Propagation properties of a sinh-Gaussian beam in a Kerr medium

The effect of the Kerr nonlinearity on a sinh-Gaussian beam is investigated by using the nonlinear Schrödinger equation (NLS). Based on the method of moments, the evolution of the sinh-Gaussian beam width in the root-mean-square (RMS) sense is analytically described. Numerical simulations indicate that the central parts of each lobe of the sinh-Gaussian beam give rise to initially radial compression and the beam profile redistribution occurs during propagation even though the RMS beam width broadens. The partial collapse of the center parts of each lobe of the beam will appear below the threshold for a global collapse as predicted by the method of moments. The sinh-Gaussian beams eventually convert into sin-Gaussian type beams in Kerr media with low and moderate initial power.