided resonances in photonic crystal slabs,” Physical Review B, vol. 65, pp. 235112–235119, June 2002. [ bib | http ]
We present a three-dimensional analysis of guided resonances in photonic crystal slab structures that leads to a new understanding of the complex spectral properties of such systems. Specifically, we calculate the dispersion diagrams, the modal patterns, and transmission and reflection spectra of these resonances. From these calculations, a key observation emerges involving the presence of two temporal pathways for transmission and reflection processes. Using this insight, we introduce a general physical model that explains the essential features of complex spectral properties. Finally, we show that the quality factors of these resonances are strongly influenced by the symmetry of the modes and the strength of the index modulation.

[212]
P. A. Bermel and M. Warner, “Photonic band structure of cholesteric elastomers,” Physical Review E, vol. 65, p. 056614, May 2002. [ bib | http ]
We calculate the photonic band structure along and oblique to the helix axis of cholesteric elastomers. They are highly deformable, self-assembling systems. They display brilliantly colored reflections and lasing owing to stop bands in their photonic band structure. This band structure varies sensitively and extensively with strain. We show how additional stop bands open up and how they all shift in frequency. We predict a “total” stop band, that is, for both circular polarizations and show analytically how stop bands scale with strain. The extension of stop bands to a range of angles thereby creates pseudogaps, and the relevance to low-threshold lasing is discussed.

[213]
S. D. Hart, G. R. Maskaly, B. Temelkuran, P. H. Prideaux, J. D. Joannopoulos, and Y. Fink, “External reflection from omnidirectional dielectric mirror fibers,” Science, vol. 296, pp. 510–513, April 2002. [ bib | DOI ]
We report the design and fabrication of a multilayered macroscopic fiber preform and the subsequent drawing and optical characterization of extended lengths of omnidirectional dielectric mirror fibers with submicrometer layer thickness. A pair of glassy materials with substantially different indices of refraction, but with similar thermomechanical properties, was used to construct 21 layers of alternating refractive index surrounding a tough polymer core. Large directional photonic band gaps and high reflection efficiencies comparable to those of the best metallic reflectors were obtained. Potential applications of these fibers include woven fabrics for radiation barriers, spectral authentication of cloth, and filters for telecommunications.

[214]
S. Y. Lin, E. Chow, J. Bur, S. G. Johnson, and J. D. Joannopoulos, “Low-loss, wide-angle Y splitter at approximately ∼1.6 μm wavelengths built with a two-dimensional photonic crystal,” Optics Letters, vol. 27, pp. 1400–1402, 2002. [ bib | .pdf ]
We report a successful experimental realization of a photonic-crystal Ysplitter operating at λ∼1.6μm. Our device has a large splitting angle of 120o and a miniature size of ∼3μm×3μm. Furthermore, the Y-splitter loss is measured to be 0.5–1dB at λ = 1640–1680 nm , making the Ysplitter promising for integrated photonic- circuit applications. These unique properties are attributed to the new guiding principle made possible by the photonic bandgap.

[215]
M. R. Watts, S. G. Johnson, H. A. Haus, and J. D. Joannopoulos, “Electromagnetic cavity with arbitrary Q and small modal volume without a complete photonic bandgap,” Optics Letters, vol. 27, pp. 1785–1787, 2002. [ bib | .pdf ]
We show how an electromagnetic cavity with arbitrarily high Q and small (bounded) modal volume can be formed in two or three dimensions with a proper choice of dielectric constants. Unlike in previous work, neither a complete photonic bandgap nor a trade-off in mode localization for Q is required. Rather, scattering and radiation are prohibited by a perfect mode match of the TE-polarized modes in each subsection of a Bragg resonator. Q values in excess of 105 are demonstrated through finite-difference time-domain simulations of two- and three-dimensional structures with modal areas or volumes of the order of the wavelength squared or cubed.

[216]
C. Luo, S. G. Johnson, and J. D. Joannopoulos, “All-angle negative refraction without negative effective index,” Physical Review B, vol. 65, p. 201104, 2002. [ bib | .pdf ]
We describe an all-angle negative refraction effect that does not employ a negative effective index of refraction and involves photonic crystals. A few simple criteria sufficient to achieve this behavior are presented. To illustrate this phenomenon, a microsuperlens is designed and numerically demonstrated.

[217]
S. G. Johnson, M. Ibanescu, M. A. Skorobogatiy, O. Weisberg, J. D. Joannopoulos, and Y. Fink, “Perturbation theory for Maxwell's equations with shifting material boundaries,” Physical Review E, vol. 65, p. 066611, 2002. [ bib | .pdf ]
Perturbation theory permits the analytic study of small changes on known solutions, and is especially useful in electromagnetism for understanding weak interactions and imperfections. Standard perturbation-theory techniques, however, have difficulties when applied to Maxwell's equations for small shifts in dielectric interfaces (especially in high-index-contrast, three-dimensional systems) due to the discontinous field boundary conditions—in fact, the usual methods fail even to predict the lowest-order behavior. By considering a sharp boundary as a limit of anisotropically smoothed systems, we are able to derive a correct first-order perturbation theory and mode-coupling constants, involving only surface integrals of the unperturbed fields over the perturbed interface. In addition, we discuss further considerations that arise for higher-order perturbative methods in electromagnetism.

[218]
M. Soljačić, M. Ibanescu, S. G. Johnson, Y. Fink, and J. D. Joannopoulos, “Optimal bistable switching in nonlinear photonic crystals,” Physical Review E, vol. 66, p. 055601, 2002. [ bib | .pdf ]
We present an analytical model and numerical experiments to describe optimal bistable switching in a nonlinear photonic crystal system. It is proved that only three parameters are needed to characterize a bistable switch: the resonant frequency ωres, the quality factor Q, and parameter κ that measures nonlinear “feedback strength.” A photonic crystal enables the device to operate in single-mode fashion, as if it were effectively one dimensional. This provides optimal control over the input and output and facilitates further large-scale optical integration.

[219]
S. G. Johnson, P. Bienstman, M. A. Skorobogatiy, M. Ibanescu, E. Lidorikis, and J. D. Joannopoulos, “Adiabatic theorem and continuous coupled-mode theory for efficient taper transitions in photonic crystals,” Physical Review E, vol. 66, p. 066608, 2002. [ bib | .pdf ]
We prove that an adiabatic theorem generally holds for slow tapers in photonic crystals and other strongly grated waveguides with arbitrary index modulation, exactly as in conventional waveguides. This provides a guaranteed pathway to efficient and broad-bandwidth couplers with, e.g., uniform waveguides. We show that adiabatic transmission can only occur, however, if the operating mode is propagating (nonevanescent) and guided at every point in the taper. Moreover, we demonstrate how straightforward taper designs in photonic crystals can violate these conditions, but that adiabaticity is restored by simple design principles involving only the independent band structures of the intermediate gratings. For these and other analyses, we develop a generalization of the standard coupled-mode theory to handle arbitrary nonuniform gratings via an instantaneous Bloch-mode basis, yielding a continuous set of differential equations for the basis coefficients. We show how one can thereby compute semianalytical reflection and transmission through crystal tapers of almost any length, using only a single pair of modes in the unit cells of uniform gratings. Unlike other numerical methods, our technique becomes more accurate as the taper becomes more gradual, with no significant increase in the computation time or memory. We also include numerical examples comparing to a well-established scattering-matrix method in two dimensions.

[220]
C. Luo, S. G. Johnson, and J. D. Joannopoulos, “All-angle negative refraction in a three-dimensionally periodic photonic crystal,” Applied Physics Letters, vol. 81, pp. 2352–2354, 2002. [ bib | .pdf ]
We introduce a photonic crystal that has a large range of effective negative refractive index in three dimensions (3D) and demonstrate its negative-refraction property by numerical simulations. With slight modifications, our design is also amenable to layer-by-layer fabrication. This work should enable experimental observation of negative refraction and related phenomena in 3D at optical frequencies.

[221]
M. Skorobogatiy, S. Jacobs, S. G. Johnson, and Y. Fink, “Geometric variations in high index-contrast waveguides, coupled mode theory in curvilinear coordinates,” Optics Express, vol. 10, pp. 1227–1243, 2002. [ bib | http | .pdf ]
Perturbation theory formulation of Maxwell's equations gives a theoretically elegant and computationally efficient way of describing small imperfections and weak interactions in electro-magnetic systems. It is generally appreciated that due to the discontinuous field boundary conditions in the systems employing high dielectric contrast profiles standard perturbation formulations fail when applied to the problem of shifted material boundaries. In this paper we developed a novel coupled mode and perturbation theory formulations for treating generic non-uniform (varying along the direction of propagation) perturbations of a waveguide cross-section based on Hamiltonian formulation of Maxwell equations in curvilinear coordinates. We show that our formulation is accurate and rapidly converges to an exact result when used in a coupled mode theory framework even for the high index-contrast discontinuous dielectric profiles. Among others, our formulation allows for an efficient numerical evaluation of induced PMD due to a generic distortion of a waveguide profile, analysis of mode filters, mode converters and other optical elements such as strong Bragg gratings, tapers, bends etc., and arbitrary combinations of thereof. To our knowledge, this is the first time perturbation and coupled mode theories are developed to deal with arbitrary non-uniform profile variations in high index-contrast waveguides.

