Cross-focusing of two hollow Gaussian laser beams in plasmas

This article presents the cross-focusing of two high power dark hollow Gaussian beams in plasma when relativistic nonlinearity is operative. A paraxial like approach has been used in the present analysis. In this study, the non-linear dielectric function has been expanded in terms of radial distance from the maximum of the irradiance, rather than from the axis, as is the case of Gaussian beams. The nature of propagation of a hollow Gaussian beam propagating in plasmas has been studied under the influence of relativistic non-linearity. The effect on the order (n) of hollow Gaussian beam on the cross-focusing of two beams has been explored in relativistic non-linearity in this publication.