Relativistic Propagation of Linearly/Circularly Polarized Laser Radiation in Plasmas

Paraxial theory of relativistic self-focusing of Gaussian laser beams in plasmas for arbitrary magnitude of intensity of the beam has been presented in this paper. The nonlinearity in the dielectric constant arises on account of relativistic variation of mass. An appropriate expression for the nonlinear dielectric constant has been used to study laser beam propagation for linearly/circularly polarized wave. The variation of beamwidth parameter with distance of propagation, self-trapping condition, and critical power has been evaluated. The saturating nature of nonlinearity yields two values of critical power of the beam ( and ) for self-focusing. When the beam diverges. When the beam first converges then diverges and so on. When the beam first diverges and then converges and so on. Numerical estimates are made for linearly/circularly polarized wave applicable for typical values of relativistic laser-plasma interaction process in underdense and overdense plasmas. Since the relativistic mechanism is instantaneous, this theory is applicable to understanding of self-focusing of laser pulses.