File:Wavefront distortion.gif
Wavefront_distortion.gif (543 × 543 pixels, file size: 1.5 MB, MIME type: image/gif, looped, 11 frames, 1.1 s)
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Summary
editDescriptionWavefront distortion.gif |
English: If your surface is not flat, Snell's law still apply locally, but the overall result can be a very complicated wavefront, that doesn't resemble the original Gaussian beam any more. |
Date | |
Source | https://twitter.com/j_bertolotti/status/1392778520498147329 |
Author | Jacopo Bertolotti |
Permission (Reusing this file) |
https://twitter.com/j_bertolotti/status/1030470604418428929 |
Mathematica 12.0 code
edit\[Lambda]0 = 1.; 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]0/15; \[CapitalDelta] = 40*\[Lambda]0; (*Parameters for the grid*)
\[Sigma] = 10 \[Lambda]0; (*width of the gaussian beam*)
sourcef[x_, y_] := E^(-(x^2/(2 \[Sigma]^2))) 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]}]; (*Discretized source*)
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[\[Phi]in][[1]];
L = -1/\[Delta]^2*KirchhoffMatrix[GridGraph[{dim, dim}]]; (*Discretized Laplacian*)
ReMapC[x_] := RGBColor[(Cos[2 \[Pi] x] + 1)/2 UnitStep[x - 0.5], 0, (Cos[2 \[Pi] x] + 1)/2 UnitStep[0.5 - x]];
surface2[x_, t_] := -(\[CapitalDelta]/4) + \[CapitalDelta]/10 + 0.3 (Chop[(Sin[Sqrt[2] x] + Sin[\[Pi] x] + Cos[E x]), 0.01]);
surface1[x_] := -(\[CapitalDelta]/4) - \[CapitalDelta]/40;
frames1 = Table[
ren = Table[ If[y < Re@Evaluate[surface2[x, t]] && y > Re@surface1[x], 1.5, 1], {x, -\[CapitalDelta]/2, \[CapitalDelta]/2, \[Delta]}, {y, -\[CapitalDelta]/2, \[CapitalDelta]/2, \[Delta]}];
n = ren + I imn;
b = -(Flatten[n]^2 - 1) k0^2 Flatten[\[Phi]in]; (*Right-hand side of the equation we want to solve*)
M = L + DiagonalMatrix[ SparseArray[Flatten[n]^2 k0^2]]; (*Operator on the left-hand side of the equation we want to solve*)
\[Phi]s = Partition[LinearSolve[M, b], dim]; (*Solve the linear system*)
ImageAdd[
ArrayPlot[ Transpose[(Re[(\[Phi]in + \[Phi]s) E^(I 2 \[Pi] t)]/Max[Re[\[Phi]in + \[Phi]s]])][[(4 d)/\[Delta] ;; (-4 d)/\[Delta], (4 d)/\[Delta] ;; (-4 d)/\[Delta]]], ColorFunction -> ReMapC, DataReversed -> True, Frame -> False, PlotRange -> {-1, 1}], ArrayPlot[Transpose@Re[(n - 1)/5] , DataReversed -> True , ColorFunctionScaling -> False, ColorFunction -> GrayLevel, Frame -> False] ](*Plot everything*)
, {t, 0, 1, 0.1}]
Licensing
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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.
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 | 11:54, 14 May 2021 | ![]() | 543 × 543 (1.5 MB) | Berto (talk | contribs) | Uploaded own work with UploadWizard |
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