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two_beams.m

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+clc
+clear
+
+%% User choices %%
+lambda = 1; % wavelength in um
+k0 = 2 * pi / lambda; % wavenumber
+N = 2^10; % number of points
+Lz = 1000; % z-limit of visualization in um
+Lx = 1200; % x-limit of visualization in um
+
+x0_1 = 200; % x-position of the 1st beam in um
+x0_2 = -200; % x-position of the 2nd beam in um
+
+r_1 = 60; % radius of the 1st beam in um
+r_2 = 60; % radius of the 2nd beam in um
+
+t_1 = 10; % tilt of the 1st beam in degrees
+t_2 = 10; % tilt of the 2nd beam in degrees
+%%%%%
+
+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;
+
+%% Gaussian beam %%
+E1 = exp(-((x - x0_1) / r_1).^2 + 1i * k0 * sind(t_1) * x); 
+E2 = exp(-((x - x0_2) / r_2).^2 - 1i * k0 * sind(t_2) * x);
+%% Uniform beam %%
+% E1 = rect((x - x0_1) / (2 * r_1)) .* exp(1i * k0 * sind(t_1) * x); 
+% E2 = rect((x - x0_2) / (2 * r_2)) .* exp(-1i * k0 * sind(t_2) * x);
+%%%%%
+E = E1 + E2;
+
+I = zeros(N, N); % resulting intensity
+for n = 1:N
+    E = exp(-1i * k0 * dz) .* ifft(fftshift(exp(-1i * sqrt(k0^2 - kx.^2) * dz) .* fftshift(fft(E))));
+    I(n, :) = abs(E);    
+end   
+
+imagesc(z, x, rot90(I));
+s_1 = "Two crossing beams";
+s_2 = sprintf("First beam: {x_0} = %.1f {\\mu}m; radius = %.1f {\\mu}m; tilt = %.1f{\\deg}", x0_1, r_1, t_1);
+s_3 = sprintf("Second beam: {x_0} = %.1f {\\mu}m; radius = %.1f {\\mu}m; tilt = %.1f{\\deg}", x0_2, r_2, t_2);
+title({s_1; s_2; s_3})
+xlabel("z, {\\mu}m")
+ylabel("x, {\\mu}m")
+colorbar
+% colormap(gray)