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function fs_abcd = abcd_free_space( distance)
fs_abcd=[1, distance; 0,1];
endfunction
function lens_abcd =abcd_lens(focal_distance)
lens_abcd = [1, 0; -1/focal_distance, 1];
endfunction
function qnew=q_afteer_element(q_old,abcd)
qnew=(q_old*abcd(1,1)+abcd(1,2))/(q_old*abcd(2,1)+abcd(2,2));
endfunction
function q = prop_forward(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
%
% all x_pos must be to the right of x_in
if (any(x_pos < x_in))
error('all beam positions must be to the right of the x_in');
end
optics_elements=arrange_optics_along_x(optics_elements);
% Forward propagation to the right of x_in
Np=length(x_pos); % number of 'x' points
Nel=length(optics_elements) ;
q=0*x_pos; % q vector initialization
q_last_calc=q_in;
x_last_calc=x_in; % the furthest calculated point
for i=1:Np
x_pos_i=x_pos(i);
for k=1:length(optics_elements)
% iterates through optics_elements to make sure
% we take them in account for the beam propagation
el=optics_elements{k};
if ( (x_last_calc < el.x) && (el.x <= x_pos_i) )
abcd=abcd_free_space(el.x-x_last_calc);
q_last_calc=q_afteer_element(q_last_calc,abcd);
q_last_calc=q_afteer_element(q_last_calc,el.abcd);
x_last_calc=el.x;
endif
endfor
if (x_pos_i > x_last_calc);
abcd=abcd_free_space(x_pos_i-x_last_calc);
q_last_calc=q_afteer_element(q_last_calc,abcd);
x_last_calc=x_pos_i;
endif
q(i)=q_last_calc;
endfor
end
function optics = arrange_optics_along_x(optics_unsorted)
% arrange optics in proper order so it x position increases with number
N=length(optics_unsorted);
% assign x positions
x=zeros(1,N);
for i=1:N
x(i)=optics_unsorted{i}.x;
end
[xs,indx]=sort(x);
cntr=1;
for i=indx
optics{cntr}=optics_unsorted{i};
cntr=cntr+1;
end
end
function q = prop(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
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) = prop_forward(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 = prop_forward(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
function waste =q2waste(q, lambda)
for i=1:size(q,2)
waste(i)=sqrt (-lambda/pi/imag(1/q(i)));
endfor
endfunction
function radius =q2radius(q, lambda)
for i=1:size(q,2)
radius(i)=(1/real(1/q(i)));
endfor
endfunction
function q=waste_r2q(waste,R,lambda)
q=1/(1/R-I*lambda/pi/waste/waste);
endfunction
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