Hey, I would like know how to find the field amplitude with equation 26 shown in figure 6 using the listings below:
d = 1; lam = d; a = 25*d; b = 100*d ; x2 = 0.5 a; k = 2 \[Pi]/d
u[0][x_] := 1; v[0][x_] := 0
Do[{u[q] =
Interpolation[
Re[c*NIntegrate[(u[q - 1][x1] +
I*v[q - 1][x1])*(Exp[-I*k*a*Sqrt[b^2 + (x1 - x2)^2]]/
Sqrt[Sqrt[b^2 + (x1 - x2)^2]])*(1 +
b/Sqrt[b^2 + (x1 - x2)^2]), {x1, -1, 1}]]],
v[q] = Interpolation[
Im[c*NIntegrate[(u[q - 1][x1] +
I*v[q - 1][x1])*(Exp[-I*k*a*Sqrt[b^2 + (x1 - x2)^2]]/
Sqrt[Sqrt[b^2 + (x1 - x2)^2]])*(1 +
b/Sqrt[b^2 + (x1 - x2)^2]), {x1, -1, 1}]]]}, {q, 1, 10}];
amp = Interpolation[
Table[{q, (Abs[u[q][.5] + I*v[q][.5]])^2}, {q, 0, 10}]];
{Show[{ListPlot[
Table[{q, (Abs[u[q][.5] + I*v[q][.5]])^2}, {q, 0, 10}],
PlotRange -> All, Frame -> True,
FrameLabel -> {"Number of Transits", "Amplitude"}],
Plot[amp[q], {q, 0, 10}, PlotRange -> All]}],
Plot[Table[(Abs[u[q][x] + I*v[q][x]])^2, {q, 1, 10, 1}], {x, -1, 1},
ColorFunction -> Hue, Frame -> True,
FrameLabel -> {"x", "Amplitude"}, Axes -> False]}
Cordially.
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