[222]
M. Soljačić, S. G. Johnson, S. Fan, M. Ibanescu, E. Ippen, and J. D. Joannopoulos, “Photonic-crystal slow-light enhancement of nonlinear phase sensitivity,” Journal of the Optical Society of America B, vol. 19, pp. 2052–2059, 2002. [ bib | .pdf ]
We demonstrate how slow group velocities of light, which are readily achievable in photonic-crystal systems, can dramatically increase the induced phase shifts caused by small changes in the index of refraction. Such increased phase sensitivity may be used to decrease the sizes of many devices, including switches, routers, all-optical logical gates, wavelength converters, and others. At the same time a low group velocity greatly decreases the power requirements needed to operate these devices. We show how these advantages can be used to design switches smaller than 20μm ×200μm in size by using readily available materials and at modest levels of power. With this approach, one could have ∼105 such devices on a surface that is 2 cm ×2 cm, making it an important step towards large-scale all-optical integration.

[223]
M. Skorobogatiy, M. Ibanescu, S. G. Johnson, O. Weisberg, T. D. Engeness, M. Soljačić, S. A. Jacobs, and Y. Fink, “Analysis of general geometric scaling perturbations in a transmitting waveguide: Fundamental connection between polarization-mode dispersion and group-velocity dispersion,” Journal of the Optical Society of America B, vol. 19, pp. 2867–2875, 2002. [ bib | .pdf ]
We develop a novel perturbation theory formulation to evaluate polarization-mode dispersion (PMD) for a general class of scaling perturbations of a waveguide profile based on generalized Hermitian Hamiltonian formulation of Maxwell's equations. Such perturbations include elipticity and uniform scaling of a fiber cross section, as well as changes in the horizontal or vertical sizes of a planar waveguide. Our theory is valid even for discontinuous high-index contrast variations of the refractive index across a waveguide cross section. We establish that, if at some frequencies a particular mode behaves like pure TE or TM polarized mode (polarization is judged by the relative amounts of the electric and magnetic longitudinal energies in the waveguide cross section), then at such frequencies for fibers under elliptical deformation its PMD as defined by an intermode dispersion parameter τ becomes proportional to group-velocity dispersion D such that τ= λδ|D|, where δ is a measure of the fiber elipticity and λ is a wavelength of operation. As an example, we investigate a relation between PMD and group-velocity dispersion of a multiple-core step-index fiber as a function of the coreclad index contrast. We establish that in this case the positions of the maximum PMD and maximum absolute value of group-velocity dispersion are strongly correlated, with the ratio of PMD to group-velocity dispersion being proportional to the coreclad dielectric contrast.

[224]
S. G. Johnson, M. Ibanescu, M. A. Skorobogatiy, O. Weisberg, T. D. Engeness, M. Soljačić, S. A. Jacobs, J. D. Joannopoulos, and Y. Fink, “Breaking the glass ceiling: Hollow OmniGuide fibers,” Proc. SPIE, vol. 4655, pp. 1–15, 2002. [ bib | .pdf ]
We argue that OmniGuide fibers, which guide light within a hollow core by concentric multilayer films having the property of omnidirectional reflection, have the potential to lift several physical limitations of silica fibers. We show how the strong confinement in OmniGuide fibers greatly suppresses the properties of the cladding materials: even if highly lossy and nonlinear materials are employed, both the intrinsic losses and nonlinearities of silica fibers can be surpassed by orders of magnitude. This feat, impossible to duplicate in an index-guided fiber with existing materials, would open up new regimes for long-distance propagation and dense wavelengthdivision multiplexing (DWDM). The OmniGuide-fiber modes bear a strong analogy to those of hollow metallic waveguides; from this analogy, we are able to derive several general scaling laws with core radius. Moreover, there is strong loss discrimination between guided modes, depending upon their degree of confinement in the hollow core: this allows large, ostensibly multi-mode cores to be used, with the lowest-loss TE01 mode propagating in an effectively single-mode fashion. Finally, because this TE01 mode is a cylindrically symmetrical (“azimuthally” polarized) singlet state, it is immune to polarization-mode dispersion (PMD), unlike the doubly-degenerate linearly-polarized modes in silica fibers that are vulnerable to birefringence.

[225]
M. Soljačić, S. G. Johnson, S. Fan, M. Ibanescu, E. P. Ippen, and J. D. Joannopoulos, “Enhancement of phase sensitivity by exploring slow light in photonic crystals,” Proc. SPIE, vol. 4870, pp. 248–258, 2002. [ bib | .pdf ]
We demonstrate how dramatic increases in the induced phase shifts caused by small changes in the index of refraction can be achieved by using very slow group velocities of light, which are readily achievable in photonic crystal systems. Combined with the fact that small group velocity greatly decreases the power requirements needed to operate a device, enhanced phase sensitivity may be used to decrease the size and power requirements of many devices, including switches, routers, all-optical logical gates, wavelength converters, etc. We demonstrate how these advantages can be used to design switches smaller than 20*200 square microns in size, using readily available materials, and at modest levels of power. With this approach, one could have ∼105 such devices on a surface 2*2 square cm, making it an important step towards large-scale all-optical integration.

[226]
E. K. Chow, S.-Y. Lin, S. G. Johnson, and J. D. Joannopoulos, “Transmission measurement of quality factor in two-dimensional photonic-crystal microcavity,” Proc. SPIE, vol. 4646, pp. 199–204, 2002. [ bib | .pdf ]
A new micro-cavity design is proposed and structures are realized using a 2D photonic-crystal slab. The cavity consists of seven defect holes that encompass a hexagon and is designed to reduce vertical light leakage. From a direct transmission measurement, a Q-value of 816 ±30 is achieved at λ=1.55μm. This high-Q cavity will enable realistic realization of spontaneous emission modification and on-off optical switches.

[227]
S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and H. A. Haus, “Loss-induced on/off switching in a channel add/drop filter,” Physical Review B, vol. 64, pp. 245302–245308, December 2001. [ bib | http ]
We introduce a mechanism that provides an on/off switching capability in channel add-drop filter structures. These filters consist of two waveguides, a bus and a drop, coupled through a frequency-selective element. The switching functionality is achieved by incorporating materials with variable absorbing characteristics into the coupling element. When the variable material displays minimum absorption, the frequency channel of interest is transferred completely from the bus waveguide to the drop waveguide. When the variable material displays maximum absorption, the frequency channel is not transferred and remains essentially undisturbed in the bus waveguide. We also discuss the practical feasibility of realizing this approach using either electrical or mechanical means.

[228]
J. D. Joannopoulos, “Photonics: Self-assembly lights up,” Nature, vol. 414, pp. 257–258, November 2001. [ bib | DOI ]
Opals do it, even biomolecules do it, so why can't self-assembly be harnessed to create photonic crystals with near-perfect order? A new technique shows that absolute order may not require absolute control.

[229]
B. Temelkuran, E. L. Thomas, J. D. Joannopoulos, and Y. Fink, “Low-loss infrared dielectric material system for broadband dual-range omnidirectional reflectivity,” Optics Letters, vol. 26, pp. 1370–1372, September 2001. [ bib | http ]
A material system for broadband thermal IR applications based on branched polyethylene and tellurium is introduced. This system exhibits low absorption losses from 3.5 to 35 μm , has a large index contrast, and is readily deposited as a thin film. These unique features were used to investigate the formation of an omnidirectional reflector that exhibits two distinct, broadband omnidirectional ranges at thermal wavelengths. Reflectivity measurements are presented that confirm the existence of two omnidirectional ranges in the solar atmospheric windows extending from 8 to 12 μm and from 4.5 to 5.5 μm . The measurements are in good agreement with simulations.

