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function q = gbeam_propagation(x_pos, q_in, x_in, optics_elements)
% calculate the 'q' parameter of the Gaussian beam propagating through optical
% 'optics_elements' array along 'x' axis at points 'x_pos'
% takes the gaussian beam with initial q_in parameter at x_in
% x_pos must be monotonic!
q=0*x_pos; % q vector initialization
if any(x_pos >= x_in)
% Forward propagation to the right of x_in
q(x_pos >= x_in) = gbeam_propagation_froward_only(x_pos(x_pos>=x_in), q_in, x_in, optics_elements);
end
if any(x_pos < x_in)
% Backward propagation part the left of x_in
% do it as forward propagation of the reverse beam
x_backw=x_pos(x_pos<x_in);
% now let's reflect the beam with respect to x_in
% and solve the problem as forward propagating.
x_backw=x_in-x_backw;
% now we need to flip x positions
x_backw=fliplr(x_backw);
% reflected beam means inverted radius of curvature or real part of q parameter
q_in_backw = -real(q_in) + 1i*imag(q_in);
optics_elements_backw=optics_elements;
% we need to flip all optics elements around x_in as well
for i=1:length(optics_elements_backw)
optics_elements_backw{i}.x=x_in-optics_elements_backw{i}.x;
end
q_backw = gbeam_propagation_froward_only(x_backw, q_in_backw, 0, optics_elements_backw);
% now we need to flip the radius of curvature again
q_backw = -real(q_backw) + 1i*imag(q_backw);
% final assignment of the backwards propagating beam
% which we need to flip back
q(x_pos<x_in) = fliplr(q_backw);
end
endfunction
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