File:Bragg Diffraction.gif
Summary
| Description |
English: A line of point scatterers behave approximately as a partial mirror. When the scatterers are arranged in a crystal, each line will reflect light, and all of those reflections will interfere with each other.
(Animation made for scalar fields in 2D) |
| Date | |
| Source | https://twitter.com/j_bertolotti/status/1261314633673080835 |
| Author | Jacopo Bertolotti |
| Permission (Reusing this file) |
https://twitter.com/j_bertolotti/status/1030470604418428929 |
Mathematica 12.0 code
sinstep[t_] := Sin[\[Pi]/2 t]^2
stopstep[t_] := t (2 - t);
\[Lambda] = Sqrt[2];
k0 = (2 \[Pi])/\[Lambda];
c = 1;
\[Omega] = c k0;
\[Alpha] = 4/(k0^2 I);
\[Sigma] = (k0^3 Norm[\[Alpha]]^2)/4;
G[r_] := N[I/4 HankelH1[0, k0 Norm[r] ]];
ReMapC[x_] := RGBColor[(Cos[2 \[Pi] x] + 1)/2 UnitStep[x - 0.5], 0, (Cos[2 \[Pi] x] + 1)/2 UnitStep[0.5 - x]];
\[Theta] = -\[Pi]/4;
E0[x_, y_] := E^(I k0 (Cos[\[Theta]] x + Sin[\[Theta]] y))/4 E^(-((-Sin[\[Theta]] x + Cos[\[Theta]] y)^2/(2 3^2)));
p0 = Table[
sources = {stopstep[t] ({-5, 0} - {11, 0}) + {11, 0}};
nsources = Dimensions[sources][[1]];
DensityPlot[
Re[E0[x, y]/4 + Sum[G[{x, y} - sources[[j]]] E0[sources[[j, 1]], sources[[j, 2]] ], {j, 1, nsources}] ], {x, -10, 10}, {y, -10, 10}, PlotPoints -> 100, ColorFunction -> ReMapC, Frame -> False, PlotRange -> {-0.5, 0.5}, RegionFunction -> Function[{x, y}, And @@ Table[Norm[{x, y} - sources[[j]]] > 0.2, {j, 1, nsources}] ], Epilog -> { Black, Thick, Table[Circle[sources[[j]], 0.2], {j, 1, nsources}]}]
, {t, 0, 1, 0.05}];
p1 = Table[
sources = Table[{j, 0}, {j, -5, k, 1}];
nsources = Dimensions[sources][[1]];
DensityPlot[
Re[E0[x, y]/10 + Sum[G[{x, y} - sources[[j]]] E0[sources[[j, 1]], sources[[j, 2]] ], {j, 1, nsources}] ], {x, -10, 10}, {y, -10, 10}, PlotPoints -> 100, ColorFunction -> ReMapC, Frame -> False, PlotRange -> {-0.5, 0.5}, RegionFunction -> Function[{x, y}, And @@ Table[Norm[{x, y} - sources[[j]]] > 0.2, {j, 1, nsources}] ], Epilog -> {White, Table[Disk[sources[[j]], 0.2], {j, 1, nsources}], Black, Thick,
Table[Circle[sources[[j]], 0.2], {j, 1, nsources}]}]
, {k, -4, 5, 1}];
p2 = Table[
sources =
sinstep[t]*(Table[{j, j - 5}, {j, -5, 5, 1}] - Table[{j, 0}, {j, -5, 5, 1}]) + Table[{j, 0}, {j, -5, 5, 1}];
nsources = Dimensions[sources][[1]];
DensityPlot[
Re[E0[x, y]/10 + Sum[G[{x, y} - sources[[j]]] E0[sources[[j, 1]], sources[[j, 2]] ], {j, 1, nsources}] ], {x, -10, 10}, {y, -10, 10}, PlotPoints -> 100, ColorFunction -> ReMapC, Frame -> False, PlotRange -> {-0.5, 0.5}, RegionFunction -> Function[{x, y}, And @@ Table[ Norm[{x, y} - sources[[j]]] > 0.2, {j, 1, nsources}] ], Epilog -> {White, Table[Disk[sources[[j]], 0.2], {j, 1, nsources}], Black, Thick,
Table[Circle[sources[[j]], 0.2], {j, 1, nsources}]}]
, {t, 0, 1, 0.051}];
p3 = Table[
sources = Flatten[Table[{x, y} , {x, -5, 5, 1}, {y, 0, -k, -1}], 1];
nsources = Dimensions[sources][[1]];
DensityPlot[
Re[E0[x, y]/10 + Sum[G[{x, y} - sources[[j]]] E0[sources[[j, 1]], sources[[j, 2]] ], {j, 1, nsources}] ], {x, -10, 10}, {y, -10, 10}, PlotPoints -> 100, ColorFunction -> ReMapC, Frame -> False, PlotRange -> {-0.5, 0.5}, RegionFunction -> Function[{x, y}, And @@ Table[Norm[{x, y} - sources[[j]]] > 0.2, {j, 1, nsources}] ], Epilog -> {White, Table[Disk[sources[[j]], 0.2], {j, 1, nsources}], Black, Thick,
Table[Circle[sources[[j]], 0.2], {j, 1, nsources}]}]
, {k, 0, 3, 1}];
ListAnimate[Join[p0, p1, p2, Reverse[p2], p3, Table[p3[[-1]], {10}] , Reverse[p3], Reverse[p1], Reverse[p0] ] ]
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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