Self-focusing of an elliptic-Gaussian laser beam in relativistic ponderomotive plasma using a ramp density profile

Abstract

The propagation characteristics of an elliptic-Gaussian beam in non-uniform plasma have been investigated by taking into account the combined effects of relativistic and ponderomotive types of nonlinearity. Self-trapping, self-phase modulation, and beam width variation with propagation distance are given particular attention in the study. It is observed that the plasma density function significantly affects the propagation behavior of the beam. The beam radius along the x axis and y axis is separately influenced due to the density function, which, as a result of the cross-focusing phenomenon, results in the reduction of the effective beam radius during propagation of the beam. The longitudinal phase shift increases in the present case in comparison to uniform plasma. Self-trapping is also observed, which is, however, not comparable with that of a cylindrically symmetrical Gaussian beam. We have used the variational approach to set up the coupled nonlinear differential equations for the beam width parameters along the x and y axes and the longitudinal phase of the beam.