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diff --git a/axial/prop.m b/axial/prop.m
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+function [q,p]=prop(q1,abcd,varargin)
+% Propagates a Gaussian beam. [q,p]=prop(q1,abcd <,[l,m],p1>);
+%--------------------------------------------------------------------
+% Propagates a Gaussian beam with complex radius of curvature q1
+% and amplitude factor p1 (optional), according to the ABCD matrix
+% supplied.
+%
+% Returns the new complex beam radius q=(A*q1+B)/(C*q1+D) and the 
+% new amplitude factor p = 1/(A+B/q1)^(1+l+m) by which the field is
+% multiplied. (See eqn 4.7.30 in Principles of Lasers by O. Svelto.)
+% If q1 is a vector q and p will be vectors of the same size.
+%
+% For a Hermite Gaussian l,m are the mode designators.
+% For a Laguerre Gaussian l=2p and m is the usual m.
+%
+% SYNTAX: [q,p]=prop(q1,abcd <,[l,m],p1>);
+%           <...> indicates optional arguments
+%--------------------------------------------------------------------
+
+if ( nargin>=3 && ~isempty(varargin{1}) ), mode=varargin{1}; else mode=[0,0]; end
+if nargin>=4, p1=varargin{2}; else p1=ones(size(q1)); end
+
+A=abcd(1,1);
+B=abcd(1,2);
+C=abcd(2,1);
+D=abcd(2,2);
+
+ell=mode(1);
+emm=mode(2);
+
+q = (A*q1 + B)./(C*q1 + D);
+p = p1.*exp(i*angle(1./(A+B./q1).^(1+ell+emm)));
+\ No newline at end of file