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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
+