File:Multiple scattering interference.gif

Summary[edit]

Mathematica 11.0 code[edit]

\[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] ]];
source[x_] := E^(I k0 x); (*Plane wave illuminating the scatterers*)
p0 = GraphicsRow[{
   DensityPlot[Re[source[x] ], {x, -10, 10}, {y, -10, 10}, PlotPoints -> 50, Frame -> False, PlotLabel -> "Re[E]", LabelStyle -> {Black, Bold}],
   DensityPlot[Abs[source[x]]^2, {x, -10, 10}, {y, -10, 10}, PlotPoints -> 50, ColorFunction -> "AvocadoColors", PlotRange -> {0, 1}, Frame -> False, PlotLabel -> "|E\!\(\*SuperscriptBox[\(|\), \(2\)]\)", 
    LabelStyle -> {Black, Bold}]
   }, ImageSize -> Large];
scatterers = {{0, 0}};
plots = Reap[Do[
     dim = Dimensions[scatterers][[1]];
     E0 = Table[N[source[scatterers[[j, 1]] ]], {j, 1, dim}] ;(*source field on each scatterer*)
     iME = Inverse@Table[If[k == j, 1, \[Alpha] k0^2 G[scatterers[[j]] - scatterers[[k]] ] ], {j, 1, dim}, {k, 1, dim}];
     Es = iME.E0 ;(*Total field on each scatterer*)
     Etot = source[x] + \[Alpha] k0^2 Sum[Es[[j]]*G[{x, y} - scatterers[[j]]], {j, 1, dim}];
     Sow@GraphicsRow[{
        DensityPlot[Re[Etot ], {x, -10, 10}, {y, -10, 10}, PlotPoints -> 50, Epilog -> {Black, PointSize[0.02], Point[scatterers]}, Frame -> False, PlotLabel -> "Re[E]", LabelStyle -> {Black, Bold}]
        ,
        DensityPlot[Abs[Etot ]^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}]
        }, ImageSize -> Large];
     AppendTo[scatterers, RandomReal[{-7, 7}, 2]];
     , 20];][[2, 1]];
ListAnimate[plots]

Licensing[edit]

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