[230]
J. D. Joannopoulos, S. Fan, A. Mekis, and S. G. Johnson, “Novelties of light with photonic crystals,” in Photonic Crystals and Light Localization in the 21st Century (C. M. Soukoulis, ed.), vol. 563 of NATO Science Series C: Mathematical and Physical Sciences, pp. 1–24, Dordrecht, Netherlands: Kluwer, May 2001. [ bib | http ]
[231]
A. Mekins and J. D. Joannopoulos, “Tapered couplers for efficient interfacing between dielectric and photonic crystal waveguides,” Journal of Lightwave Technology, vol. 19, no. 9, pp. 861–865, 2001. [ bib | DOI | http ]
We design tapered waveguide junctions for coupling between photonic crystal and traditional dielectric waveguides and evaluate their transmission efficiency. While the transmission efficiency is less than 60% using no taper,the tapered couplers have over 90% power transmission. We show that different types of couplers are needed for efficient coupling into and out of photonic crystal waveguides.

[232]
A. A. Erchak, D. J. Ripin, S. Fan, P. Rakich, J. D. Joannopoulos, E. P. Ippen, G. S. Petrich, and L. A. Kolodziejski, “Enhanced coupling to vertical radiation using a two-dimensional photonic crystal in a semiconductor light-emitting diode,” Applied Physics Letters, vol. 78, pp. 563–565, January 2001. [ bib | http ]
Enhanced coupling to vertical radiation is obtained from a light-emitting diode using a two-dimensional photonic crystal that lies entirely inside the upper cladding layer of an asymmetric quantum well structure. A sixfold enhancement in light extraction in the vertical direction is obtained without the photonic crystal penetrating the active material. The photonic crystal is also used to couple pump light at normal incidence into the structure, providing strong optical excitation.

[233]
S. G. Johnson and J. D. Joannopoulos, “Block-iterative frequency-domain methods for Maxwell's equations in a planewave basis,” Optics Express, vol. 8, pp. 173–190, 2001. [ bib | http | .pdf ]
We describe a fully-vectorial, three-dimensional algorithm to compute the definite-frequency eigenstates of Maxwell's equations in arbitrary periodic dielectric structures, including systems with anisotropy (birefringence) or magnetic materials, using preconditioned block-iterative eigensolvers in a planewave basis. Favorable scaling with the system size and the number of computed bands is exhibited. We propose a new effective dielectric tensor for anisotropic structures, and demonstrate that Ox2) convergence can be achieved even in systems with sharp material discontinuities. We show how it is possible to solve for interior eigenvalues, such as localized defect modes, without computing the many underlying eigenstates. Preconditioned conjugate-gradient Rayleigh-quotient minimization is compared with the Davidson method for eigensolution, and a number of iteration variants and preconditioners are characterized. Our implementation is freely available on the Web.

[234]
S. G. Johnson, M. Ibanescu, M. Skorobogatiy, O. Weisberg, T. D. Engeness, M. Soljačić, S. A. Jacobs, J. D. Joannopoulos, and Y. Fink, “Low-loss asymptotically single-mode propagation in large-core OmniGuide fibers,” Optics Express, vol. 9, pp. 748–779, 2001. [ bib | http | .pdf ]
We present the light-propagation characteristics of OmniGuide fibers, which guide light by concentric multi-layer dielectric mirrors having the property of omnidirectional reflection. We show how the lowest-loss TE01 mode can propagate in a single-mode fashion through even large-core fibers, with other modes eliminated asymptotically by their higher losses and poor coupling, analogous to hollow metallic microwave waveguides. Dispersion, radiation leakage, material absorption, nonlinearities, bending, acircularity, and interface roughness are considered with the help of leaky modes and perturbation theory, and both numerical results and general scaling relations are presented. We show that cladding properties such as absorption and nonlinearity are suppressed by many orders of magnitude due to the strong confinement in a hollow core, and other imperfections are tolerable, promising that the properties of silica fibers may be surpassed even when nominally poor materials are employed.

[235]
E. Chow, S. Y. Lin, J. R. Wendt, S. G. Johnson, and J. D. Joannopoulos, “Quantitative analysis of bending efficiency in photonic-crystal waveguide bends at λ= 1.55μm wavelengths,” Optics Letters, vol. 26, pp. 286–288, 2001. [ bib | .pdf ]
Based on a photonic-crystal slab structure, a 60 photonic-crystal waveguide bend is successfully fabricated. Its bending efficiency within the photonic bandgap is measured, and near 100% efficiency is observed at certain frequencies near the valence band edge. The bending radius is ∼1μm at a wavelength of λ∼1.55μm. The measured η spectrum also agrees well with a finite-difference time-domain simulation.

[236]
S. Y. Lin, E. Chow, S. G. Johnson, and J. D. Joannopoulos, “Direct measurement of the quality factor in a two-dimensional photonic-crystal microcavity,” Optics Letters, vol. 26, pp. 1903–1905, 2001. [ bib | .pdf ]
A new microcavity design is proposed and structures are realized with a two-dimensional photonic-crystal slab. The cavity consists of seven defect holes that encompass a hexagon and is designed to reduce vertical light leakage. From a direct transmission measurement, a Q value of 816 ±30 is achieved at λ= 1.55μm. This high-Q cavity will permit the realistic realization of spontaneous-emission modification and on–off optical switches.

[237]
S. G. Johnson, S. Fan, A. Mekis, and J. D. Joannopoulos, “Multipole-cancellation mechanism for high-Q cavities in the absence of a complete photonic band gap,” Applied Physics Letters, vol. 78, pp. 3388–3390, 2001. Invited paper. [ bib | .pdf ]
We describe and demonstrate a new mechanism for low radiation losses in structures lacking a complete band gap, and show how resonant cavities with Q>103 can be achieved without sacrificing strong localization in 3d. This involves a forced cancellation in the lowest-order term(s) of the multipole far-field radiation expansion. We focus on the system of photonic-crystal slabs, one- to two-dimensionally periodic dielectric structures of finite height with vertical index guiding. Simulations and analytical results in 2d and 3d are presented.

[238]
S. G. Johnson, A. Mekis, S. Fan, and J. D. Joannopoulos, “Molding the flow of light,” Computing in Science and Engineering, vol. 3, no. 6, pp. 38–47, 2001. Invited paper. [ bib | .pdf ]
A new class of materials, called photonic crystals, affects a photon's properties in much the same way that a semiconductor affects an electron's properties. The ability to mold and guide light leads naturally to novel applications in several fields, including optoelectronics and telecommunications. The authors present an introductory survey of the basic concepts and ideas, including results for never before possible photon phenomena.

[239]
S. Fan, S. G. Johnson, J. D. Joannopoulos, C. Manolatou, and H. A. Haus, “Waveguide branches in photonic crystals,” Journal of the Optical Society of America B, vol. 18, pp. 162–165, 2001. [ bib | .pdf ]
Theoretical and numerical analyses of waveguide branches in a photonic crystal are presented. Conditions for perfect transmission and zero reflection are discussed. Based upon these conditions, numerical simulations of electromagnetic-wave propagation in photonic crystals are performed to identify structures with near-complete transmission.

[240]
M. L. Povinelli, S. G. Johnson, S. Fan, and J. D. Joannopoulos, “Emulation of two-dimensional photonic crystal defect modes in a photonic crystal with a three-dimensional photonic band gap,” Physical Review B, vol. 64, p. 075313, 2001. [ bib | .pdf ]
Using numerical simulations, we demonstrate the construction of two-dimensional- (2D-) like defect modes in a recently proposed 3D photonic crystal structure. These modes, which are confined in all three dimensions by a complete photonic band gap, bear a striking similarity to those in 2D photonic crystals in terms of polarization, field profile, and projected band structures. It is expected that these results will greatly facilitate the observation of widely studied 2D photonic-crystal phenomena in a realistic, 3D physical system.

[241]
S. G. Johnson, M. L. Povinelli, and J. D. Joannopoulos, “New photonic crystal system for integrated optics,” Proc. SPIE, vol. 4532, pp. 167–179, 2001. Invited paper. [ bib | .pdf ]
We describe a new photonic-crystal structure with a complete three-dimensional photonic band gap (PBG) and its potential application to integrated optics. The structure not only has a large band gap and is amenable to layer-by-layer litho-fabrication, but also introduces the feature of high-symmetry planar layers resembling two-dimensional photonic crystals. This feature enables integrated optical devices to be constructed by modification of only a single layer, and supports waveguide and resonant-cavity modes that strongly resemble the corresponding modes in the simpler and well-understood 2d systems. In contrast to previous attempts to realize 2d crystals in 3d via finite-height “slabs,” however, the complete PBG of the new system eliminates the possibility of radiation losses. Thus, it provides a robust infrastructure within which to embed complex optical networks, combining elements such as compact filters, channel-drops, and waveguide bends/junctions that have previously been proposed in 2d photonic crystals.

