File:Frequency doubling with perfect pase matching.gif

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Frequency_doubling_with_perfect_pase_matching.gif ‎(457 × 244 pixels, file size: 396 KB, MIME type: image/gif, looped, 21 frames)

Summary

Description
English: Numerical solution of equations 2.7.10 and 2.7.11 on Boyd's "Nonlinear optics"
Date
Source https://twitter.com/j_bertolotti/status/1196848654675533824
Author Jacopo Bertolotti
Permission
(Reusing this file)		 https://twitter.com/j_bertolotti/status/1030470604418428929

Mathematica 11.0 code

d = 0.05; c = 1; \[Omega]1 = 1; \[Omega]2 = 2 \[Omega]1; n1 = 1; n2 = 1;
k1 = (n1 \[Omega]1)/c; k2 = (n2 \[Omega]2)/c; \[CapitalDelta]k =  2 k1 - k2;
K1 = (2 I \[Omega]1^2 d)/(k1 c^2); K2 = (I \[Omega]2^2 d)/(k2 c^2); 
sol = NDSolve[{A1'[z] == K1 Conjugate[A1[z]] A2[z] E^(-I \[CapitalDelta]k z), A2'[z] == K2 (A1[z])^2 E^(I \[CapitalDelta]k z), A2[0] == 0, A1[0] == 1}, {A1[z], A2[z]}, {z, 0, 50}]

t1 = Re[Evaluate[(A1[z] /. sol) /. {z -> 20}] E^(I (k1 (z) - \[Omega]1 t))];
t2 = Re[(Evaluate[A2[z] /. sol /. {z -> 20}]) E^(I (k2 (z) - \[Omega]2 t))];
p1 = Table[
   Show[
    Plot[{Re[ E^(I (k1 z - \[Omega]1 t))], 0}, {z, -10, 0}, PlotStyle -> {Purple, Orange},  Axes -> False], Plot[{Re[Evaluate[A1[z] /. sol] E^(I (k1 z - \[Omega]1 t))], Re[Evaluate[A2[z] /. sol] E^(I (k2 z - \[Omega]2 t))]}, {z, 0, 20}, PlotPoints -> 40, PlotStyle -> {Purple, Orange}, PlotLegends -> LineLegend[{"\[Omega]=\!\(\*SubscriptBox[\(\[Omega]\), \(1\)]\)", "\[Omega]=2\!\(\*SubscriptBox[\(\[Omega]\), \(1\)]\)"}]],
    Plot[ t1, {z, 20, 30}, PlotStyle -> {Purple}], Plot[ t2, {z, 20, 30}, PlotStyle -> {Orange}], PlotRange -> All, Prolog -> {LightGray, Polygon[{{0, 1}, {0, -1}, {20, -1}, {20, 1}, {0, 1}}]}, 
    PlotLabel -> "\!\(\*SuperscriptBox[\(\[Chi]\), \((2)\)]\) crystal", LabelStyle -> {Black, Bold}
    ]
   , {t, 0, (2 \[Pi])/\[Omega]1, (2 \[Pi])/\[Omega]1 1/20}];
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

Schematic of frequency doubling (SHG) with perfect phase matching.

inception

19 November 2019

MIME type

image/gif

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Date/TimeThumbnailDimensionsUserComment
current11:19, 20 November 2019Thumbnail for version as of 11:19, 20 November 2019457 × 244 (396 KB)BertoUser created page with UploadWizard
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