  Using a generalized Gaussian beam decomposition method we determine the
propagation of a Laguerre-Gaussian beam that has passed through a thin
nonlinear optical Kerr medium. The orbital angular momentum per photon of the
beam is found to be conserved while the component beams change. As an
illustration of applications, we propose and demonstrate a z-scan experiment
using an $LG_0^1$ beam and a dye-doped polymer film.
