brknvddll/beam-propagation-method
1
0
Fork 0
Code Issues Pull Requests Actions Packages Projects Releases Wiki Activity

Add files via upload

Browse Source
This commit is contained in:
BrokenVoodooDoll
2021-01-29 19:09:50 +03:00
committed by GitHub
parent d0773c9435
commit 3d45750509
10 changed files with 472 additions and 0 deletions
Download Patch File Download Diff File Expand all files Collapse all files

51
GRIN_lens.m Normal file
View File

@@ -0,0 +1,51 @@
clc
clear
%% User choices %%
lambda = 1; % wavelength in um
N = 2^10; % number of points
Lz = 600; % z-limit of visualization in um
Lx = 600; % x-limit of visualization in um
r = 50; % radius of the beam in um
l_start = 150; % z-coordinate of the input surface of the lens
l_end = 250; % z-coordinate of the output surface of the lens
p = 0.01; % parameter of the lens
%%%%%
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 = exp(-(x / r).^2); % Gaussian beam
% E = rect(x / (2 * r)); % uniform beam
l_width = l_end - l_start; % width of the gradient lens
dn = @(x, z) -0.5 * p^2 * x.^2 * rect((z - l_start - (l_width / 2)) / l_width); % function of the GRIN lens
I = zeros(N, N); % resulting intensity
for n = 1:N
E = exp(-1i * k0 * dn(x, dz * n) * dz) .* ifft(fftshift(exp(-1i * sqrt(k0^2 - kx.^2) * dz) .* fftshift(fft(E))));
I(n, :) = abs(E);
end
figure
imagesc(z, x, rot90(I))
colorbar
title(sprintf("Beam radius = %.1f {\\mu}m. Lens start = %.1f {\\mu}m. Lens end = %.1f {\\mu}m. Lens parameter = %.3f", r, l_start, l_end, p))
xlabel("z, mm")
ylabel("x, mm")
line([l_start l_start], [-Lx/2 Lx/2], 'Color','red','LineStyle','--');
line([l_end l_end], [-Lx/2 Lx/2], 'Color','red','LineStyle','--');
% colormap(gray)

45
axicon.m Normal file
View File

@@ -0,0 +1,45 @@
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)

76
axicon_telescope.m Normal file
View File

@@ -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','--');

49
bragg.m Normal file
View File

@@ -0,0 +1,49 @@
clc
clear
%% User choices %%
lambda = 1; % wavelength in um
N = 2^9; % number of points
Lz = 3000; % z-limit of visualization in um
Lx = 1500; % x-limit of visualization in um
r = 240; % radius of the beam in um
phi = 7 % incident angle of the beam in degrees
T = lambda / (2 * sind(phi)); % period of the grating in um
% T = 5 * lambda;
g_start = 500; % z-coordinate of the input surface of the grating
g_end = 1000; % z-coordinate of the output surface of the grating
%%%%%
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;
tau = exp(-1i * k0 * sind(phi) * x); % phase function of the grating
E = exp(-(x / r).^2) .* tau;
%E = rect(x / (2*r)) .* tau; %uniform beam
g_width = g_end - g_start; % width of the gradient grating
dn = @(x, z) 0.001 * rect((z - g_start - (g_width / 2)) / g_width) * cos(2 * pi / T * x);
I = zeros(N, N); % resulting intensity
for n = 1:N
E = exp(-1i * k0 * dn(x, dz*n) * dz) .* ifft(fftshift(exp(-1i * sqrt(k0^2 - kx.^2) * dz) .* fftshift(fft(E))));
I(n, :) = abs(E);
end
figure
imagesc(z, x, rot90(I))
colorbar
title(sprintf("Beam radius = %.1f {\\mu}m. Incident angle = %.1f{\\deg} Grating start = %.1f {\\mu}m. Grating end = %.1f {\\mu}m. Grating period = %.3f {\\mu}m", r, phi, g_start, g_end, T))
xlabel("z, mm")
ylabel("x, mm")
line([g_start g_start], [-Lx/2 Lx/2], 'Color','red','LineStyle','--');
line([g_end g_end], [-Lx/2 Lx/2], 'Color','red','LineStyle','--');

