File:Photonic Band Gap vs Wavelength.webm
Photonic_Band_Gap_vs_Wavelength.webm (WebM audio/video file, VP9, length 40 s, 462 × 462 pixels, 239 kbps overall, file size: 1.14 MB)
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Summary
[edit]DescriptionPhotonic Band Gap vs Wavelength.webm |
English: If you send a wave on a periodic arrangement of scatterers, there might be (depending on the spatial arrangement and scattering strength) frequency regions where the wave is unable to penetrate in the medium. |
Date | |
Source | https://twitter.com/j_bertolotti/status/1415282156243402758 |
Author | Jacopo Bertolotti |
Permission (Reusing this file) |
https://twitter.com/j_bertolotti/status/1030470604418428929 |
Mathematica 12.0 code
[edit]\[Lambda]0 = 0.5; k0 = N[(2 \[Pi])/\[Lambda]0]; (*The wavelength in vacuum is set to 1, so all lengths are now in units of wavelengths*)
\[Delta] = \[Lambda]0/10; \[CapitalDelta] = 50*\[Lambda]0; (*Parameters for the grid*)
ReMapC[x_] := RGBColor[(2 x - 1) UnitStep[x - 0.5], 0, (1 - 2 x) UnitStep[0.5 - x]];
\[Sigma] = 7 \[Lambda]0;
d = \[Lambda]0/2; (*typical scale of the absorbing layer*)
imn = Table[
Chop[5 (E^-((x + \[CapitalDelta]/2)/d) + E^((x - \[CapitalDelta]/2)/d) + E^-((y + \[CapitalDelta]/2)/d) + E^((y - \[CapitalDelta]/2)/d))], {x, -\[CapitalDelta]/2, \[CapitalDelta]/2, \[Delta]}, {y, -\[CapitalDelta]/2, \[CapitalDelta]/2, \[Delta]}]; (*Imaginary part of the refractive index (used to emulate absorbing boundaries)*)
dim = Dimensions[imn][[1]];
L = -1/\[Delta]^2*KirchhoffMatrix[GridGraph[{dim, dim}]]; (*Discretized Laplacian*)
ren0 = 2;
ren = Total[ Flatten[Table[RotateRight[DiskMatrix[7, dim], {30 i, 30 j}] , {i, -8, 8}, {j, -3, 8} ], 1] ] + 1;
n = ren + I imn;
\[Lambda] =.;
frames = Table[
k = N[(2 \[Pi])/\[Lambda]];
sourcef[x_, y_] := E^(-(x^2/(2 \[Sigma]^2))) E^(-((y + \[CapitalDelta]/2)^2/(2 (\[Lambda]/2)^2))) E^(I k y);
\[Phi]in = Table[Chop[sourcef[x, y] ], {x, -\[CapitalDelta]/2, \[CapitalDelta]/2, \[Delta]}, {y, -\[CapitalDelta]/2, \[CapitalDelta]/2, \[Delta]}];
b = -(Flatten[n]^2 - 1) k^2 Flatten[\[Phi]in]; (*Right-hand side of the equation we want to solve*)
M = L + DiagonalMatrix[SparseArray[Flatten[n]^2 k^2]]; (*Operator on the left-hand side of the equation we want to solve*)
\[Phi] = Partition[LinearSolve[M, b], dim]; (*Solve the linear system*)
ImageAdd[
ArrayPlot[Transpose[(Re@\[Phi]/Max[Abs@\[Phi][[(4 d)/\[Delta] ;; (-4 d)/\[Delta], (4 d)/\[Delta] ;; (-4 d)/\[Delta]]]])][[(4 d)/\[Delta] ;; (-4 d)/\[Delta], (4 d)/\[Delta] ;; (-4 d)/\[Delta]]], DataReversed -> True, Frame -> False, PlotRange -> {-1, 1}, LabelStyle -> {Black, Bold}, ColorFunctionScaling -> True, ColorFunction -> ReMapC]
,
ArrayPlot[Transpose[(ren - 1)/5] , DataReversed -> True , ColorFunctionScaling -> False, ColorFunction -> GrayLevel, Frame -> False]
]
, {\[Lambda], 1., 2., 0.005}];
ListAnimate[frames,5]
Licensing
[edit]This file is made available under the Creative Commons CC0 1.0 Universal Public Domain Dedication. | |
The person who associated a work with this deed has dedicated the work to the public domain by waiving all of their rights to the work worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law. You can copy, modify, distribute and perform the work, even for commercial purposes, all without asking permission.
http://creativecommons.org/publicdomain/zero/1.0/deed.enCC0Creative Commons Zero, Public Domain Dedicationfalsefalse |
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Date/Time | Thumbnail | Dimensions | User | Comment | |
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current | 07:23, 15 July 2021 | 40 s, 462 × 462 (1.14 MB) | Berto (talk | contribs) | Imported media from uploads:25567b94-e53d-11eb-8cae-e263f171fcab |
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