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Complex Number Ignition Error: Ray transfer matrix analysis

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종성 김
종성 김 2024-8-7
编辑： Torsten 2024-8-7
I'm trying to simulate beam propagation with Ray transfer matrix analysis.
But, the result graphs are not that I expected.(Graph of Beam radius is just flat)
I hope someone could find my mistake.
clear,clc
clear;
clc;
% Parameters
lambda = 632.8e-6; % Wavelength in millimeters (632.8 nm)
w0 = 0.24; % Initial beam waist (0.24 mm)
zR = pi * w0^2 / lambda; % Rayleigh range in mm
z1 = 10; % Position of the first lens (10 mm)
z2 = 250; % Position of the second lens (250 mm)
f1 = -25; % Focal length of the first lens (-25 mm)
f2 = 250; % Focal length of the second lens (250 mm)
% Initial complex beam parameter q0
q0 = vpa(1i * zR);
% Discretize the propagation distance for plotting
z = linspace(0, 500, 1000); % Range from 0 to 500 mm
% Initialize arrays for q, beam radius, and curvature radius
q = zeros(size(z));
wz = zeros(size(z));
Rz = zeros(size(z));
% Calculate q, beam radius, and curvature radius
for i = 1:length(z)
if z(i) <= z1
% Propagation from 0 to 10 mm
ABCD = [1, z(i); 0, 1];
elseif z(i) <= z2
% Propagation from 10 mm to 250 mm through first lens
ABCD = [1, z1; 0, 1] * [1, 0; -1/f1, 1] * [1, z(i) - z1; 0, 1];
else
% Propagation from 250 mm to 500 mm through second lens
ABCD = [1, z1; 0, 1] * [1, 0; -1/f1, 1] * [1, z2 - z1; 0, 1] * [1, 0; -1/f2, 1] * [1, z(i) - z2; 0, 1];
end
q(i) = (ABCD(1,1) * q0 + ABCD(1,2)) / (ABCD(2,1) * q0 + ABCD(2,2));
wz(i) = sqrt(lambda / pi * imag(1/q(i)));
Rz(i) = 1 / real(1/q(i));
end
% Plotting the beam radius along the propagation
figure;
plot(z, wz); % Already in mm
xlabel('Propagation distance z (mm)');
ylabel('Beam radius w(z) (mm)');
title('Gaussian Beam Propagation Through Two Lenses');
grid on;
% Plotting the curvature radius along the propagation
figure;
plot(z, Rz); % Already in mm
xlabel('Propagation distance z (mm)');
ylabel('Curvature radius R(z) (mm)');
title('Curvature Radius of Gaussian Beam Through Two Lenses');
grid on;
% Display final parameters at specific positions
fprintf('Beam waist at 500 mm: %.3f mm\n', wz(end));
fprintf('Curvature radius at 500 mm: %.3f mm\n', Rz(end));

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回答（1 个）

Torsten
Torsten 2024-8-7
编辑：Torsten 2024-8-7
imag(1./q)*lambda/pi
is negative, thus
sqrt(imag(1./q)*lambda/pi)
is complex.
MATLAB does not know how you want it to plot complex numbers (and I don't know either).

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