Under the combined effect of relativistic and ponderomotive nonlinearity, resonant second harmonic generation of an intense Hermite-Gaussian (H-Gaussian) laser beam in a plasma having upward density ramp profile has been theoretically investigated. Under WKB approximation and with the use of the moment theory approach the coupled differential equations are derived which govern the spot size of the H-Gaussian laser beam. The ponderomotive force creates the density gradient in the background plasma electrons which is responsible for the excitation of the electron plasma wave. The large-amplitude electron plasma wave interacts with the fundamental beam which produces coherent radiations with double the frequency of the incident beam. In addition, the Gouy phase shift is observed for the H-Gaussian laser beam in plasma under the effect of density transition. The analysis shows the vital role of the different modes of the H-Gaussian laser beam and density ramp on the efficiency of generated harmonics and self-phase shift of laser beams in plasma.
In this work, the generation of second harmonics of a Hermite–Gaussian laser beam in collisionless plasma has been presented. On incidence of the Hermite–Gaussian laser beam in plasma, the charge carriers shift from the high field region to the low field region on account of the ponderomotive force which results in the generation of a transverse density gradient in the background plasma which in turn generates plasma waves at incident beam frequency ω0. Interaction of this plasma wave with the pump beam generates the second harmonics of the incident laser beam with frequency 2ω0. The moment theory approach has been used to derive the coupled differential equations for the beam widths of the laser beam in the transverse x- and y-directions which are further solved numerically. The effect of different modes and initial beam widths of the Hermite–Gaussian beam in the x- and y-directions has been investigated for the self-focusing and second harmonic yield (SHY) of the laser beam in plasma. Also, the effect of increasing plasma density is visualized on the self-focusing and SHY of the beam. It has been observed that the SHY significantly depends on different modes and initial widths of the Hermite–Gaussian laser beam as well as on plasma density.
In this paper, the scheme of generation of second harmonics of incident electromagnetic wave having a Hermite–Gaussian intensity profile in an under dense relativistic plasma has been presented. The relativistic mass variation of electrons by the intense electric field of incident beam generates the density gradients in background plasma which further excites the electron plasma wave (EPW) at resonant frequency and coupling of the EPW with the incident beam results in the generation of second harmonics of incident beam. Propagation dynamics of the Hermite–Gaussian laser beam in plasma has been studied by the formulation of differential equation for the spot size of the laser beam with the help of method of moments. Numerical simulations have been carried out to solve the differential equation for the dimensionless beam width parameters. Solution of the nonlinear wave equation for the electric field vector of second harmonics of incident beam gives the expression for second-harmonic yield. It has been observed that second-harmonic yield is affected by the different modes of Hermite–Gaussian laser beam in relativistic plasma.
In the present work, the scheme of optical guiding of the Hermite–Gaussian laser beam and the generation of second-harmonic 2ω 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 2ω generation of the Hermite–Gaussian laser beam in plasma.
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