File:Birifrangence k-surface.gif
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Birifrangence_k-surface.gif (360 × 368 pixels, file size: 1.19 MB, MIME type: image/gif, looped, 64 frames)
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This is a file from the Wikimedia Commons. The description on its description page there is shown below.
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Summary
| Description |
English: In a birefringent crystal, at each frequency and direction correspond two possible values of the wavenumber, as the surface of allowed k-vectors has two sheets.
For some special directions these two values are degenerate (optic axes). |
| Date | |
| Source | https://twitter.com/j_bertolotti/status/1194199575562739712 |
| Author | Jacopo Bertolotti |
| Permission (Reusing this file) |
https://twitter.com/j_bertolotti/status/1030470604418428929 |
Mathematica 11.0 code
f = \[Omega]^2 c^2 e1 e2 e3 (\[Omega]^4 c^4 - \[Omega]^2 c^2 ((kx^2 + ky^2)/e3 + (kx^2 + kz^2)/e2 + (ky^2 + kz^2) e1) + (kx^2/(e2 e3) + ky^2/(e1 e3) + kz^2/(e1 e2)) (kx^2 +
ky^2 + kz^2)) /. {c -> 1, e1 -> 1, e2 -> 2, e3 -> 3, \[Omega] -> 1};
p1 = Table[
Show[
ContourPlot3D[{f == 0}, {kx, -2, 2}, {ky, -2, 2}, {kz, -2, 2}, ContourStyle -> Directive[Opacity[0.5], Orange], AxesLabel -> {"\!\(\*SubscriptBox[\(k\), \(x\)]\)", "\!\(\*SubscriptBox[\(k\), \(y\)]\)",
"\!\(\*SubscriptBox[\(k\), \(z\)]\)"}, Mesh -> None, Ticks -> None, LabelStyle -> {Bold, Black}, RegionFunction -> Function[{kx, ky, kz}, kx < a], BoxRatios -> {1, 1, 1}]
,
Graphics3D[{Black, Thick, Line[{2*{-1.24, 0, -0.68}, 2*{1.24, 0, 0.68}}], Line[{2*{-1.24, 0, 0.68}, 2*{1.24, 0, -0.68}}]}]
]
, {a, 1.8, 1.24, -0.05}];
p2 = Show[
ContourPlot3D[{f == 0}, {kx, -2, 2}, {ky, -2, 2}, {kz, -2, 2}, ContourStyle -> Directive[Opacity[0.5], Orange], AxesLabel -> {"\!\(\*SubscriptBox[\(k\), \(x\)]\)", "\!\(\*SubscriptBox[\(k\), \(y\)]\)",
"\!\(\*SubscriptBox[\(k\), \(z\)]\)"}, Mesh -> None, Ticks -> None, LabelStyle -> {Bold, Black}, RegionFunction -> Function[{kx, ky, kz}, kx < 1.24], BoxRatios -> {1, 1, 1}]
,
Graphics3D[{Black, Thick, Line[{2*{-1.24, 0, -0.68}, 2*{1.24, 0, 0.68}}], Line[{2*{-1.24, 0, 0.68}, 2*{1.24, 0, -0.68}}]}]
];
p3 = Table[
Show[
ContourPlot3D[{f == 0}, {kx, -2, 2}, {ky, -2, 2}, {kz, -2, 2}, ContourStyle -> Directive[Opacity[0.5], Orange], AxesLabel -> {"\!\(\*SubscriptBox[\(k\), \(x\)]\)", "\!\(\*SubscriptBox[\(k\), \(y\)]\)",
"\!\(\*SubscriptBox[\(k\), \(z\)]\)"}, Mesh -> None, Ticks -> None, LabelStyle -> {Bold, Black}, RegionFunction -> Function[{kx, ky, kz}, kx < a], BoxRatios -> {1, 1, 1}]
,
Graphics3D[{Black, Thick, Line[{2*{-1.24, 0, -0.68}, 2*{1.24, 0, 0.68}}], Line[{2*{-1.24, 0, 0.68}, 2*{1.24, 0, -0.68}}]}]
]
, {a, 1.24, 0.5, -0.05}];
ListAnimate[
Join[p1, Table[p2, 5], p3, Reverse[p3], Table[p2, 5], Reverse[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. |
| 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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File history
Click on a date/time to view the file as it appeared at that time.
| Date/Time | Dimensions | User | Comment | |
|---|---|---|---|---|
| current | 03:20, 14 November 2019 | 360 × 368 (1.19 MB) | Berto | User created page with UploadWizard |
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