File:Frequency doubling with imperfect phase matching.gif
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Summary
| Description |
English: Numerical solution of equations 2.7.10 and 2.7.11 on Boyd's "Nonlinear optics".
If the phase matching is not perfect having your crystal too long can be detrimental, as the energy flows back into the pump. |
| Date | |
| Source | https://twitter.com/j_bertolotti/status/1196849637904322561 |
| 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 = 1.1;
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]
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 11:27, 20 November 2019 | | 457 × 244 (325 KB) | Berto | User created page with UploadWizard |
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