# Find the field amplitude using the following equation?

Posted 7 months ago
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 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. Attachments: