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axicon.m

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+clc
+clear
+
+%% User choices %%
+lambda = 1; %% wavelength in um
+N = 2^10; % number of points
+Lz = 200; % z-limit of visualization in um
+Lx = 600; % x-limit of visualization in um
+r = 100; % radius of the beam in um
+n0 = 1.5; % refractive index of the axicon
+a = 140; % apex angle of the axicon in degrees
+%%%%%
+
+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;
+
+%% Axicon parameters %%
+g = 90 - a / 2;
+b = asind(n0 * cosd(a / 2)) + a / 2 - 90;
+p = sind(b);
+%%%%%
+
+tau = exp(1i * k0 * p * abs(x)); % phase function of the axicon
+E = exp(-x.^2 / r^2) .* tau; % Gaussian beam
+% E = rect(x / (2 * r)) .* tau; % uniform beam
+
+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).^2;
+end
+
+imagesc(z, x, rot90(I));
+title(sprintf("Beam radius = %.1f {\\mu}m. Apex angle = %.1f{\\deg}. Refractive index = %.1f", r, a, n0))
+xlabel("z, mm")
+ylabel("x, mm")
+colorbar
+%colormap(gray)