[242]
E. K. Chow, S.-Y. Lin, S. G. Johnson, J. D. Joannopoulos, J. A. Bur, and P. R. Villeneuve, “Demonstration of high waveguide bending efficiency (>90%) in a photonic-crystal slab at 1.5-μm wavelengths,” Proc. SPIE, vol. 4283, pp. 453–461, 2001. [ bib | .pdf ]
Using a two-dimensional (2D) photonic-crystal slab structure, we have demonstrated a strong 2D photonic band gap with the capability of fully controlling light in all three dimensions. Our demonstration confirms the predictions on the possibility of achieving 3D light control using 2D band gaps, with strong index guiding providing control in the third dimension, and raise the prospect of being able to realize novel photonic-crystal devices. Based on such slab structure with triangular lattice of holes, a 60-degree photonic-crystal waveguide bend is fabricated. The intrinsic bending efficiency (η) is measured within the photonic band gap. As high as 90% bending efficency is observed at some frequencies.

[243]
S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “Rate-equation analysis of output efficiency and modulation rate of photonic-crystal light-emitting diodes,” IEEE Journal of Quantum Electronics, vol. 36, pp. 1123–1130, October 2000. [ bib | DOI ]
The performance characteristics of photonic-crystal light-emitting diodes (LEDs) are analyzed, taking into account the effects of both nonradiative recombination and photon reabsorption processes using multimode rate equations. It is shown that, in the presence of strong photon reabsorption, the optimum output efficiency and modulation rates are achieved when the width of the photon density-of-state distribution function is comparable to the width of the spontaneous emission lineshape of the active material. On the other hand, when photon reabsorption is weak, it becomes beneficial to construct high-Q cavities. Based on this analysis, the characteristics of different photonic crystal LED configurations are discussed.

[244]
A. Mekis, A. Dodabalapur, R. E. Slusher, and J. D. Joannopoulos, “Two-dimensional photonic crystal couplers for unidirectional light output,” Optics Letters, vol. 25, pp. 942–944, July 2000. [ bib | http ]
We investigate the use of two-dimensional photonic crystal slabs to improve the directionality of output coupling from planar waveguides and distributed-feedback lasers. We present the theory underlying the operation of such structures and design criteria for emission in desired directions. As an example, we demonstrate a vertical coupler that is integrated with an organic distributed-feedback laser, use computer simulations to find its coupling constant and efficiency, and then discuss its feasibility.

[245]
M. Ibanescu, Y. Fink, S. Fan, E. L. Thomas, and J. D. Joannopoulos, “An all-dielectric coaxial waveguide,” Science, vol. 289, pp. 415–419, July 2000. [ bib | DOI ]
An all-dielectric coaxial waveguide that can overcome problems of polarization rotation and pulse broadening in the transmission of optical light is presented here. It consists of a coaxial waveguiding region with a low index of refraction, bounded by two cylindrical, dielectric, multilayer, omnidirectional reflecting mirrors. The waveguide can be designed to support a single mode whose properties are very similar to the unique transverse electromagnetic mode of a traditional metallic coaxial cable. The new mode has radial symmetry and a point of zero dispersion. Moreover, because the light is not confined by total internal reflection, the waveguide can guide light around very sharp corners.

[246]
M. Skorobogatiy and J. D. Joannopoulos, “Photon modes in photonic crystals undergoing rigid vibrations and rotations,” Physical Review B, vol. 61, pp. 15554–15557, June 2000. Erratum: ibid., vol. 62, pp. 13230–13231 (2000). [ bib | http ]
We explore the nature of photon modes associated with photonic crystals undergoing rigid time-dependent spatial displacements in a noninertial frame of reference and prove that under certain conditions these modes retain many of the spatial symmetries allowed in a static photonic crystal. Moreover, it is proved quite generally that such noninertial modes possess a temporal Bloch-like symmetry. Conserved “quantum numbers” are identified and a convenient scheme for labeling noninertial modes is presented.

[247]
M. Skorobogatiy and J. D. Joannopoulos, “Rigid vibrations of a photonic crystal and induced interband transitions,” Physical Review B, vol. 61, pp. 5293–5302, February 2000. [ bib | http ]
We investigate the behavior of electromagnetic states associated with photonic crystals, which are undergoing rigid time-dependent translations in position space. It is shown, quite generally, that the Bloch wave vector q remains a conserved quantity and that an analogue of Bloch's theorem for a time-dependent solution of the states can be formulated. Special attention is focussed on time-dependent translations involving harmonic rigid vibrations of the photonic crystal. Under these conditions it is shown how, and to what extent, inter-band transitions can be induced between the various bands in a photonic crystal in a microwave regime. In particular, a characteristic resonance transition time can be derived, which scales inversely with the amplitude of vibration and interband frequency. Finally, it is argued that given all parameters other than Bloch wave vector fixed, an interband transition time is minimized if the transition is made at a Bragg plane.

[248]
D. J. Ripin, K.-Y. Lim, G. S. Petrich, P. R. Villeneuve, S. Fan, E. R. Thoen, J. D. Joannopoulos, E. P. Ippen, and L. A. Kolodziejski, “Photonic band gap airbridge microcavity resonances in GaAs/AlxOy waveguides,” Journal of Applied Physics, vol. 87, pp. 1578–1580, February 2000. [ bib | http ]
Photonic band gap waveguide microcavities were designed, fabricated, and measured in a high-dielectric-contrast GaAs/AlxOy III–V compound semiconductor structure. The photonic crystal is defined by a regularly spaced one-dimensional array of holes in the waveguide. By controlling the spacing between the two central holes, the microcavity is formed. The waveguide microcavity is suspended in the airbridge geometry to further increase optical confinement. Resonance states with cavity quality factors as high as 360 were measured at wavelengths near 1.55 μm, with modal volumes as small as 0.026 μm3.

[249]
S. Y. Lin, E. Chow, S. G. Johnson, and J. D. Joannopoulos, “Demonstration of highly efficient waveguiding in a photonic crystal slab at the 1.5-μm wavelength,” Optics Letters, vol. 25, pp. 1297–1299, 2000. [ bib | .pdf ]
Highly efficient transmission of 1.5-μm light in a two-dimensional (2D) photonic crystal slab waveguide is experimentally demonstrated. Light waves are shown to be guided along a triple-line defect formed within a 2D crystal and vertically by a strong index-guiding mechanism. At certain wavelength ranges, complete transmission is observed, suggesting lossless guiding along this photonic one-dimensional conduction channel.

[250]
S. G. Johnson, P. R. Villeneuve, S. Fan, and J. D. Joannopoulos, “Linear waveguides in photonic-crystal slabs,” Physical Review B, vol. 62, pp. 8212–8222, 2000. [ bib | .pdf ]
Linear waveguides in photonic-crystal slabs, two-dimensionally periodic dielectric structures of finite height, are fundamentally different from waveguides in two-dimensional photonic crystals. The most important distinctions arise from the fact that photonic-crystal slab waveguides must be index-confined in the vertical direction (while a band gap confines them horizontally). We present a systematic analysis of different families of waveguides in photonic-crystal slabs, and illustrate the considerations that must be applied to achieve single-mode guided bands in these systems. In this way, the unusual features of photonic-crystal waveguides can be realized in three dimensions without the fabrication complexity required by photonic crystals with complete three-dimensional band gaps.

[251]
E. Chow, S. Y. Lin, S. G. Johnson, P. R. Villeneuve, J. D. Joannopoulos, J. R. Wendt, G. A. Vawter, W. Zubrzycki, H. Hou, and A. Alleman, “Three-dimensional control of light in a two-dimensional photonic crystal slab,” Nature, vol. 497, pp. 983–986, 2000. [ bib | .pdf ]
Optoelectronic devices are increasingly important in communication and information technology. To achieve the necessary manipulation of light (which carries information in optoelectronic devices), considerable efforts are directed at the development of crystals photonicperiodic dielectric materials that have so-called photonic bandgaps, which prohibit the propagation of photons having energies within the bandgap region. Straightforward application of the bandgap concept is generally thought to require three-dimensional (3D) photonic crystals; their two-dimensional (2D) counterparts confine light in the crystal plane, but not in the perpendicular z direction, which inevitably leads to diffraction losses. Nonetheless, 2D photonic crystals still attract interest because they are potentially more amenable to fabrication by existing techniques and diffraction losses need not seriously impair utility. Here we report the fabrication of a waveguide-coupled photonic crystal slab (essentially a free-standing 2D photonic crystal) with a strong 2D bandgap at wavelengths of about 1.5 μm, yet which is capable of fully controlling light in all three dimensions. These features confirm theoretical calculations on the possibility of achieving 3D light control using 2D bandgaps, with index guiding providing control in the third dimension, and raise the prospect of being able to realize unusual photonic-crystal devices, such as thresholdless lasers.

[252]
S. G. Johnson and J. D. Joannopoulos, “Three-dimensionally periodic dielectric layered structure with omnidirectional photonic band gap,” Applied Physics Letters, vol. 77, pp. 3490–3492, 2000. [ bib | .pdf ]
A three-dimensionally periodic dielectric structure with a large complete photonic band gap (PBG) is presented. The structure is distinguished by a sequence of planar layers, identical except for a horizontal offset, and repeating every three layers to form an fcc lattice. The layers can be thought of as an alternating stack of the two basic two-dimensional (2D) PBG slab geometries: rods in air and air cylinders in dielectric. These high-symmetry planar cross-sections should simplify the integration of optical devices and components by allowing modification of only a single layer, using simple defects of the same form as in the corresponding 2D systems. A process for fabricating the structure with conventional planar microfabrication technology is described. Gaps of over 21% are obtained for Si/air substrates. Reasonable gaps, over 8%, can be achieved even for the moderate index ratio of 2.45 (Si/SiO2).

[253]
A. Mekis, S. Fan, and J. D. Joannopoulos, “Absorbing boundary conditions for FDTD simulations of photonic crystal waveguides,” IEEE Microwave and Guided Wave Letters, vol. 9, pp. 502–504, December 1999. [ bib | DOI ]
We present a novel numerical scheme for the reduction of spurious reflections in simulations of electromagnetic wave propagation in photonic crystal waveguides. We use a distributed Bragg reflector waveguide termination to reduce reflection from photonic crystal waveguide ends by improving k-matching for photonic crystal waveguided modes. We describe computational procedures and show that a significant reduction in reflection amplitude can be achieved across a large part of the guided mode spectrum. This method enables one to reduce simply and effectively the computational requirements in photonic crystal waveguide simulations.

[254]
Y. Fink, D. J. Ripin, S. Fan, C. Chen, J. D. Joannopoulos, and E. L. Thomas, “Guiding optical light in air using an all dielectric structure,” Journal of Lightwave Technology, vol. 17, pp. 2039–2041, November 1999. [ bib | http ]
The emergence of a dielectric omnidirectional multilayer structure [1]-[4] opens new opportunities for low loss broad-band guiding of light in air. We demonstrate the effectiveness of such an approach by fabricating a broad-band, low-loss hollow waveguide in the 10-μm region and measuring its transmission around a 90o bend. The generality of the solution enables the application of the method to many wavelengths of interest important in telecommunication applications as well as for guiding high-power lasers in medical and other fields of use.

[255]
D. J. Ripin, K.-Y. Lim, G. S. Petrich, P. R. Villeneuve, S. Fan, E. R. Thoen, J. D. Joannopoulos, E. P. Ippen, and L. A. Kolodziejski, “One-dimensional photonic bandgap microcavities for strong optical confinement in GaAs and GaAs/AlxOy semiconductor waveguides,” Journal of Lightwave Technology, vol. 17, pp. 2152–2160, November 1999. [ bib | http ]
Photonic bandgap (PBG) waveguide microcavities with tightly confined resonant optical modes have been designed, fabricated using high-dielectric-contrast GaAs/AlxOy III–V compound semiconductor structures, and characterized optically. The photonic crystal lattices are defined by one-dimensional (1-D) arrays of holes in waveguides, and a controlled defect in the spacing between two holes of an array defines a microcavity. Waveguide microcavity resonances have been studied in both monorail and suspended air-bridge geometries. Resonance states with cavity Q's as high as 360 were measured at wavelengths near 1.55 μm, with modal volumes as small as 0.026 μm3, which corresponds to only two times (λ/2n)3.

[256]
S. Fan, I. Appelbaum, and J. D. Joannopoulos, “Near-field scanning optical microscopy as a simultaneous probe of fields and band structure of photonic crystals: A computational study,” Applied Physics Letters, vol. 75, pp. 3461–3463, November 1999. [ bib | http ]
We demonstrate the feasibility of employing near-field scanning optical microscopy (NSOM) imaging to simultaneously obtain both the eigenfield distribution and the band-structure information of a photonic crystal. We introduce the NSOM measurement configuration required and simulate the imaging process, with both the tip and the sample included, using three-dimensional finite-difference time-domain calculations. Both the field-pattern and the frequency–wave-vector relations of photonic crystal eigenmodes are revealed by analyzing simulated images.

[257]
M. J. Khan, C. Manolatou, S. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, “Mode-coupling analysis of multipole symmetric resonant add/drop filters,” IEEE Journal of Quantum Electronics, vol. 35, pp. 1451–1460, October 1999. [ bib | DOI ]
Time-dependent mode-coupling theory is used to analyze a type of resonant add/drop filter based on the excitation of degenerate symmetric and antisymmetric modes. Flat-top transfer functions are achieved with higher order filters that utilize multiple resonator pairs, designed to satisfy the degeneracy conditions. The resulting analytic expressions lead to an equivalent circuit and the transfer characteristics of the filter are related to standard L-C circuit designs.

[258]
C. Manolatou, M. J. Khan, S. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, “Coupling of modes analysis of resonant channel add-drop filters,” IEEE Journal of Quantum Electronics, vol. 35, pp. 1322–1331, September 1999. [ bib | DOI ]
The operation principle of resonant channel add-drop filters based on degenerate symmetric and antisymmetric standing-wave modes has been described elsewhere using group theoretical arguments. In this paper, the analysis is carried out using coupling of modes in time. A possible implementation of such a filter is a four-port system utilizing a pair of identical single-mode standing wave resonators. The analysis allows a simple derivation of the constraints imposed on the design parameters in order to establish degeneracy. Numerical simulations of wave propagation through such a filter are also shown, as idealized by a two-dimensional geometry.

[259]
A. Mekis, M. Meier, A. Dodabalapur, R. E. Slusher, and J. D. Joannopoulos, “Lasing mechanism in two-dimensional photonic crystal lasers,” Applied Physics A, vol. 69, pp. 111–114, July 1999. [ bib | DOI ]
We conduct a comprehensive investigation of the lasing mechanism in a photonic crystal slab laser with a refractive index that is periodic in two dimensions. Experimental spectra of laser structures fabricated with organic gain media are presented. It is found that lasing frequencies can be explained in terms of Van Hove singularities in the density of modes. We also observe lasing spectra that cannot be obtained from structures with one-dimensional periodicity, such as traditional distributed feedback lasers. Lasing frequencies are computed using numerical techniques.

[260]
S. Fan, P. R. Villeneuve, J. D. Joannopoulos, M. J. Khan, C. Manolatou, and H. A. Haus, “Theoretical analysis of channel drop tunneling processes,” Physical Review B, vol. 59, pp. 15882–15892, June 1999. [ bib | http ]
We investigate general channel drop tunneling processes using both analytic theory and first-principles simulations. These tunneling processes occur when two one-dimensional continuums are brought into close proximity with a resonator system that supports localized states. Propagating states can be transferred between the continuums through the resonator system. We show that the transport properties are intricately related to the symmetries of the resonant states. Complete transfer can be achieved by manipulating the symmetries of the system, and by forcing an accidental degeneracy between states with different symmetries. In addition, the line shape of the transfer spectrum can be engineered by varying the number of localized states in the resonator system. The theoretical analysis is confirmed by first-principles simulations of transport properties in a two-dimensional photonic crystal.

[261]
K.-Y. Lim, D. J. Ripin, G. S. Petrich, L. A. Kolodziejski, E. P. Ippen, M. Mondol, H. I. Smith, P. R. Villeneuve, S. Fan, and J. D. Joannopoulos, “Photonic band-gap waveguide microcavities: Monorails and air bridges,” Journal of Vacuum Science and Technology B, vol. 17, pp. 1171–1174, February 1999. [ bib | DOI ]
Photonic band-gap monorail and air-bridge waveguide microcavities, operating at the wavelength regime of 1550 nm, are fabricated using GaAs-based compound semiconductors. The fabrication process involves gas-source molecular beam epitaxy, electron-beam lithography, reactive ion etching, and thermal wet oxidation of Al0.93Ga0.07As. The fabrication of the air-bridge microcavity, in particular, also entails the sacrificial wet etch of AlxOy to suspend the micromechanical structure. The monorail and air-bridge microcavities have been optically characterized and the transmission spectra exhibit resonances in the 1550 nm wavelength regime. Tunability of the resonant wavelength is demonstrated through changing the defect size in the one-dimensional photonic crystal. The quality factors (Q) of the microcavities are about 140 for the monorail and 230 for the air bridge, respectively.

