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(x_final, q_in, elements)
	q(size(x_final,2))=0;
	for i=1:size(x_final,2)
		x_final_i=x_final(i);
		xend=0;
		q_end=q_in;
		for k=1:size(elements,2) 
			el=nth(elements,k);
			if ( el.x <= x_final_i)
				abcd=abcd_free_space(el.x-xend);
				q_end=q_afteer_element(q_end,abcd);
				q_end=q_afteer_element(q_end,el.abcd);
				xend=el.x;
			endif
		endfor
		if (x_final_i > xend);
			abcd=abcd_free_space(x_final_i-xend);
			q_end=q_afteer_element(q_end,abcd);
			xend=x_final_i;
		endif
		q(i)=q_end;
	endfor
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




########################################## 
lambda= 1.064E-6 ;
Ltot= 1 ;
r0= 1.0E+100 ;
w0= 25.63e-6;
#w0= 3.79E-4 ;
lns1.abcd=abcd_lens( 0.25 ) ;
lns1.x= 0.37680270021479 ;
lns2.abcd=abcd_lens( 0.1 ) ;
lns2.x= 0.90277021575519 ;
rf=1e100;
wf=25.630e-6;
########################################## 
source("answ.txt")


q0=waste_r2q(w0,r0,lambda);
optics=list(lns1,lns2,lns3);
optics_forward=optics;

x=0:.01:Ltot;
printf("=================================\n")
q1=prop(x,q0,optics);
printf("=================================\n")
w1=q2waste(q1, lambda);
r1=q2radius(q1,lambda);

printf("=================================\n")
#q1b=prop(Ltot,q0,optics)
#wb=q2waste(q1b, lambda)
#rb=-q2radius(q1b,lambda)
#because of back propogation
rf=-rf;
q1b=waste_r2q(wf,rf,lambda);

lns1.x=Ltot-lns1.x;
lns2.x=Ltot-lns2.x;
lns3.x=Ltot-lns3.x;
optics=list(lns3,lns2,lns1);
q2b=prop(x,q1b,optics);
printf("=================================\n")
wb=q2waste(q2b, lambda);
rb=q2radius(q2b,lambda);
xb=Ltot-x;
#plot (x,w1, "1")
plot (x,w1, "1", xb, wb, "2")

printf("=================================\n")
printf("======= final check =============\n")
printf("======= after propogatin ========\n")
printf("following are theoretical values: \n")
w0
r0
wf
rf
q0=waste_r2q(w0,r0,lambda);
optics=list(lns1,lns2,lns3);
qtf=prop(Ltot, q0, optics_forward);
printf("values below should match 'wf' and 'rf': \n")
waste = q2waste(qtf, lambda)
radius = q2radius(qtf,lambda)

pause(100)
quit()
system("cat answ.txt answ.txt")
answ=menu("Is it reasonable mode matching?","yes","no")
if (answ ==1)
	printf("xxxxxxxxxxxxxxxxxxxxxxxxxxxx")
	system("cat answ.txt >>good_mode_matching.txt")
else
	printf("------------------------------")
endif	

exit
#
#gset term postscript
#gset output "foo.ps"
#plot (x,w1, "1", xb, wb, "2")