Generation of second harmonics by a self-focused Hermite-Gaussian laser beam in collisionless 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 omega(0). Interaction of this plasma wave with the pump beam generates the second harmonics of the incident laser beam with frequency 2 omega(0). 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.