Polarization_change_in_uniaxial_crystal.gif
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Summary
| Description |
English:
A wave in a uniaxial crystal will separate in two components, one parallel and one perpendicular to the optic axis, that will accumulating phase at different rates. This can be used to manipulate the polarization state of the wave.
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| Date | |
| Source | https://twitter.com/j_bertolotti/status/1198606136586444801 |
| Author | Jacopo Bertolotti |
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Permission
( Reusing this file ) |
https://twitter.com/j_bertolotti/status/1030470604418428929 |
Mathematica 11.0 code
\[Theta] = \[Pi]/4;
\[Epsilon]r = FullSimplify@RotationMatrix[\[Theta], {1, 0, 0}].DiagonalMatrix[{\[Epsilon]1, \[Epsilon]1, \[Epsilon]2}].RotationMatrix[-\[Theta], {1, 0, 0}];
eq = Table[
(D[{Ex[x], Ey[x], Ez[x]}, {x, 2}])[[j]] == -(\[Epsilon]r.{Ex[x], Ey[x], Ez[x]})[[j]], {j, 1, 3, 1}];
sol = FullSimplify[DSolveValue[Flatten[{eq, Ex[0] == 0, Ex'[0] == 0, Ey[0] == 0, Ey'[0] == 0, Ez[0] == 1, Ez'[0] == 0}], {Ex[x], Ey[x], Ez[x]}, x] ];
p1 = Table[ Show[
Graphics3D[{Lighting -> "Neutral", Gray, Opacity[0.3], Cuboid[{0, -1, -1}, {62.8, 1, 1}], Opacity[1], Thick, Black, Arrowheads[0.002], Arrow[{{0, -1, -1}, {0, 1, 1}}]}]
,
ParametricPlot3D[Piecewise[{{{x, 0, Cos[x - \[Tau]]} /. {\[Epsilon]1 -> 1, \[Epsilon]2 -> 1.1}, x < 0}, {{x, sol2[[2]], sol2[[3]]} /. {\[Epsilon]1 -> 1, \[Epsilon]2 -> 1.1}, 0 < x < 62.8}, {{x, Cos[x - \[Tau]], 0} /. {\[Epsilon]1 -> 1, \[Epsilon]2 -> 1.1}, x > 62.8}}], {x, -20, 80}, BoxRatios -> {3, 1, 1}, PlotStyle -> {Orange}, PlotPoints -> 50]
, PlotRange -> {{-20, 80}, {-1, 1}, {-1, 1}}, BoxRatios -> {3, 1, 1}, Boxed -> False
]
, {\[Tau], 0, 2 \[Pi], (2 \[Pi])/30}];
ListAnimate[p1]
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 . |
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