File:Impedance mismatch due to absorption.gif
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Impedance_mismatch_due_to_absorption.gif (360 × 359 pixels, file size: 2.44 MB, MIME type: image/gif, looped, 73 frames, 7.3 s)
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Summary
| Description |
English: A positive imaginary part of the refractive index means the wave will be absorbed.
But, contrary to intuition, if you keep increasing absorption, the material will behave like a mirror, not a perfect absorber. |
| Date | |
| Source | https://twitter.com/j_bertolotti/status/1465294009325260802 |
| Author | Jacopo Bertolotti |
| Permission (Reusing this file) |
https://twitter.com/j_bertolotti/status/1030470604418428929 |
Mathematica 12.0 code
\[Sigma] = 5.; \[Lambda]0 = 2.; k0 = N[(2 \[Pi])/\[Lambda]0]; \[Delta] = \[Lambda]0/10; \[CapitalDelta] = 40*\[Lambda]0;
\[Phi]in = Table[0, {x, -\[CapitalDelta]/2, \[CapitalDelta]/2, \[Delta]}, {y, -\[CapitalDelta]/2, \[CapitalDelta]/2, \[Delta]}];
dim = Dimensions[\[Phi]in][[1]]
d = \[Lambda]0/2; (*typical scale of the absorbing layer*)
Imn = Table[10 (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]}];
L = -1/\[Delta]^2*KirchhoffMatrix[GridGraph[{dim, dim}]]; (*Discretized Laplacian*)
ReMapC[x_] := RGBColor[(2 x - 1) UnitStep[x - 0.5], 0, (1 - 2 x) UnitStep[0.5 - x]];
\[Alpha][t_] := 2*t^3;
frames = Table[
Ren = Table[ If[y < 0, 1, 1 + I*\[Alpha][t] ], {x, -\[CapitalDelta]/2, \[CapitalDelta]/2, \[Delta]}, {y, -\[CapitalDelta]/2, \[CapitalDelta]/2, \[Delta]}];
n = Ren + I Imn;
M = L + DiagonalMatrix[SparseArray[Flatten[n]^2 k0^2]]; (*Operator on the left-hand side of the equation we want to solve*)
sourcef[x_, y_] := E^(-((x + (\[CapitalDelta]/4) )^2/(2 \[Sigma]^2))) E^(I 1.5 x) E^(-((y + \[CapitalDelta]/2)^2/(2 (\[Lambda]0/2)^2))) E^(I k0 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) k0^2 Flatten[\[Phi]in]; (*Right-hand side of the equation we want to solve*)
\[Phi]s = Partition[LinearSolve[M, b], dim]; (*Solve the linear system*)
ArrayPlot[
Transpose[((Re[\[Phi]s])[[(4 d)/\[Delta] ;; (-4 d)/\[Delta], (4 d)/\[Delta] ;; (-4 d)/\[Delta]]]/0.012)^1], ColorFunction -> ReMapC , DataReversed -> True, Frame -> False, PlotRange -> {-1, 1}, ClippingStyle -> {Blue, Red}, Epilog -> {White, Line[{{0, 180}, {400, 180}}], Text[Style["n=1", Bold, 20], {30, 160}], Text[Style[ StringForm["n=1+i``", NumberForm[\[Alpha][t], {3, 2}]], Bold, 20], {60, 200}]}]
, {t, 0.000, 1, 0.03}];
ListAnimate[Join[frames, Table[frames[[-1]], 5], Reverse[frames]]]
Licensing
I, the copyright holder of this work, hereby publish it under the following license:
 
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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.
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File history
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 14:48, 30 November 2021 | | 360 × 359 (2.44 MB) | Berto | Uploaded own work with UploadWizard |
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