Generation of second harmonics of self-focused quadruple-Gaussian laser beams in collisional plasmas with density ramp

This paper presents a scheme for generation of second harmonics of intense laser beams propagating through collisional plasmas. In order to see the effect of uniformity as well as nonuniformity of the irradiance over the cross section of the laser beam on yield of generated harmonics, the field distribution in the medium has been expressed in terms of quadruple Gaussian (Q.G) profile instead of Gaussian profile. Moment theory has been adopted to find semi-analytical solution of the wave equation for the slowly varying envelope of the laser beam. When laser beam with frequency omega(0) propagates through plasma it makes the plasma electrons to oscillate at pump frequency omega(0). These oscillations of the plasma electrons in the presence of thermal velocity generate an electron plasma wave (EPW) at frequency omega(0). The generated EPW beats with the pump beam to produce its second harmonics. By using hydrodynamic fluid model of plasma, nonlinear current density for the SHG has been obtained. Emphasis are put on investigation of the effect of various laser and plasma parameters on propagation dynamics of pump beam and conversion efficiency of second harmonics.