Self-focusing and defocusing phenomena of super-Gaussian laser beams in plasmas carrying density gradient

Considering nonlinearities due to relativistic mass variation and ponderomotive force driven depression in the electron density, a model is developed for the self-focusing of a super-Gaussian laser beam in inhomogeneous plasmas. Since paraxial ray approximation is not appropriate for the beams of super-Gaussian profile, the formulation is developed based on the moment theory. To have an in-depth understanding of self-focusing and defocusing phenomena and to develop generalized treatment, three different types of plasma density profiles namely linear, tangent and exponential density profiles, are considered and the results are compared. Due to the saturating nature of nonlinear permittivity with laser intensity, the beam is found to undergo periodic focusing because of competition between the diffraction divergence and nonlinear self-focusing effects. The ponderomotive nonlinearity enhances the self-focusing. As the super-Gaussian beam moves into higher density plasma region up to several Rayleigh lengths, stronger self-focusing is achieved and the value of minimum spot size decreases.