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 ATF eLog Not logged in Message ID: 763     Entry time: Sat May 8 17:24:55 2010
 Author: Zach Type: Misc Category: General Subject: function for calculating parameters of an arbitrary cavity

EDIT: I found a small error in the code. I was not including the right factors of r(j) for the transmitted fields in the line beginning coefs_e(:,j) = ... . This has been fixed now.

I made a MATLAB function that will calculate and plot a reflection/transmission spectrum for an arbitrary cavity (any number of mirrors, any distances between them). The m file is attached, and I have pasted the documentation below for reference. I figured it might be useful for this oft-encountered calculation.

Here is a sample output for the aLIGO PMC: %ARBCAV - ARBitrary CAVity calculator

%Zach Korth - 05/08/2010

%

%arbcav(T,L,loss,lambda,num_pts) takes information about an arbitrary cavity

%and returns a transmission/reflection coefficient spectrum for the cavity,

%as well as the finesse.

%

% Arguments:

%

%   T: vector containing the power transmission coefficients (i.e. T(i) = T

%   of the ith mirror)

%

%   L: vector containing distances between mirrors (i.e. L(1) = distance

%   from mirror 1 to mirror 2; final element is the distance from the last

%   mirror back to mirror 1). Note that for a linear cavity you must

%   treat the return leg as an extra distance (e.g. for a linear 2-mirror

%   cavity of 1-m length, L = [1 1], etc).

%

%   loss: power loss of each mirror--assumed to be the same for all

%

%   lambda: nominal laser wavelength

%

%   num_pts: number of points for scan

%

% Outputs:

%

%   finesse: duh

%

%   coefs: a matrix of size(num_pts,length(L)) containing the power

%   coupling coefficients between the input coupler (mirror 1) and each

%   cavity mirror (i.e. coefs(:,1) = the cavity reflection coefficient,

%   coefs(:,j) = the transmission coefficient between the input coupler and

%   the jth mirror

%

%   delta_f: frequency vector along which to plot coefs(:,i)

%

 Attachment 2: arbcav.m  2 kB  Uploaded Mon May 10 17:35:56 2010
```function [finesse,coefs,delta_f] = arbcav(T,L,loss,lambda,num_pts)
%ARBCAV - ARBitrary CAVity calculator
%Zach Korth - 05/08/2010
%
%arbcav(T,L,loss,lambda,num_pts) takes information about an arbitrary cavity
%and returns a transmission/reflection coefficient spectrum for the cavity,
%as well as the finesse.
%
% Arguments:
%
```
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