initial

The optics_toolkit code taken from
http://mercury.pr.erau.edu/~greta9a1/downloads/index.html

the older version is also available at mathwork web site
http://www.mathworks.com/matlabcentral/fileexchange/15459-basic-paraxial-optics-toolkit

1 files changed, 136 insertions, 0 deletions

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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