File:Born series.gif
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:
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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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