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function [qrefl,qtrans,qcav,prefl,ptrans,pcav]=cav(qin,l,m,lambda,L,R1,R2,r1,r2,l1,l2,n_iter,varargin)
% Propagates a Gaussian beam through a cavity.
% The function returns the q-factors of the reflected beam, the transmitted
% beam and the cavity beam at the first mirror. Also returns the reflected,
% transmitted and intracavity field amplitudes. (Notation: prefl,ptrans,pcav
% refer to the complex field amplitudes from each bounce, not power. Thus the
% total transmitted power, for example, is Ptransmitted = epsilon0*abs(sum(ptrans))^2.
%
% AUTHOR: Andri M. Gretarsson, 2003.
% LAST MODIFIED: 2007 by AMG.
%
% SYNTAX: [qrefl,qtrans,qcav,prefl,ptrans,pcav]=...
% cav(qin,l,m,lambda,L,R1,R2,r1,r2,l1,l2,n_iter <,n,Lmirr,pin>);
%
% INPUT VARIABLES
% ---------------
% R1,R2 = Radii of curvature of the end mirrors. Positive if mirror is
% concave as seen from inside the cavity, negative otherwise.
% (Sides facing outwards are assumed to be flat.) R1 corresponds
% to the input mirror and R2 to the end mirror.
%
% FIGURE:
%
% Input beam Input mirror End Mirror Transmitted beam
% -----------------|(==============)|- - - - - - - - - - -
% Cavity beam
%
% Note: Reflected beam is in same location as the Input beam but
% travels in the opposite direction (away from the cavity).
%
% L = Cavity length
% l,m = TEM_lm Gaussian mode incidnet on the cavity.
% lambda = wavelength
% qin = q of the incoming beam immediately before the input optic
% outward facing side (assumed flat).
% r1 = Reflectoin coefficient (fraction of field _amplitude_ reflected) of input mirror.
% r2 = Reflection coefficient of end mirror.
% l1 = Loss coefficient for a single pass through the input mirror.
% (Fraction of field _amplitude_ lost.)
% l2 = Loss coefficient for a single pass through the end mirror.
% (Fraction of field _amplitude_ lost.)
% n_iter = Number of iterations (cavity traversals) to calculate.
% n = Optional: 1x3 vector of indices of ref. of: mirror substrates,
% cavity medium, external medium.
% Default is n=[1.46,1,1].
% Lmirr = Optional: 1x2 vector of mirror thicknesses (on the optic
% axis). First value corresponds to the input mirror, second to
% the end mirror. Default: Lmirr=[0,0].
% pin = Amplitude factor of the beam entering the cavity
%
% NOTES: In the current version, antireflective coatings on the outside
% faces (flat faces) of the mirrors are assumed to be perfect. This could
% be improved in future versions. Also, the reflectivity and transmissivity
% of the coatings are assumed to be the same for light incident from
% either the substrate side or cavity side of the coating. Clearly, this
% could be improved also.
%
%--------------------------------------------------------------------------
% SYNTAX: [qrefl,qtrans,qcav,prefl,ptrans,pcav]=...
% cav(qin,l,m,lambda,L,R1,R2,r1,r2,l1,l2,n_iter <,n,Lmirr,pin>);
%--------------------------------------------------------------------------
if ( nargin>=13 && ~isempty(varargin{1}) ), n=varargin{1}; else n=[1.46,1,1]; end
if ( nargin>=14 && ~isempty(varargin{2}) ), Lmirr=varargin{2}; else Lmirr=[0,0]; end
if ( nargin>=15 && ~isempty(varargin{3}) ), pin=varargin{3}; else pin=1; end
nsubs=n(1);
ncav=n(2);
noutside=n(3);
L1=Lmirr(1);
L2=Lmirr(2);
% Variable initialization
t1 = sqrt(1-r1^2-l1^2);
t2 = sqrt(1-r2^2-l2^2);
qrefl = zeros(n_iter,1); qcav = zeros(n_iter,1); qtrans = zeros(n_iter,1);
prefl = zeros(n_iter,1); pcav = zeros(n_iter,1); ptrans = zeros(n_iter,1);
% #cav -> immediately inside input mirror travelling towards end mirror
% #refl -> immediately outside input mirror (outside cavity) travelling towards laser
% #trans-> immediately outside end mirror (outside cavity) travelling away from cavity
% Note the poor notation for field amplitudes throughout: prefl, pcav,
% etc. The letter p does NOT mean power in this case!
% Commonly used quantitites
freeL = free(L,ncav);
freeL1 = free(L1,nsubs);
freeL2 = free(L2,nsubs);
mirrR1 = mirr(R1); % input mirror
mirrR2 = mirr(R2); % end mirror
% mirrR1phase=exp(i*2*pi*(nsubs*L1/lambda-floor(nsubs*L1/lambda)));
% mirrR2phase=exp(i*2*pi*(nsubs*L2/lambda-floor(nsubs*L2/lambda)));
% tripphase=exp(i*2*pi*(ncav*L/lambda-floor(ncav*L/lambda)));
mirrR1phase=exp(i*2*pi*(nsubs*L1/lambda));
mirrR2phase=exp(i*2*pi*(nsubs*L2/lambda));
tripphase=exp(i*2*pi*(ncav*L/lambda));
% Prompt reflection
[qrefl(1),prefl(1)]= prop(qin,...
fdie(nsubs,noutside)*freeL1*mirr(-R1)*freeL1*fdie(noutside,nsubs),...
[l,m],-r1*mirrR1phase^2*pin);
qcav(1)=i*1; pcav(1)=0;
qtrans(1)=i*1; pcav(1)=0;
% First entry into cavity
[qcav(2),pcav(2)] = prop(qin,...
sdie(-R1,nsubs,ncav)*freeL1*fdie(noutside,nsubs),...
[l,m],t1*mirrR1phase*pin);
% First transmission through end mirror
[qtrans(2),ptrans(2)] = prop(qcav(2),...
fdie(nsubs,noutside)*freeL2*sdie(R2,ncav,nsubs)*freeL,...
[l,m],t2*tripphase*mirrR2phase*pcav(2));
% First round trip leakage through input mirror
[qrefl(2),prefl(2)] = prop(qcav(2),...
fdie(nsubs,noutside)*freeL1*sdie(R1,ncav,nsubs)*freeL*mirrR2*freeL,...
[l,m],t1*r2*mirrR1phase*tripphase^2*pcav(2));
for s = 3:n_iter+2
[qcav(s),pcav(s)] = prop(qcav(s-1),...
mirrR1*freeL*mirrR2*freeL,...
[l,m],r1*r2*tripphase^2*pcav(s-1));
[qtrans(s),ptrans(s)] = prop(qcav(s),...
fdie(nsubs,noutside)*freeL2*sdie(R2,ncav,nsubs)*freeL,...
[l,m], t2*tripphase*mirrR2phase*pcav(s));
[qrefl(s),prefl(s)] = prop(qcav(s),...
fdie(nsubs,noutside)*freeL1*sdie(R1,ncav,nsubs)*freeL*mirrR2*freeL,...
[l,m],t1*r2*mirrR1phase*tripphase^2*pcav(s));
end
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