Effect of a thin optical Kerr medium on a Laguerre-Gaussian beam

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.