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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=fliplr(optics_elements);
% we need to flip all optics elements around x_in as well
n_elements = length(optics_elements);
for i=1:n_elements
optics_elements_backw{i}.x=x_in-optics_elements_backw{i}.x;
% there is a tricky case: if position of any optics element coincides
% with x_in i.e it is 0 in backwards x coordinates (or at index 1) then
% we need to apply abcd matrix of that element in advance.
if ( optics_elements_backw{i}.x == 0)
q_in_backw(1) = q_after_abcd( q_in_backw(1), optics_elements_backw{i}.abcd);
end
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
end
%!test
%! lambda= 1.064E-6 ;
%! f1=0.1526;
%! lns1.abcd=abcd_lens( f1) ;
%! lns1.x= 0.2;
%! f2=0.019;
%! lns2.abcd=abcd_lens( f2) ;
%! lns2.x= lns1.x+ f1 + f2;
%! lns3.abcd=abcd_lens( 0.0629) ;
%! lns3.x= 0.500;
%! q0=-1.5260e-01 + 1.7310e-04i;
%! x0=0.2;
%! optics={lns1,lns2,lns3};
%! x=[0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7];
%! q0=1.8098e-96 + 1.3453e+02i;
%! x0=0;
%! q_test = gbeam_propagation(x,q0,x0,optics);
%!
%! % test beam is the same but starting point is taken midway
%! % and coincides with optics element{1}.x since (x(3) = 0.2)
%! q=gbeam_propagation(x,q_test(3),x(3),optics);
%! assert(q,q_test, -1e-6)
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