Self-focusing of Gaussian laser beam in weakly relativistic and ponderomotive cold quantum plasma

Abstract

The paper presents investigation on self-focusing and self-phase modulation of Gaussian laser beam in a weakly relativistic and ponderomotive regime by taking into account the quantum effects. We have reported additional self-focusing for reduced value of beam width parameter on account of nonlinear dielectric contribution of relativistic ponderomotive plasma. Moreover, the significant contribution of the quantum effects to enhance the self-focusing and minimize the longitudinal phase shift has been noticed. A comparison has also been attempted with relativistic and ponderomotive, relativistic cold quantum and classical relativistic regimes. In the present investigation, we have observed that for the case of relativistic ponderomotive cold quantum plasma, the focusing is found to be earlier and strongest. Also, the minimum amount of phase shift is obtained. We have setup the nonlinear differential equations for the beam-width parameter and self-phase modulation by using variational approach and solved them numerically by the Runge-Kutta method.