Nonlinear relativistic self-focusing of laser radiation in plasmas: Arbitrary intensity

Abstract

A paraxial theory of relativistic self-focusing of a Gaussian laser beam in plasmas, when the nonlinear part of the effective dielectric constant is arbitrarily large, is presented. The plasma is taken to be homogeneous without any density fluctuations being necessary. The approach of Akhmanov et al. based on the WKB and paraxial ray approximations has been followed. It is seen that the saturating nature of nonlinearity leads to two values of critical power of the beam (Pcrl and Pcr2) for self-focusing. When the power of the beam P lies between the two critical values (i.e., Pcr1 < P < Pcr2), the medium behaves as an oscillatory waveguide; the beam first converges and then diverges, converges again, and so on. For P > Pcr2 the beam first diverges, then converges, then diverges, and so on. Because the relativistic mechanism is instantaneous, the theory is applicable to the understanding of selffocusing of laser pulses also.