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In the present work, the scheme of optical guiding of the Hermite–Gaussian laser beam and the generation of second-harmonic 2 ω  radiation ( ω  being the frequency of incident beam) is presented in plasma having the preformed collisional plasma channel in which density variation is parabolic. The nonlinear coupling of excited electron plasma wave with the carrier or incident beam results in the production of second harmonics of the latter. The method of moments is used for finding the coupled differential equations for the beam diameter to study the dynamics of the Hermite–Gaussian laser beam in plasma under the effect of the collisional parabolic channel. For numerical simulations, the Runge–Kutta fourth-order numerical method is used. Standard perturbation theory gives the equation for excitation of electron plasma wave which further acts as the source term for the second harmonic generation. The numerical results show that the preformed plasma channel has a significant effect on the guiding as well as on the 2 ω  generation of the Hermite–Gaussian laser beam in plasma.

Study of optical guiding of the Hermite–Gaussian laser beam in preformed collisional parabolic plasma channel and second harmonic generation