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File:Polarization change in uniaxial crystal.gif

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Polarization_change_in_uniaxial_crystal.gif (360 × 244 pixels, file size: 339 KB, MIME type: image/gif, looped, 31 frames)

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.
Date
Source https://twitter.com/j_bertolotti/status/1198606136586444801
Author Jacopo Bertolotti
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:
Creative Commons CC-Zero 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.

Captions

In a uniaxial crystal the polarization state change from linear to elliptical to circular and to linear again.

inception

24 November 2019

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Date/TimeThumbnailDimensionsUserComment
current09:30, 25 November 2019Thumbnail for version as of 09:30, 25 November 2019360 × 244 (339 KB)BertoUser created page with UploadWizard

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