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kerr_effect.m

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+clc
+clear
+
+%% User choices %%
+lambda = 1; % wavelentgh in um
+N = 2^9; % number of points
+Lz = 3000; % z-limit of visualization in um
+Lx = 300; % x-limit of visualization in um
+A = 0.8; % amplitude of the beam
+r = 30; % radius of the beam in um;
+%%%%%
+
+k0 = 2 * pi / lambda; % wavenumber
+
+dz = Lz / (N - 1);
+dx = Lx / (N - 1);
+dkx = 2 * pi / Lx;
+
+z = 0:dz:Lz;
+x = -Lx/2:dx:Lx/2;
+kx = -pi/dx:dkx:pi/dx;
+
+E = A * exp(-(x / r).^2); % Gaussian beam
+% E = A * rect(x / (2 * r)); % uniform beam
+
+dn = @(E) (10^-3) * abs(E).^2; % change of refractive index vs field
+
+I = zeros(N, N); % resulting intensity
+for n = 1:N
+    E = exp(-1i * k0 * dn(E) * dz) .* ifft(fftshift(exp(-1i * sqrt(k0^2 - kx.^2) * dz) .* fftshift(fft(E))));
+    I(n, :) = abs(E);    
+end
+
+imagesc(z, x, rot90(I));
+title(sprintf("beam amplitude = %.1f. Beam radius = %.1f mm", A, r))
+xlabel("z, mm")
+ylabel("x, mm")
+colorbar