[262]
J. N. Winn, S. Fan, J. D. Joannopoulos, and E. P. Ippen, “Interband transitions in photonic crystals,” Physical Review B, vol. 59, pp. 1551–1554, January 1999. [ bib | http ]
We present a formalism to describe transitions between photon modes in a photonic crystal with a temporally and spatially varying dielectric constant, in analogy to optical transitions between electronic states in metals and semiconductors. Resonant transitions between different photonic bands are discussed, and predictions of the theory are compared to electromagnetic simulations. We contrast the cases of electronic and photonic transitions, and explore how the photonic band structure allows opportunities for phase matching and stationary-wave generation in nonlinear optical frequency-conversion processes.

[263]
Y. Fink, A. M. Urbas, M. G. Bawendi, J. D. Joannopoulos, and E. L. Thomas, “Block copolymers as photonic bandgap materials,” Journal of Lightwave Technology, vol. 17, no. 11, pp. 1963–1969, 1999. [ bib | DOI | http ]
Block copolymers self-assemble into one-, two-, and three-dimensional periodic equilibrium structures, which can exhibit photonic bandgaps. This paper outlines a methodology for producing photonic crystals at optical length scales from block copolymers. Techniques for enhancing the intrinsic dielectric contrast between the block copolymer domains, as well as increasing the characteristic microdomain distances, and controlling defects are presented. To demonstrate the applicability of this methodology, a self-assembled one-dimensional periodic structure has been fabricated that reflects visible light. The wealth of structures into which block copolymers can assemble and the multiple degrees of freedom that can be built into these materials on the molecular level offer a large parameter space for tailoring new types of photonic crystals at optical length scales.

[264]
C. Manolatou, S. G. Johnson, S. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, “High-density integrated optics,” Journal of Lightwave Technology, vol. 17, no. 9, pp. 1682–1692, 1999. [ bib | .pdf ]
This paper presents two-dimensional (2-D) finite difference time domain (FDTD) simulations of low-loss rightangle waveguide bends, T-junctions and crossings, based on high index-contrast waveguides. Such structures are essential for the dense integration of optical components. Excellent performance characteristics are obtained by designing the waveguide intersection regions as low-Q resonant cavities with certain symmetries and small radiation loss. A simple analysis, based on coupled mode theory in time, is used to explain the operation principles and agrees qualitatively with the numerical results.

[265]
S. G. Johnson, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and L. A. Kolodziejski, “Guided modes in photonic crystal slabs,” Physical Review B, vol. 60, pp. 5751–5758, 1999. [ bib | .pdf ]
We analyze the properties of two-dimensionally periodic dielectric structures that have a band gap for propagation in a plane and that use index guiding to confine light in the third dimension. Such structures are more amenable to fabrication than photonic crystals with full three-dimensional band gaps, but retain or approximate many of the latter's desirable properties. We show how traditional band-structure analysis can be adapted to slab systems in the context of several representative structures, and describe the unique features that arise in this framework compared to ordinary photonic crystals.

[266]
Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, “A dielectric omnidirectional reflector,” Science, vol. 282, pp. 1679–1682, November 1998. [ bib | DOI ]
A design criterion that permits truly omnidirectional reflectivity for all polarizations of incident light over a wide selectable range of frequencies was used in fabricating an all-dielectric omnidirectional reflector consisting of multilayer films. The reflector was simply constructed as a stack of nine alternating micrometer-thick layers of polystyrene and tellurium and demonstrates omnidirectional reflection over the wavelength range from 10 to 15 micrometers. Because the omnidirectionality criterion is general, it can be used to design omnidirectional reflectors in many frequency ranges of interest. Potential uses depend on the geometry of the system. For example, coating of an enclosure will result in an optical cavity. A hollow tube will produce a low-loss, broadband waveguide, whereas a planar film could be used as an efficient radiative heat barrier or collector in thermoelectric devices.

[267]
J. N. Winn, Y. Fink, S. Fan, and J. D. Joannopoulos, “Omnidirectional reflection from a one-dimensional photonic crystal,” Optics Letters, vol. 23, pp. 1573–1575, October 1998. [ bib | http ]
We demonstrate that one-dimensional photonic crystal structures (such as multilayer films) can exhibit complete reflection of radiation in a given frequency range for all incident angles and polarizations. We derive a general criterion for this behavior that does not require materials with very large indices. We perform numerical studies that illustrate this effect.

[268]
S.-Y. Lin, E. Chow, V. Hietala, P. R. Villeneuve, and J. D. Joannopoulos, “Experimental demonstration of guiding and bending of electromagnetic waves in a photonic crystal,” Science, vol. 282, pp. 274–276, October 1998. [ bib | DOI ]
The routing and interconnection of optical signals through narrow channels and around sharp corners are important for large-scale all-optical circuit applications. A recent computational result suggests that photonic crystals may offer a novel way of achieving this goal by providing a mechanism for guiding light that is fundamentally different from traditional index guiding. Waveguiding in a photonic crystal and near 100 percent transmission of electromagnetic waves around sharp 90 degree corners were observed experimentally. Bending radii were made smaller than one wavelength.

[269]
A. Mekis, S. Fan, , and J. D. Joannopoulos, “Bound states in photonic crystal waveguides and waveguide bends,” Physical Review B, vol. 58, pp. 4809–4817, August 1998. [ bib | http ]
We investigate the mechanism for the appearance of bound states in two-dimensional photonic crystal waveguides and contrast it with the corresponding mechanism for conventional guides. It is shown that the periodicity of the photonic crystal can give rise to frequency ranges above cutoff where no guided modes exist in the waveguides. Such mode gaps make possible the creation of bound states in constrictions and in bends. Bound states are found to correspond to analogous cavity modes and it is shown that their appearance strongly depends on the lattice geometry and cannot be described in a one-dimensional framework.

[270]
D. F. Sievenpiper, E. Yablonovitch, J. N. Winn, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “3d metallo-dielectric photonic crystals with strong capacitive coupling between metallic islands,” Physical Review Letters, vol. 80, pp. 2829–2832, March 1998. [ bib | http ]
We introduce a new type of metallo-dielectric photonic band gap structure (PBG), intentionally incorporating very strong capacitive interactions between the periodic metallic islands. The band gaps become huge, with the lower band edge frequency being pushed down by the capacitive interaction between metallic islands, while the upper band edge frequency continues to depend primarily on the lattice constant, as in normal PBG's. With this new type of photonic crystal, the spatial periodicity can be much smaller than the corresponding electromagnetic wavelength, allowing PBG structures to play a role at radio frequencies.

[271]
S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and H. A. Haus, “Channel drop tunneling through localized states,” Physical Review Letters, vol. 80, pp. 960–963, February 1998. [ bib | http ]
We present a general analysis of the tunneling process through localized resonant states between one-dimensional continuums. We show that complete transfer can occur between the continuums by creating resonant states of different symmetry, and by forcing an accidental degeneracy between them. The degeneracy must exist in both the real and imaginary parts of the frequency. We illustrate the results of the analysis by performing computational simulations on the transport properties of electromagnetic waves in a two-dimensional photonic crystal.

[272]
P. R. Villeneuve, S. Fan, S. G. Johnson, and J. D. Joannopoulos, “Three-dimensional photon confinement in photonic crystals of low-dimensional periodicity,” IEE Proceedings: Optoelectronics, vol. 145, no. 6, pp. 384–390, 1998. [ bib | .pdf ]
Photonic crystals of one- or two-dimensional periodicity can be used to achieve three-dimensional photon confinement in dielectric waveguides with modal volumes of the order of a cubic half-wavelength. Since photonic crystals of low-dimensional periodicity do not have full three-dimensional bandgaps, the microcavities undergo increasing radiation losses with decreasing modal volumes. High-Q resonant modes can be generated by reducing the strength of the photon confinement. Increasingly, larger modal volumes lead to lower radiation losses and more efficient coupling to waveguide modes outside the cavity.

[273]
S. G. Johnson, C. Manolatou, S. Fan, P. Villeneuve, J. D. Joannopoulos, and H. A. Haus, “Elimination of cross talk in waveguide intersections,” Optics Letters, vol. 23, no. 23, pp. 1855–1857, 1998. [ bib | .pdf ]
We present general criteria for crossing perpendicular waveguides with nearly 100% throughput and 0% cross talk. Our design applies even when the waveguide width is of the order of the wavelength. The theoretical basis for this phenomenon is explained in terms of symmetry considerations and resonant tunneling and is then illustrated with numerical simulations for both a two-dimensional photonic crystal and a conventional high-index-contrast waveguide crossing. Cross-talk reduction by up to 8 orders of magnitude is achieved relative to unmodified crossings.

