Second harmonic generation of self-focused Cosh-Gaussian laser beam in collisional plasma

This paper presents theoretical investigation of effect of self-focusing of Cosh-Gaussian (ChG) laser beam on second harmonic generation (SHG) in collisional plasma. Due to non uniform intensity distribution along the wave front of ChG laser beam non uniform Ohmic heating of plasma electrons takes place. Non uniform heating of plasma the laser beam leads to self-focusing of the laser beam which in turn produces strong density gradients in the transverse direction. The generated density gradients excite electron plasma wave at pump frequency that interacts with the incident laser beam to produce its second harmonics. Following moment theory approach in Wentzel–Kramers–Brillouin (W.K.B) approximation second order differential equation governing the evolution of spot size of laser beam with distance of propagation has been derived. Numerical simulations have been carried out to investigate the effect of laser intensity as well as plasma parameters on self-focusing of the laser beam and also on yield of second harmonics. Results predict that ChG laser beams show smaller divergence as they propagate and, thus, lead to enhanced conversion efficiency of second harmonics.