The Effect of Kerr Nonlinearity on a Cosh-Gaussian Beam
R-P. Chen and C-Q. Dai
The nonlinear dynamic properties of a cosh-Gaussian beam in a Kerr medium are investigated analytically and numerically using the nonlinear Schrödinger equation (NLS) in this work. Based on the moments method the evolution of a cosh-Gaussian beam width in the root-meansquare (RMS) sense has been analytically described. The critical powers and beam quality factors of the cosh-Gaussian beams are demonstrated. By using numerical simulation it was found that although the beam RMS width broadens, the central parts of the beam give rise to radial compression and significant redistribution occurs during propagation. The partial collapse of the centre parts of the beam appears below the threshold for a global collapse as predicted by the moments method. When the initial power is low and moderate the cosh-Gaussian beam eventually converts into a cos-Gaussian type beam in Kerr media.
Keywords: Nonlinear optics, Kerr effect, moments method, optical collapse, Hermite-Sinusoidal-Gaussian (HSG) beams.