[274]
J. S. Foresi, P. R. Villeneuve, J. Ferrera, E. R. Thoen, G. Steinmeyer, S. Fan, J. D. Joannopoulos, L. C. Kimerling, H. I. Smith, and E. P. Ippen, “Photonic-bandgap microcavities in optical waveguides,” Nature, vol. 390, pp. 143–145, November 1997. [ bib | DOI ]
Confinement of light to small volumes has important implications for optical emission properties: it changes the probability of spontaneous emission from atoms, allowing both enhancement and inhibition. In photonic-bandgap (PBG) materials (also known as photonic crystals), light can be confined within a volume of the order of (λ/2n)3, where λ is the emission wavelength and n the refractive index of the material, by scattering from a periodic array of scattering centres. Until recently, the properties of two- and three-dimensional PBG structures have been measured only at microwave frequencies. Because the optical bandgap scales with the period of the scattering centres, feature sizes of around 100 nm are needed for manipulation of light at the infrared wavelength (1.54 μm) used for optical communications. Fabricating features this small requires the use of electron-beam or X-ray lithography. Here we report measurements of microcavity resonances in PBG structures integrated directly into a sub-micrometre-scale silicon waveguide. The microcavity has a resonance at a wavelength of 1.56 μm, a quality factor of 265 and a modal volume of 0.055 μm3. This level of integration might lead to new photonic chip architectures and devices, such as zero-threshold microlasers, filters and signal routers.

[275]
S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and E. F. Schubert, “High extraction efficiency of spontaneous emission from slabs of photonic crystals,” Physical Review Letters, vol. 78, pp. 3294–3297, April 1997. [ bib | http ]
A thin slab of two-dimensional photonic crystal is shown to alter drastically the radiation pattern of spontaneous emission. More specifically, by eliminating all guided modes at the transition frequencies, spontaneous emission can be coupled entirely to free space modes, resulting in a greatly enhanced extraction efficiency. Such structures might provide a solution to the long-standing problem of poor light extraction from high refractive-index semiconductors in light-emitting diodes.

[276]
J. D. Joannopoulos, P. R. Villeneuve, and S. Fan, “Photonic crystals,” Solid State Communications, vol. 102, pp. 165–173, April 1997. [ bib | DOI ]
A new class of composite materials has emerged which provides a means to control and manipulate light. These materials, known as photonic crystals, are periodic arrays of dielectric scatteres in homogeneous dielectric matrices. They affect the properties of photons in much the same way a semiconductor affects the properties of an electron. Consequently, photons can have band structures, localized defect states, surface states, etc. The ability to mold and guide light will lead to many applications in the control of spontaneous emission and in the fabrication of novel optoelectronic devices.

[277]
J. D. Joannopoulos, P. R. Villeneuve, and S. Fan, “Photonic crystals: Putting a new twist on light,” Nature, vol. 386, pp. 143–149, March 1997. Erratum: ibid. vol. 387, p. 830 (1997). [ bib | DOI ]
Photonic crystals are materials patterned with a periodicity in dielectric constant, which can create a range of “forbidden” frequencies called a photonic bandgap. Photons with energies lying in the bandgap cannot propagate through the medium. This provides the opportunity to shape and mould the flow of light for photonic information technology.

[278]
P. R. Villeneuve, D. S. Abrams, S. Fan, and J. D. Joannopoulos, “Single-mode waveguide microcavity for fast optical switching,” Optics Letters, vol. 21, pp. 2017–2019, December 1996. [ bib | http ]
We investigate the proper ties of a tunable single-mode waveg uide microcavity that is well suited for frequency modulation and switching. The cavity mode has a volume of less than one cubic half-wavelength, and the resonant frequency is tuned by refractive-index modulation. We suggest using a photorefractive ef fect to drive the device, based on the photoionization of deep donor levels known as DX centers in compound semiconductors. Picosecond on 2013 of f switching times are achievable when two of these cavities are placed in ser ies. The resulting switch has the advantages of being compact and requir ing as little as 10 pJ of energ y of operate.

[279]
J. C. Chen, H. A. Haus, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “Optical filters from photonic band gap air bridges,” Journal of Lightwave Technology, vol. 14, pp. 2575–2580, November 1996. [ bib | DOI ]
Surrounding waveguides by air reduces radiation losses so the air bridge geometry can produce optical filters with sharp transmission resonances and very wide stop bands.

[280]
S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “Large omnidirectional band gaps in metallodielectric photonic crystals,” Physical Review B, vol. 54, pp. 11245–11251, October 1996. [ bib | http ]
Using a finite-difference time-domain method, we study the band-structure and transmission properties of three-dimensional metallodielectric photonic crystals. The metallodielectric crystals are modeled as perfect electrical conducting objects embedded in dielectric media. We investigate two different lattice geometries: the face-centered-cubic (fcc) lattice and the diamond lattice. Partial gaps are predicted in the fcc lattice, in excellent agreement with recent experiments. Complete gaps are found in a diamond lattice of isolated metal spheres. The gaps appear between the second and third bands and their sizes can be larger than 60% when the radius of the spheres exceeds 21% of the cubic unit cell size. A possible fabrication scheme for this structure is proposed and transmission calculations are performed.

[281]
A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission through sharp bends in photonic crystals waveguides,” Physical Review Letters, vol. 77, pp. 3787–3790, October 1996. [ bib | http ]
We demonstrate highly efficient transmission of light around sharp corners in photonic band-gap waveguides. Numerical simulations reveal complete transmission at certain frequencies, and very high transmission (>95%) over wide frequency ranges. High transmission is observed even for 90o bends with zero radius of curvature, with a maximum transmission of 98% as opposed to 30% for analogous conventional dielectric waveguides. We propose a simple one-dimensional scattering theory model with a dynamic frequency-dependent well depth to describe the transmission properties.

[282]
P. R. Villeneuve, S. Fan, and J. D. Joannopoulos, “Microcavities in photonic crystals: Mode symmetry, tunability, and coupling efficiency,” Physical Review B, vol. 54, pp. 7837–7842, September 1996. [ bib | http ]
We investigate the properties of resonant modes which arise from the introduction of local defects in two-dimensional (2D) and 3D photonic crystals. We show that the properties of these modes can be controlled by simply changing the nature and size of the defects. We compute the frequency, polarization, symmetry, and field distribution of the resonant modes by solving Maxwell2019s equations in the frequency domain. The dynamic behavior of the modes is determined by using a finite-difference time-domain method which allows us to compute the coupling efficiency and the losses in the microcavity.

[283]
S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “Theoretical investigation of fabrication-related disorder on the properties of photonic crystals,” Journal of Applied Physics, vol. 78, pp. 1415–1418, August 1995. [ bib | http ]
How various deviations in perfect photonic crystals, which may arise during fabrication, can affect the size of photonic band gaps is investigated theoretically. The emphasis is on determining the effects of misalignment of basic structural elements and overall surface roughness, because of their general fabrication relevance. As an example, calculations on a newly proposed three-dimensional photonic crystal are performed. It is shown that the size of the gap is tolerant to significant amounts of deviation from the perfect structure.

[284]
S. Fan, J. N. Winn, A. Devenyi, J. C. Chen, R. D. Meade, and J. D. Joannopoulos, “Guided and defect modes in periodic dielectric waveguides,” Journal of the Optical Society of America B, vol. 12, pp. 1267–1272, July 1995. [ bib | http ]
The nature of guided modes and defect modes in periodic dielectric waveguides is investigated computationally for model systems in two dimensions. It is shown that defect states that exist within the band gap of guided modes can be excited to form tightly localized high-Q resonances.

[285]
P. R. Villeneuve, S. Fan, J. D. Joannopoulos, K.-Y. Lim, G. S. Petrich, L. A. Kolodziejski, and R. Reif, “Air-bridge microcavities,” Applied Physics Letters, vol. 67, pp. 167–169, July 1995. [ bib | http ]
We introduce and analyze a new type of high-Q microcavity consisting of a channel waveguide and a one-dimensional photonic crystal. A band gap for the guided modes is opened and a sharp resonant state is created by adding a single defect in the periodic system. An analysis of the eigenstates shows that strong field confinement of the defect state can be achieved with a modal volume less than half of a cubic half-wavelength. We also present a feasibility study for the fabrication of suspended structures with micron-sized features using semiconductor materials.

[286]
S. Fan, J. N. Winn, A. Devenyi, J. C. Chen, R. D. Meade, and J. D. Joannopoulos, “Guided and defect modes in periodic dielectric waveguides,” Journal of the Optical Society of America B, vol. 12, pp. 1267–1272, July 1995. [ bib | http ]
The nature of guided modes and defect modes in periodic dielectric waveguides is investigated computationally for model systems in two dimensions. It is shown that defect states that exist within the band gap of guided modes can be excited to form tightly localized high-Q resonances.

