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This work presents an analytical and numerical study for the mutual interaction and propagation of two intense hollow Gaussian laser beams (HGLBs) at difference frequency in a magnetized plasma. This work has been done in the presence of relativistic nonlinearity, which depends on the intensity of both laser beams. In this process, the propagation of both laser beams in the plasma is described by cross-focusing, as the behavior of one laser beam affects that of another laser beam. The nonlinear differential equations for the beamwidth of HGLBs have been obtained within the Wentzel–Kramers–Brillouin (WKB) method and higher-order paraxial theory. The expression for the nonlinear dielectric constant of the plasma has been obtained from the maximum irradiance of the HGLBs. The obtained equations have been solved numerically to explore the effect of the well-established laser and plasma parameters on the focusing of both laser beams in a magnetized plasma. The results have been compared with paraxial ray theory and Gaussian profile of the laser beams. The focusing/intensity of both laser beams increases in the extended paraxial region compared to the paraxial region in the magnetized plasma. The focusing of both laser beams increases even at high values of beam order and electron cyclotron frequency in the extended paraxial region.

This paper presents a scheme for the generation of terahertz (THz) radiation by self-focusing of a cosh-Gaussian laser beam in the magnetized and rippled density plasma, when relativistic nonlinearity is operative. The strong coupling between self-focused laser beam and pre-existing density ripple produces nonlinear current that originates THz radiation. THz radiation is produced by the interaction of the cosh-Gaussian laser beam with electron plasma wave under the appropriate phase matching conditions. Expressions for the beamwidth parameter of cosh-Gaussian laser beam and the electric vector of the THz radiation have been obtained using higher-order paraxial theory and solved numerically. The self-focusing of the cosh-Gaussian laser beam and its effect on the generated THz amplitude have been studied for specific laser and plasma parameters. Numerical study has been performed on various values of the decentered parameter, incident laser intensity, magnetic field, and relative density. The results have also been compared with the paraxial region as well as the Gaussian profile of laser beam. Numerical results suggest that the self-focusing of the cosh-Gaussian laser beam and the amplitude of THz radiation increase in the extended paraxial region compared to the paraxial region. It is also observed that the focusing of the cosh-Gaussian laser beam in the magnetized plasma and the amplitude of the THz radiation increases at higher values of the decentered parameter.