Self-action effects of quadruple-Gaussian laser beams in collisional plasmas and their resemblance to Kepler’s central force problem

Abstract

This paper presents theoretical investigation on the self-action effects of intense laser beams propagating through collisional plasmas. Particularly, the phenomena of self-focussing, self-trapping and self-phase modulation of the laser beam have been investigated in detail. In order to see the effect of uniformity as well as non-uniformity of the irradiance over the cross-section of the laser beam on its propagation characteristics field distribution in the medium has been expressed in terms of quadruple Gaussian (QG) profile instead of Gaussian profile. Following the moment theory approach, the nonlinear partial differential equation for the slowly varying envelope of the laser beam has been reduced to a set of coupled ordinary differential equations for the evolution of beam width and longitudinal phase. The equations so obtained have been solved numerically to envision the effect of laser as well as medium parameters on the propagation characteristics of the laser beam.