Effect of self-focusing of an intense cosh-Gaussian laser beam on second harmonic generation in a collisionless plasma: Higher-order paraxial theory

Abstract

This paper presents the study of second harmonic generation in a collisionless plasma by an intense self-focused cosh-Gaussian laser beam under the combined effect of relativistic and ponderomotive nonlinearities. The second harmonics of a cosh-Gaussian laser beam is generated by the excitation of an electron plasma wave at the pump frequency. The excited electron plasma wave coupled with the pump laser beam and generate the radiation of double frequency. This study is carried out in a higher-order paraxial ray approximation where higher order terms are taken into account in the expansion of the dielectric function and the eikonal. Nonlinear differential equations have been established for the self-focusing of cosh-Gaussian laser beam in the plasma, the generation of electron plasma wave at the pump frequency, and the second harmonic generation. Numerical simulations have been carried out to investigate the effects of laser and plasma parameters such as decentred parameter (b), incident laser intensity (a), and relative plasma density (ωp0/ω0) on the self-focusing of the cosh-Gaussian laser beam and the electric field associated with electron plasma wave and second harmonic wave. A well-established set of laser and plasma parameters have been used in numerical analysis. The results show that the focusing of the cosh-Gaussian laser beam leads to an increase in the electric field of the electron plasma wave and the second harmonic wave. The results are also compared to the paraxial-ray approximation. The focusing of the cosh-Gaussian laser beam in the plasma is strengthened in the higher-order paraxial region, which increases the electric field of both the electron plasma wave and the second harmonic wave at high values of b, a, and ωp0/ω0.