File:Born series.gif

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Summary

Description
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
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

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

Scattering from a set of dipoles including different number of terms of the Born series

Items portrayed in this file

depicts

3 June 2019

image/gif

903782f021a0ffc4df8854346d4434339e29f7b4

694,529 byte

11 second

382 pixel

360 pixel

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current15:32, 4 June 2019Thumbnail for version as of 15:32, 4 June 2019360 × 382 (678 KB)wikimediacommons>BertoUser created page with UploadWizard

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