Self-focusing of Hermite-Gaussian laser beam with relativistic nonlinearity

This paper presents an investigation of self-focusing of Hermite-Gaussian laser beams in plasma considering relativistic nonlinearity. The differential equations for beam width parameters are obtained using the usual Wentzel–Kramers–Brillouin and paraxial approximations. The nonlinearity in the dielectric constant is assumed to be aroused mainly due to the relativistic mass correction of electron. To highlight the nature of focusing, graphical results of the behavior of beam-width parameters with the dimensionless distance of propagation is presented. The numerical computation is completed by using Taylor series method. The present work is helpful to understand issues related to the beam propagation in laser plasma interaction experiments.