1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
|
%----------------------------------------------------------------------------------------------
% PROGRAM: recompose
% AUTHOR: Andri M. Gretarsson
% DATE: 7/10/04
%
% SYNTAX: z=recompose(domain,type,coeffs,[q <,lambda,accuracy>]);
% <...> indicates optional arguments
%
% Calculates the complex field amplitude resulting from summing the specified terms of
% a Hermite or Laguerre Gaussian mode expansion.
%
% INPUT ARGUMENTS:
% ----------------
% domain = the domain over which to do the recomposition. domain is a NxMx2 matrix
% where domain(:,:,1) is the x mesh and domain(:,:,2) is the y mesh
% (or r mesh and theta mesh respectively in the case of a Laguerre Gaussian
% mode expansion).
% type = 'hg' for a Hermite Gaussian mode expansion, and 'lg' for a Laguerre
% Gaussian mode expansion.
% coeffs = the matrix of coefficients in the same form as returned by decompose.m
% q = the complex radius of curvature "q" of the Gaussian basis.
% lambda = wavelength of the light in the Gaussian basis. Default is 1.064 microns
% accuracy = only calculate the coefficients of the decomposition to th
% specified accuracy. For example, if accuracy=0.3, then coeffs(i,j)= 1.4
% would be rounded to 1.3.
%
% OUTPUT ARGUMENTS:
% -----------------
% z(i,j) = Resultant complex field of the recomposed modes at over the domain.
%
% Last updated: July 18, 2004 by AMG
%----------------------------------------------------------------------------------------------
% SYNTAX: z=recompose(domain,type,coeffs,[q <,lambda,accuracy>]);
%----------------------------------------------------------------------------------------------
function z=recompose(domain,type,coeffs,params)
z=zeros(size(domain(:,:,1)));
% HERMITE GAUSSIAN EXPANSION --------------------------------------------------------------------------
if strcmpi(type,'hg')
q=params(1);
if length(params)>=2, lambda=params(2); else lambda=1.064e-6; end
if length(params)>=3, accuracy=params(3); else accuracy=1e-4; end
for s=1:size(coeffs,1)
l=s-1;
for t=1:size(coeffs,2)
m=t-1;
if abs(coeffs(s,t))>accuracy
z=z+HermiteGaussianE([l,m,q,lambda,coeffs(s,t)],domain(:,:,1),domain(:,:,2));
else
coeffs(s,t)=0;
end
end
end
% LAGUERRE GAUSSIAN EXPANSION --------------------------------------------------------------------------
elseif strcmpi(type,'lg')
q=params(1);
if length(params)>=2, lambda=params(2); else lambda=1.064e-6; end
if length(params)>=3, accuracy=params(3); else accuracy=1e-4; end
for s=1:size(coeffs,1)
p=s-1;
for t=1:size(coeffs,2)
m=t-1;
if abs(coeffs(s,t,1))>accuracy
z=z+LaguerreGaussianE([p,m,q,lambda,coeffs(s,t,1)],domain(:,:,1),domain(:,:,2));
else
coeffs(s,t,1)=0;
end
end
end
for s=1:size(coeffs,1)
p=s-1;
for t=2:size(coeffs,2) % skip terms with m=0
m=t-1;
if abs(coeffs(s,t,2))>accuracy
z=z+LaguerreGaussianE([p,-m,q,lambda,coeffs(s,t,2)],domain(:,:,1),domain(:,:,2));
else
coeffs(s,t,2)=0;
end
end
end
end
|
