File:Born series.gif

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File:Born series.gif - Wikipedia

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Summary

DescriptionBorn series.gif	English: In the "first Born approximation", commonly used in Condensed Matter Physics, a wave is assumed to scatter only once from each scattering center. Higher orders of the "Born series" describe the fact that a scattered wave can be scattered again.
Date	3 June 2019
Source	https://twitter.com/j_bertolotti/status/1135550283264790532
Author	Jacopo Bertolotti
Permission (Reusing this file)	https://twitter.com/j_bertolotti/status/1030470604418428929

Mathematica 11.0 code

\[Lambda] = 1;
k0 = (2 \[Pi])/\[Lambda];
\[Alpha] = 4/(k0^2 I);
\[Sigma] = (k0^3 Norm[\[Alpha]]^2)/4 // N;
G[r_] := N[I/4 HankelH1[0, k0 Norm[r] ]];
nborn = 10;
source[x_] := E^(I k0 x); (*Plane wave illuminating the scatterers*)
scatterers = RandomReal[{-7, 7}, {15, 2}];
dim = Dimensions[scatterers][[1]];
E0 = Table[
   N[source[scatterers[[j, 1]] ]], {j, 1, dim}] ;(*source field on each scatterer*)
Es = E0;
born = Reap[Do[
      tmp = Table[\[Alpha] k0^2 Sum[If[i == j, 0, Es[[j]]*G[scatterers[[i]] - scatterers[[j]] ] ], {j, 1, dim}], {i, 1, dim}];
      Es = tmp;
      Sow[Es];
      tmp =.
      , {nborn}];][[2, 1]];
Etot = Table[\[Alpha] k0^2 Sum[born[[i, j]]*G[{x, y} - scatterers[[j]]], {j, 1, dim}], {i, 1, nborn}];
intborn = 
 Table[DensityPlot[Abs[Sum[Etot[[i]], {i, 1, j}] ]^2, {x, -10, 10}, {y, -10, 10}, PlotPoints -> 50, ColorFunction -> "AvocadoColors", PlotRange -> {0, 5}, Epilog -> {White, PointSize[0.02], Point[scatterers]}, Frame -> False, PlotLabel -> "|E\!\(\*SuperscriptBox[\(|\), \(2\)]\)", LabelStyle -> {Black, Bold}], {j, 1, nborn}]

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. CC0falsefalse

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	Date/Time	Thumbnail	Dimensions	User	Comment
current	15:32, 4 June 2019		360 × 382 (678 KB)	Berto	User created page with UploadWizard

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GIF file comment	Created with the Wolfram Language : www.wolfram.com

Summary

Mathematica 11.0 code

Licensing

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wave

scattering

field

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some value

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3 June 2019

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