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