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lens.m

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+clc
+clear
+
+%% User choices %%
+x_max = 2; % % maximum x in mm
+r = 2; % radius of the beam in mm
+f = 100; % focal length of the lens
+lambda = 1e-3; % wavelemgth in mm
+N = 2^10; % number of points
+%%%%%
+
+k0 = 2 * pi / lambda; % wavenumber
+Lz = 2 * f; % z-limit of visualization in mm
+Lx = 2 * x_max; % x-limit of visualization in mm
+
+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;
+
+tau = exp(1i * k0 * x.^2 * 0.5 / f); % lens phase function
+
+E = exp(-(x / r).^2) .* tau; % Gaussian beam
+% E = rect(x / (2 * r)) .* tau; % Uniform beam
+
+I = zeros(N, N); % resulting intensity
+
+for n = 1:N
+    E = 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("Focal length = %.1f mm. Beam radius = %.1f mm", f, r))
+xlabel("z, mm")
+ylabel("x, mm")
+colorbar
+% colormap(gray)