Pulse-compression and self-focusing of Gaussian laser pulses in plasma having relativistic-ponderomotive nonlinearity

The mathematical model for the propagation of intense laser pulse in a plasma having Gaussian profile is investigated. The model has been formulated considering that the relativistic-ponderomotive nonlinearity dominates over other nonlinearities in the plasma. Model equation for self-compression and self-focusing properties of the laser pulse has been set up and solved by both semi-analytical and numerical methods. The result indicates that due to the effect of group velocity dispersion, diffraction of the laser pulse and the nonlinearity of medium, the pulse width parameter as well as beam width parameter of pulse gets focused at a different normalized distance, and hence the normalized intensity is also deferred at those points. Numerical simulation shows an oscillatory behavior of intensity during propagation in the plasma either having minimum beam radius (r(0)) or having minimum pulse duration (t(0)) depending on the normalized distance.