Jump to content

File:Multiple Scattering.gif

Page contents not supported in other languages.
This is a file from the Wikimedia Commons
From Wikipedia, the free encyclopedia

Multiple_Scattering.gif (609 × 336 pixels, file size: 4.21 MB, MIME type: image/gif, looped, 131 frames, 13 s)

Summary

Description
English: A pulse of light scrambled by a random collection of scatterers.
Date
Source https://twitter.com/j_bertolotti/status/1460637298035503109
Author Jacopo Bertolotti
Permission
(Reusing this file)
https://twitter.com/j_bertolotti/status/1030470604418428929

Mathematica 12.0 code

c = 1; (*speed of light*)
\[Omega]min = 1.; \[Omega]max = 5.;
\[Omega]0 = Mean[{\[Omega]min, \[Omega]max}]; \[Sigma]0 = (\[Omega]max - \[Omega]min)/10;
amplitude[w_] := E^(-(1/(2 \[Sigma]0^2)) ((w - \[Omega]0)^2) );

k0 = N[\[Omega]0/c];  \[Lambda]0 = N[(2 \[Pi])/k0]; d = \[Lambda]0/2; (*typical scale of the absorbing layer*)
\[Delta] = \[Lambda]0/10; \[CapitalDelta] = 30*\[Lambda]0;  (*Parameters for the grid*)
ReMapC[x_] := RGBColor[(2 x - 1) UnitStep[x - 0.5], 0, (1 - 2 x) UnitStep[0.5 - x]];
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 = 1.5 - 1;
ren = ren0*Clip[ Total[ Table[ RotateRight[ DiskMatrix[3, dim], {RandomInteger[{0, dim}], RandomInteger[{Round[dim/8], Round[dim/2] - 5}]}], {150}] ], {0, 1}] + 1;
n = ren + I imn;
\[Sigma] = 2 \[Lambda]0;
sourcef[x_, y_, w_] := Sqrt[w/c] E^(-(x^2/(2 \[Sigma]^2))) E^(-((y + \[CapitalDelta]/2)^2/(2 (\[Lambda]0/2)^2))) E^(I w/c y);
\[Delta]\[Omega] = (\[Omega]max - \[Omega]min)/200;
\[Phi] = Table[
   \[Phi]in = Table[amplitude[\[Omega]]*sourcef[x, y, \[Omega]] , {x, -\[CapitalDelta]/2, \[CapitalDelta]/2, \[Delta]}, {y, -\[CapitalDelta]/2, \[CapitalDelta]/2, \[Delta]}];
   b = -(Flatten[n]^2 - 1) (\[Omega]/c)^2 Flatten[\[Phi]in]; (*Right-hand side of the equation we want to solve*)
   M = L + DiagonalMatrix[ SparseArray[Flatten[n]^2 (\[Omega]/c)^2]]; (*Operator on the left-hand side of the equation we want to solve*)
   Partition[LinearSolve[M, b], dim], {\[Omega], \[Omega]min, \[Omega]max, 1*\[Delta]\[Omega]}];
\[Phi]dim = Dimensions[\[Phi]][[1]];

frames = Table[
   Grid[{{Style["Re(E)", White, Bold, Large], Style["|E\!\(\*SuperscriptBox[\(|\), \(2\)]\)", White, Bold, Large]}, {
      ImageAdd[
       ArrayPlot[
        Transpose[(Re@Total[Table[\[Phi][[j]] E^(I (\[Omega]min + \[Delta]\[Omega] (j - 1) ) t), {j, 1, \[Phi]dim}] ][[(4 d)/\[Delta] ;; (-4 d)/\[Delta], (4 d)/\[Delta] ;; (-4 d)/\[Delta]]])/3], DataReversed -> True, Frame -> False, PlotRange -> {-1, 1}, LabelStyle -> {Black, Bold}, ColorFunctionScaling -> True, ColorFunction -> ReMapC, ClippingStyle -> {Blue, Red}, ImageSize -> 300, Background -> Black]
       ,
       ArrayPlot[Transpose[(ren - 1)/5] , DataReversed -> True , ColorFunctionScaling -> False, ColorFunction -> GrayLevel, Frame -> False]
       ]
      ,
      ImageAdd[
       ArrayPlot[ Transpose[((Abs@Total[Table[\[Phi][[j]] E^(I (\[Omega]min + \[Delta]\[Omega] (j - 1) ) t), {j, 1, \[Phi]dim}] ][[(4 d)/\[Delta] ;; (-4 d)/\[Delta], (4 d)/\[Delta] ;; (-4 d)/\[Delta]]])/3)^2],         DataReversed -> True, Frame -> False, PlotRange -> {0, 1}, LabelStyle -> {Black, Bold}, ColorFunctionScaling -> True, ColorFunction -> "AvocadoColors", ClippingStyle -> White, Background -> Black, ImageSize -> 300]
       ,
       ArrayPlot[Transpose[(ren - 1)/5] , DataReversed -> True , ColorFunctionScaling -> False, ColorFunction -> GrayLevel, Frame -> False]
       ]
      }}, Background -> Black]
   , {t, 50, -80, -1}];

ListAnimate[frames]

Licensing

I, the copyright holder of this work, hereby publish it under the following license:
Creative Commons CC-Zero 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.

Captions

A pulse of light scrambled by a random collection of scatterers.

Items portrayed in this file

depicts

16 November 2021

image/gif

File history

Click on a date/time to view the file as it appeared at that time.

Date/TimeThumbnailDimensionsUserComment
current09:07, 17 November 2021Thumbnail for version as of 09:07, 17 November 2021609 × 336 (4.21 MB)BertoUploaded own work with UploadWizard

The following page uses this file:

Global file usage

The following other wikis use this file:

Metadata