sechpulse.m

function u = sechpulse(t,tc,T0,P0,C)
  
% This function computes a hyperbolic secant pulse with the
% specified parameters:
%
%   sqrt(P0)*sech((t-t0)/T)*exp{-i(C/2)*[(t-t0)/T]^2}
% 
% USAGE:
% 
% u = sechpulse (t);
% u = sechpulse (t,tc);
% u = sechpulse (t,tc,T0);
% u = sechpulse (t,tc,T0,P0);
% u = sechpulse (t,tc,T0,P0,C);
% 
% INPUT:
% 
% t     vector of times at which to compute u
% tc    center of pulse (default = 0)
% T0    half width at 1/e intensity of pulse (default = 1)
% P0    peak intensity (|u|^2 at t=t0) of pulse (default = 1)
% C     chirp parameter (default = 0)
% 
% OUTPUT:
% 
% u     vector of the same size as t, representing pulse
%       amplitude

  
if (nargin < 5)
  C = 0;
end
if (nargin < 4)
  P0 = 1;
end
if (nargin < 3)
  T0 = 1;
end
if (nargin < 2)
  tc = 0;
end

% T0 = T0/(2*acosh(sqrt(2)));
% u = sqrt(P0)*sech((t-tc)/T0).*exp(-i*C*(t-tc).^2/(2*T0^2));
u = sqrt(P0) .* sech((t-tc)/T0) .* exp(-1j * C * (t-tc).^2 / (2 * T0^2));