# (Bessel Beam) Wave vector question

1. Jan 7, 2010

### kire

Hello, first post on these forums... I read up on the rules and such but please excuse me if i missed something.

I am making a simulation of a bessel beam (non-diffracting and self healing) in MatLab but I do not know how to define the wave vector. More specifically, the transverse (kT) and the propagation constant (kz). If i can find one of them, I can solve for the other.

The "governing" equation I am using is:

U(r)=J0(kT*rho)*exp(-j*kz*z)

J0 is the zero order Bessel function of the first kind, rho is just sqrt(x^2+y^2), j is imaginary number, z is distance along the z-axis.

The relationship between the wave vectors is:

kT2+kz2=k2

Now, a fellow labmate initially had told me that for a gaussian beam, you usually set z=0 and solve for kz because at the z=0 plane, all the wave vectors point only in the z-direction and thus kT=0. However this will not work because if z=0 and kT=0 then the equation above yields a plane wave.

This is just a summary of my problem . If you need more information, I will be happy to provide it.