Summary

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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