[287]
J. D. Joannopoulos, “Photonics: Minding the gap,” Nature, vol. 375, p. 278, May 1995. [ bib ]
[288]
S. Fan, P. R. Villeneuve, R. D. Meade, and J. D. Joannopoulos, “Design of three-dimensional photonic crystals at submicron lengthscales,” Applied Physics Letters, vol. 65, pp. 1466–1468, September 1994. [ bib | http ]
We present a new class of periodic dielectric structures designed specifically to be amenable for fabrication at submicron lengthscales. The structures give rise to a sizable 3D photonic band gap and can be fabricated with materials widely used today in optoelectronic devices. They are made of three materials and consist essentially of a layered structure in which a series of cylindrical air holes are etched at normal incidence through the top surface of the structure. Our results demonstrate the existence of a gap as large as 14% of the midgap frequency using Si, SiO2, and air; and 23% using Si and air.

[289]
R. D. Meade, A. Devenyi, J. D. Joannopoulos, O. L. Alerhand, D. A. Smith, and K. Kash, “Novel applications of photonic band gap materials: low-loss bends and high Q cavities,” Journal of Applied Physics, vol. 75, pp. 4753–4755, May 1994. [ bib | http ]
In this paper we discuss a novel material which has nearly ideal properties at optical frequencies. It combines the low dissipation of a dielectric with the reflectivity of a metal. This material employs a two-dimensional photonic band gap structure to achieve in-plane confinement of light and uses index contrast to achieve vertical confinement. We discuss how this material can be used to create microcavities for the production of low threshold lasers and waveguides capable of low-loss bends.

[290]
J. N. Winn, R. D. Meade, and J. D. Joannopoulos, “Two-dimensional photonic band-gap materials,” Journal of Modern Optics, vol. 41, pp. 257–273, February 1994. [ bib | DOI ]
The properties of 2D photonic lattices, and especially the presence of photonic band-gaps, are reviewed. Using symmetry arguments, general conditions on the nature of the eigenmodes for all 2D periodic dielectric lattices are derived. A method of computing photonic band-structures is briefly discussed. The in-plane band-structures of the square and triangular lattices of cylinders are systematically investigated. The out-of-plane band-structure for a prototypical system is described. Effects of periodicity-breaking are discussed, including localization of light due to lattice defects, and localized surface modes.

[291]
R. D. Meade, A. M. Rappe, K. D. Brommer, J. D. Joannopoulos, and O. L. Alerhand, “Accurate theoretical analysis of photonic band-gap materials,” Physical Review B, vol. 48, pp. 8434–8437, September 1993. Erratum: ibid., vol. 55, p. 15942 (1997). [ bib | http ]
Two improvements for the solution of Maxwell's equations in periodic dielectric media are introduced, abandoning the plane-wave cutoff and interpolating the dielectric function. These improvements permit the accurate study of previously inaccessible systems. Example calculations are discussed, employing a basis of 106 plane waves for which these two improvements reduce both the memory and central processing unit requirements by 104.

[292]
W. M. Robertson, G. Arjavalingam, R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, “Observation of surface photons on periodic dielectric arrays,” Optics Letters, vol. 18, pp. 528–530, April 1993. [ bib | http ]
The first observation to the authors' knowledge of electromagnetic surface waves in a two-dimensional dielectric crystal is reported. By using the coherent microwavetransient spectroscopytechnique, surface waves are shown to exist at frequencies within the photonic band gap for certain lattice terminations. Energy at gigahertz frequencies is coupled into the surface mode using a prism coupling technique. The experimental results are in excellent agreement with theoretical predictions.

[293]
W. M. Robertson, G. Arjavalingam, R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, “Measurement of the photon dispersion relation in two-dimensional ordered dielectric arrays,” Journal of the Optical Society of America B, vol. 10, pp. 322–327, February 1993. [ bib | http ]
We characterize the dispersion relation for electromagnetic-wave propagation in two-dimensional dielectric arrays, using the coherent microwave transient spectroscopy technique. Results of measurements along various symmetry directions of square and triangular lattices are presented. The experimental results are in excellent agreement with theoretical calculations made by using the plane-wave expansion technique. The theoretical calculations predict that transmission via certain modes is forbidden by symmetry, and our experimental results confirm this prediction.

[294]
R. D. Meade, A. M. Rappe, K. D. Brommer, and J. D. Joannopoulos, “Nature of the photonic band gap: some insights from field analysis,” Journal of the Optical Society of America B, vol. 10, pp. 328–332, February 1993. [ bib | http ]
To clarify the nature of photonic band gaps, a series of calculations on two-dimensional photonic crystals is undertaken. Systems that possess a large gap for one polarization and no gap for the other polarization are analyzed. Two features of a photonic crystal that give rise to a large photonic band gap for each polarization, i.e., connectivity and concentration of the dielectric material, are elucidated. The implications for making materials with large photonic band gaps in two and three dimensions are discussed.

[295]
E. Yablonovitch, T. J. Gmitter, K. M. Leung, R. D. Meade, A. M. Rappe, K. D. Brommer, and J. D. Joannopoulos, “3-dimensional photonic band structure,” Optical and Quantum Electronics, vol. 24, pp. S273–S283, December 1992. [ bib | DOI ]
Three-dimensionally periodic dielectric structures, (photonic crystals), possessing a forbidden gap for electromagnetic wave propagation, (a photonic bandgap), are now known. If the perfect 3-dimensional periodicity is broken by a local defect, then local electromagnetic modes can occur within the forbidden bandgap. The addition of extra dielectric material locally, inside the photonic crystal, produces `donor' modes. Conversely, the local removal of dielectric material from the photonic crystal produces `acceptor' modes. It will now be possible to make high-Q electromagnetic cavities of volume ∼1 cubic wavelength, for short wavelengths at which metallic cavities are useless. These new dielectric cavities can cover the range all the way from millimeter waves, down to ultraviolet wavelengths.

[296]
R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, “Existence of a photonic band gap in two dimensions,” Applied Physics Letters, vol. 61, pp. 495–497, July 1992. [ bib | http ]
A systematic theoretical investigation is undertaken in order to identify a two-dimensional periodic dielectric structure that has a complete in-plane photonic band gap for both polarizations. Of the various structures studied, only a triangular lattice of air columns is found to have the desired band-gap properties. Microwave transmission experiments are performed to test the theoretical predictions.

[297]
W. M. Robertson, G. Arjavalingam, R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, “Measurement of photonic band structure in a two-dimensional periodic dielectric array,” Physical Review Letters, vol. 68, pp. 2023–2026, March 1992. [ bib | http ]
The photonic band structure in a two-dimensional dielectric array is investigated using the coherent microwave transient spectroscopy (COMITS) technique. The array consists of alumina-ceramic rods arranged in a regular square lattice. The dispersion relation for electromagnetic waves in this photonic crystal is determined directly using the phase sensitivity of COMITS. The experimental results are compared to theoretical predictions obtained using the plane-wave expansion technique. Configurations with the electric field parallel and perpendicular to the axis of the rods are investigated.

[298]
E. Yablonovitch, T. J. Gmitter, R. D. Meade, A. M. Rappe, K. D. Brommer, and J. D. Joannopoulos, “Donor and acceptor modes in photonic band structure,” Physical Review Letters, vol. 67, pp. 3380–3383, December 1991. [ bib | http ]
Three-dimensionally periodic dielectric structures, photonic crystals, possessing a forbidden gap for electromagnetic wave propagation, a photonic band gap, are now known. If the perfect 3D periodicity is broken by a local defect, local electromagnetic modes can occur within the forbidden band gap. Addition of extra dielectric material locally, inside the photonic crystal, produces donor modes. Conversely, removal of dielectric material from the crystal produces “acceptor” modes. It is now possible to make high-Q electromagnetic cavities of ∼1 cubic wavelength, for short wavelengths at which metallic cavities are useless. These new dielectric cavities can cover the range from mm waves to uv wavelengths.

[299]
R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, “Photonic bound states in periodic dielectric materials,” Physical Review B, vol. 44, pp. 13772–13774, December 1991. [ bib | http ]
It is demonstrated that lattice imperfections in a periodic array of dielectric material can give rise to fully localized electromagnetic states. Calculations are performed by using a plane-wave expansion to solve Maxwell's equations. The frequency of these localized states is tunable by varying the size of the defect. Potential device applications in the microwave and millimeter wave regime are proposed.

[300]
R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, “Electromagnetic Bloch waves at the surface of a photonic crystal,” Physical Review B, vol. 44, pp. 10961–10964, November 1991. [ bib | http ]
We find that electromagnetic modes are localized at the interface between air and a photonic crystal. General arguments that surface modes must always exist for some termination of any surface of a photonic crystal are presented, and the importance of the surface band structure for semiconducting laser systems is discussed.


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