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