File:Mutual Extintion.gif
Summary
| Description |
English: If you send a collimated beam toward a small obstacle, some of the light will be scattered, but most will continue in the same direction. If now you send a second beam and vary its phase, you can modulate how much light goes "straight" in the first beam.
The reason this is possible is because some of the light from the second beam is scattered in the same direction on the first one, and will interfere with it. Inspired by: https://journals.aps.org/pra/abstract/10.1103/PhysRevA.104.043515 |
| Date | |
| Source | https://twitter.com/j_bertolotti/status/1458448502363729928 |
| Author | Jacopo Bertolotti |
| Permission (Reusing this file) |
https://twitter.com/j_bertolotti/status/1030470604418428929 |
Mathematica 12.0 code
ReMapC[x_] := RGBColor[(2 x - 1) UnitStep[x - 0.5], 0, (1 - 2 x) UnitStep[0.5 - x]];
\[Sigma] = 4.; \[Lambda]0 = 2.; k0 = N[(2 \[Pi])/\[Lambda]0]; \[Delta] = \[Lambda]0/20; \[CapitalDelta] = 40*\[Lambda]0;
\[Phi]in = Table[0, {x, -\[CapitalDelta]/2, \[CapitalDelta]/2, \[Delta]}, {y, -\[CapitalDelta]/2, \[CapitalDelta]/2, \[Delta]}];
dim = Dimensions[\[Phi]in][[1]];
d = \[Lambda]0/2; (*typical scale of the absorbing layer*)
Ren = Table[ If[Sqrt[x^2 + y^2] <= \[Lambda]0/8, 4, 1], {x, -\[CapitalDelta]/2, \[CapitalDelta]/2, \[Delta]}, {y, -\[CapitalDelta]/2, \[CapitalDelta]/2, \[Delta]}];
Imn = Table[ 10 (E^-((x + \[CapitalDelta]/2)/d) + E^((x - \[CapitalDelta]/2)/d) + E^-((y + \[CapitalDelta]/2)/d) + E^((y - \[CapitalDelta]/2)/d)), {x, -\[CapitalDelta]/2, \[CapitalDelta]/2, \[Delta]}, {y, -\[CapitalDelta]/2, \[CapitalDelta]/2, \[Delta]}];
L = -1/\[Delta]^2*KirchhoffMatrix[GridGraph[{dim, dim}]]; (*Discretized Laplacian*)
n = Ren + I Imn;
M = L + DiagonalMatrix[SparseArray[Flatten[n]^2 k0^2]]; (*Operator on the left-hand side of the equation we want to solve*)
sourcef1[x_, y_, t_] := E^(-((x + (\[CapitalDelta]/4) )^2/(2 \[Sigma]^2))) E^(I 1.5 x) E^(-((y + \[CapitalDelta]/2)^2/(2 (\[Lambda]0/2)^2))) E^(I k0 y) + t*E^(-((x - (\[CapitalDelta]/4) )^2/(2 \[Sigma]^2))) E^(-I 1.5 x) E^(-((y + \[CapitalDelta]/2)^2/(2 (\[Lambda]0/2)^2))) E^(I k0 y);
frames1 = Table[
\[Phi]in = Table[Chop[sourcef1[x, y, t] ], {x, -\[CapitalDelta]/2, \[CapitalDelta]/2, \[Delta]}, {y, -\[CapitalDelta]/2, \[CapitalDelta]/2, \[Delta]}];
b = -(Flatten[n]^2 - 1) k0^2 Flatten[\[Phi]in];
\[Phi]s = Partition[LinearSolve[M, b], dim];
Grid[{{
ListPlot[(Transpose[ Abs[\[Phi]s][[(4 d)/\[Delta] ;; (-4 d)/\[Delta], (4 d)/\[Delta] ;; (-4 d)/\[Delta]]]/0.015][[-1]])^2, Axes -> False, AspectRatio -> 0.2, Joined -> True, PlotStyle -> Green, Background -> Black, PlotRange -> {0, 0.07}, ImagePadding -> 5, ImageSize -> 300]
}, {
ImageAdd[
ArrayPlot[Transpose[((Re[\[Phi]in + \[Phi]s])[[(4 d)/\[Delta] ;; (-4 d)/\[Delta], (4 d)/\[Delta] ;; (-4 d)/\[Delta]]]/0.015)^1], ColorFunction -> ReMapC , DataReversed -> True, Frame -> False, PlotRange -> {-1, 1}, ImagePadding -> None, ImageSize -> 300, ClippingStyle -> {Blue, Red}], ArrayPlot[Transpose@Re[(n - 1)/5] , DataReversed -> True , ColorFunctionScaling -> False, ColorFunction -> GrayLevel,
Frame -> False] ]
}}, Background -> Black]
, {t, 0, 1, 0.1}]
sourcef2[x_, y_, t_] := E^(-((x + (\[CapitalDelta]/4) )^2/(2 \[Sigma]^2))) E^(I 1.5 x) E^(-((y + \[CapitalDelta]/2)^2/(2 (\[Lambda]0/2)^2))) E^(I k0 y) + E^(-((x - (\[CapitalDelta]/4) )^2/(2 \[Sigma]^2))) E^(-I 1.5 x) E^(-((y + \[CapitalDelta]/2)^2/(2 (\[Lambda]0/2)^2))) E^(I k0 y) E^(I t);
frames2 = Table[
\[Phi]in = Table[Chop[sourcef2[x, y, t] ], {x, -\[CapitalDelta]/2, \[CapitalDelta]/2, \[Delta]}, {y, -\[CapitalDelta]/2, \[CapitalDelta]/2, \[Delta]}];
b = -(Flatten[n]^2 - 1) k0^2 Flatten[\[Phi]in];
\[Phi]s = Partition[LinearSolve[M, b], dim];
Grid[{{
ListPlot[(Transpose[ Abs[\[Phi]s][[(4 d)/\[Delta] ;; (-4 d)/\[Delta], (4 d)/\[Delta] ;; (-4 d)/\[Delta]]]/0.015][[-1]])^2, Axes -> False, AspectRatio -> 0.2, Joined -> True, PlotStyle -> Green, Background -> Black, PlotRange -> {0, 0.07}, ImagePadding -> 5, ImageSize -> 300]
}, {
ImageAdd[
ArrayPlot[ Transpose[((Re[\[Phi]s])[[(4 d)/\[Delta] ;; (-4 d)/\[Delta], (4 d)/\[Delta] ;; (-4 d)/\[Delta]]]/0.015)^1], ColorFunction -> ReMapC , DataReversed -> True, Frame -> False, PlotRange -> {-1, 1}, ImagePadding -> None, ImageSize -> 300, ClippingStyle -> {Blue, Red}],
ArrayPlot[Transpose@Re[(n - 1)/5] , DataReversed -> True , ColorFunctionScaling -> False, ColorFunction -> GrayLevel, Frame -> False] ]
}}, Background -> Black]
, {t, 0, 2 \[Pi] - 0.001, \[Pi]/20}]
ListAnimate[
Join[Table[frames1[[1]], 5], frames1, Table[frames1[[-1]], 5], frames2, frames2, Reverse[frames1]]]
Licensing
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