Meep Tutorial/Material dispersion
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+ | In this example, we will perform a simulation with a '''frequency-dependent dielectric''' ε(ω), corresponding to '''material dispersion'''. (See [[Dielectric materials in Meep]] for more information on how material dispersion is supported in Meep.) In particular, we will model a ''uniform medium'' of the dispersive material; see also the <code>material-dispersion.ctl</code> file included with Meep. From the dispersion relation <math>\omega(k)</math>, we will compute the numerical ε(ω) via the formula: | ||
+ | |||
+ | :<math>\varepsilon(\omega) = \left( \frac{k}{\omega} \right) ^2</math> | ||
+ | |||
+ | We will then compare this with the analytical ε(ω) that we specified. | ||
+ | |||
+ | Since this is a uniform medium, our computational cell can actually be of ''zero'' size (i.e. one pixel), where we will use Bloch-periodic boundary conditions to specify the wavevector ''k''. | ||
+ | |||
+ | (set! geometry-lattice (make lattice (size no-size no-size no-size))) | ||
+ | |||
+ | We will then fill all space with a dispersive material: | ||
+ | |||
+ | (set! default-material | ||
+ | (make dielectric (epsilon 2.25) | ||
+ | (polarizations | ||
+ | (make polarizability | ||
+ | (omega 1.1) (gamma 1e-5) (delta-epsilon 0.5)) | ||
+ | (make polarizability | ||
+ | (omega 0.5) (gamma 0.1) (delta-epsilon 2e-5)) | ||
+ | ))) | ||
+ | |||
+ | |||
+ | corresponding to the dielectric function: | ||
+ | |||
+ | :<math>\varepsilon(\omega) = 2.25 + \frac{1.1^2 \cdot 0.5}{1.1^2 - \omega^2 -i\omega \cdot 10^{-5}} + \frac{0.5^2 \cdot 2\cdot 10^{-5}}{0.5^2 - \omega^2 -i\omega \cdot 0.1}</math> | ||
[[Category:Meep examples]] | [[Category:Meep examples]] |
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In this example, we will perform a simulation with a frequency-dependent dielectric ε(ω), corresponding to material dispersion. (See Dielectric materials in Meep for more information on how material dispersion is supported in Meep.) In particular, we will model a uniform medium of the dispersive material; see also the material-dispersion.ctl
file included with Meep. From the dispersion relation ω(k), we will compute the numerical ε(ω) via the formula:
We will then compare this with the analytical ε(ω) that we specified.
Since this is a uniform medium, our computational cell can actually be of zero size (i.e. one pixel), where we will use Bloch-periodic boundary conditions to specify the wavevector k.
(set! geometry-lattice (make lattice (size no-size no-size no-size)))
We will then fill all space with a dispersive material:
(set! default-material (make dielectric (epsilon 2.25) (polarizations (make polarizability (omega 1.1) (gamma 1e-5) (delta-epsilon 0.5)) (make polarizability (omega 0.5) (gamma 0.1) (delta-epsilon 2e-5)) )))
corresponding to the dielectric function: