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, 83 insertions, 0 deletions

diff --git a/transverse/overlap.m b/transverse/overlap.m
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+%----------------------------------------------------------------------------------------------

+% PROGRAM: overlap

+% AUTHOR:  Andri M. Gretarsson

+% DATE:    7/10/04

+%

+% SYNTAX: coeff=overlap(z1,z2,domain <,metric,accuracy>)

+%           <...> indicates optional arguments

+%

+% Calculates the overlap integral of the two functions specified.

+%

+% INPUT ARGUMENTS:

+% ----------------

+% z1        = The values of the first function.  Can be a 1D vector or a 2D matrix

+% z2        = The values of the second function. z1 and z2 must be the same size.

+% domain    = the domain values at which z1 and z2 are specified.  If z1 and z2 are 1D

+%             then domain is a nx2 matrix specifying one x,y pair for each value in z1

+%             and z2. If z1 and z2 are 2D then domain is a nxmx2 array where

+%             domain(:,:,1) and domain(:,:,2) are the x and y meshes corresponding

+%             to the values in z1 and z2. These meshes are often generated using meshgrid.m.

+% metric    = value, vector or matrix by which to multiply the elemental line or area dl or dS.

+%             For example, in 2D polar coordinates the elemental area is dS=r*dr*dtheta so 

+%             metric should be specified as r.

+% accuracy  = round results to the nearest increment of accuracy.  For example, if

+%             accuracy=0.3, then coeff 1.54 would be rounded to 1.5 while coeff=1.56 would be 

+%             rounded to 1.8.

+%

+% OUTPUT ARGUMENTS:

+% -----------------

+% coeff     = the numerical result of the overlap integral.

+%

+% EXAMPLE 1 (cartesian):

+%       [x,y]=meshgrid([0:0.01:2*pi],[0:0.01:2*pi]);

+%       clear domain; domain(:,:,1)=x; domain(:,:,2)=y;

+%       z1=sin(x+y); z2=sin(x+y);

+%       coeff=overlap(z1,z2,domain,1,0.0001)       

+%       z1=sin(x+y); z2=cos(x+y);

+%       coeff=overlap(z1,z2,domain,1,0.0001)

+% 

+% EXAMPLE 2 (polar):

+%       [r,theta]=meshgrid([0.01:0.01:1],[0:0.5:360]*pi/180);

+%       clear domain; domain(:,:,1)=r; domain(:,:,2)=theta;

+%       z1=r;   z2=theta;

+%       subplot(1,3,1); [x,y]=pol2cart(theta,r); h=pcolor(x,y,z1); set(h,'EdgeColor','none'); axis square;

+%       subplot(1,3,2); [x,y]=pol2cart(theta,r); h=pcolor(x,y,z2); set(h,'EdgeColor','none'); axis square;

+%       subplot(1,3,3); [x,y]=pol2cart(theta,r); h=pcolor(x,y,z1.*z2); set(h,'EdgeColor','none'); axis square;

+%       coeff=overlap(z1,z2,domain,r,0.0001)  

+%

+% Last updated: July 18, 2004 by AMG

+%----------------------------------------------------------------------------------------------

+% SYNTAX: coeff=overlap(z1,z2,domain <,metric,accuracy>)

+%----------------------------------------------------------------------------------------------

+function coeff=overlap(z1,z2,domain,varargin)

+

+if nargin>=4;

+    metric=varargin{1};

+    if size(metric)==size(z1)

+        metric=metric(2:end,2:end);

+    end

+else

+    metric=1;

+end

+if nargin>=5; accuracy=varargin{2}; else accuracy=0; end

+if size(z1)~=size(z2), error('z1 and z2 must have same size'); end

+

+if min(size(z1))==1 & min(size(domain))==1              % 1D plot along axis

+    dl=metric.*(domain(2:end)-domain(1:end-1));

+    coeff=sum(z1(2:end).*z2(2:end).*dl)/2;

+end

+if min(size(z1))==1 & size(domain,2)==2                 % 1D plot along arbitrary axis

+    dl=metric.*sqrt((domain(2:end,1)-domain(1:end-1,1)).^2 + (domain(2:end,2)-domain(1:end-1,2)).^2);

+    coeff=sum(z1(2:end).*z2(2:end).*dl)/2;

+end

+if  min(size(z1))>= 2                                   % 2D plot over xy plane

+    coord1=domain(:,:,1); coord2=domain(:,:,2);

+    dcoord1=diff(coord1,1,2); dcoord1=dcoord1(2:end,:);

+    dcoord2=diff(coord2,1,1); dcoord2=dcoord2(:,2:end);

+    dS = metric.*dcoord1.*dcoord2;

+    coeff=sum(sum(z1(2:end,2:end).*z2(2:end,2:end).*dS));

+end

+

+if accuracy~=0

+    coeff=round(coeff/accuracy)*accuracy;

+end
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