48
gradient_glass.m Normal file
View File

@@ -0,0 +1,48 @@
clc
clear
%% User choices %%
lambda = 1; % wavelength in um
N = 2^10; % number of points
Lz = 2000; % z-limit of visualization in um
Lx = 600; % x-limit of visualization in um
r = 60; % radius of the beam in um
g_start = 500; % z-coordinate of the input surface of the glass
g_end = 1500; % z-coordinate of the output surface of the glass
p = 0.07; % parameter of the glass
%%%%%
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 = exp(-(x / r).^2); % Gaussian beam
%E = rect(x / (2 * r)); % uniform beam
g_width = g_end - g_start; % width of the gradient glass
dn = @(x, z) p * rect((z - g_start - (g_width / 2)) / g_width) * (x / Lx); % function of the gradient glass
I = zeros(N, N); % resulting intensity
for n = 1:N
E = exp(-1i * k0 * dn(x, dz*n) * dz) .* ifft(fftshift(exp(-1i * sqrt(k0^2 - kx.^2) * dz) .* fftshift(fft(E))));
I(n, :) = abs(E);
end
figure
imagesc(z, x, rot90(I))
colorbar
title(sprintf("Beam radius = %.1f {\\mu}m. Glass start = %.1f {\\mu}m. Glass end = %.1f {\\mu}m. Medium parameter = %.3f", r, g_start, g_end, p))
xlabel("z, mm")
ylabel("x, mm")
line([g_start g_start], [-Lx/2 Lx/2], 'Color','red','LineStyle','--');
line([g_end g_end], [-Lx/2 Lx/2], 'Color','red','LineStyle','--');
% colormap(gray)

38
kerr_effect.m Normal file
View File

@@ -0,0 +1,38 @@
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

41
lens.m Normal file
View File

@@ -0,0 +1,41 @@
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)

3
rect.m Normal file
View File

@@ -0,0 +1,3 @@
function r = rect(x);
r = 0.5 * (sign(x + 0.5) - sign(x - 0.5));
end

69
telescope.m Normal file
View File

@@ -0,0 +1,69 @@
clc
clear
%% User choices %%
x_max = 2; % maximum x in mm
f1 = 100; % focal length of the 1st lens of the telescope in mm
f2 = 100; % focal length of the 2nd lens of the telescope in mm
r = 0.5; % radius of the beam in mm
lambda = 1e-3; % wavelength in mm
N = 2^10; % number of points
%%%%%
k0 = 2 * pi / lambda; % wavenumber
Lz = 2 * (f1 + f2); % 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; % z coordinate array
x = -Lx/2:dx:Lx/2; % x coordinate array
kx = -pi/dx:dkx:pi/dx; % kx coordinate array
tau1 = exp(1i * k0 * x.^2 * 0.5 / f1); % 1st lens phase function
tau2 = exp(-1i * k0 * x.^2 * 0.5 / f2); % 2nd lens phase function
E = exp(-(x / r).^2); % Gaussian beam
% E = rect(x / (2 * r)); % Uniform beam
t = 0; % iterator for z
n = 1; % counter
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);
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);
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);
t = t + dz;
n = n + 1;
end
figure
imagesc(z, x, rot90(I))
line([f1 f1], [-x_max x_max], 'Color','red','LineStyle','--');
line([2*f1+f2 2*f1+f2], [-x_max x_max], 'Color','red','LineStyle','--');
colorbar
title(sprintf("Kepler telescope with {f_1 =} %.2f mm and {f_2} = %.2f mm", f1, f2))
xlabel("z, mm")
ylabel("x, mm")
% colormap(gray)

52
two_beams.m Normal file
View File

@@ -0,0 +1,52 @@
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)