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MathGroup Archive 2001

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fourier transform

  • To: mathgroup at smc.vnet.net
  • Subject: [mg30304] fourier transform
  • From: <c6wang at sciborg.uwaterloo.ca>
  • Date: Wed, 8 Aug 2001 01:33:58 -0400 (EDT)
  • Organization: University of Waterloo
  • Sender: owner-wri-mathgroup at wolfram.com

Dear All, 

I am trying to work out a free space propagation of Gaussian beam. If I do
not use any approximation, I am facing an Oscillating Fourier
integration.  Could you offer me some suggestions?  Following is an
example of my code:

(*                ********************** *)
a=1/.8; (* .8 is the wavelength *)

dd =1000;  (* free space propagation distance is 1000 *)

ff[x]=Exp[-x^2];   (* Gaussian beam *)

FF[\[Omega]_]:=Sqrt[2 \[Pi] ]* FourierTransform [ff[x], x, \[Omega]];

H[\[Omega]_]:=Exp[- I 2 \[Pi] * Sqrt[a^2 - \[Omega]^2]]  dd ;


gg[X_]:=InverseFourierTransform[H[\[Omega]] FF[\[Omega]], \[Omega], X]



(*                 ******                  *)

Best Regards


Connie Wang



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