Add files via upload

axicon_telescope.m

@@ -0,0 +1,76 @@
+clc
+clear
+
+%% User choices %%
+lambda = 1.064e-3; % wavelength in mm
+f1 = 80; % focal length of the 1st lens in mm
+f2 = 80; % focal length of the 2nd lens in mm
+N = 2^10; % number of points
+Lz = 2 * (f1 + f2); % z-limit of visualization in mm
+Lx = 10; %  x-limit of visualization in mm
+
+r = 1.5; % radius of the beam in mm
+n0 = 1.5; % refractive index of the axicon
+a = 176; % axicon apex angle 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
+tau1 = exp(1i * k0 * x.^2 * 0.5 / f1); % phase function of the 1st lens
+tau2 = exp(1i * k0 * x.^2 * 0.5 / f2); % phase function of the 2nd lens
+
+E = exp(-(x / r).^2) .* tau; % Gaussian beam
+%E = rect(x / (2 * r)) .* tau; % uniform beam
+
+n = 1; % counter
+t = 0; % current z-coordinate
+
+I = zeros(N, N); % resulting intensity
+while t <= f1
+    E = exp(-1i * k0 * dz) .* ifft(fftshift(exp(-1i * sqrt(k0^2 - kx.^2) * dz) .* fftshift(fft(E))));
+    I(n, :) = abs(E).^2;
+    t = t + dz;
+    n = n + 1;
+end
+
+E = E .* tau1;
+
+while t <= 2 * f1 + f2
+    E = exp(-1i * k0 * dz) .* ifft(fftshift(exp(-1i * sqrt(k0^2 - kx.^2) * dz) .* fftshift(fft(E))));
+    I(n, :) = abs(E).^2;
+    t = t + dz;
+    n = n + 1;
+end
+
+E = E.*tau2;
+while t <= 2 * (f1 + f2)
+    E = ifft(fftshift(exp(-1i * sqrt(k0^2 - kx.^2) * dz) .* fftshift(fft(E))));
+    I(n, :) = abs(E).^2;
+    t = t + dz;
+    n = n + 1;
+end
+
+imagesc(z, x, rot90(I), [0 4]);
+colorbar
+s_1 = sprintf("Kepler telescope with {f_1 =} %.2f mm and {f_2} = %.2f mm", f1, f2);
+s_2 = sprintf("Beam radius = %.1f mm. Apex angle = %.1f{\\deg}. Refractive index = %.1f", r, a, n0);
+title({s_1; s_2})
+xlabel("z, mm")
+ylabel("x, mm")
+line([f1 f1], [-Lx/2 Lx/2], 'Color','red','LineStyle','--');
+line([2*f1+f2 2*f1+f2], [-Lx/2 Lx/2], 'Color','red','LineStyle','--');