Generation of second harmonics of q-Gaussian laser beams in collisional plasma with upward density ramp

An investigation of frequency up-conversion of a laser beam through the phenomenon of second harmonic generation (SHG) in collisional plasma with an upward density ramp is presented. The variational method has been adopted to find a semi-analytical solution of the wave equation for the slowly varying envelope of the laser beam. When a laser beam with frequency omega(0) propagates through plasma it causes 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 a hydrodynamic fluid model of plasma, the source term for the SHG has been obtained. Emphasis is put on investigation of the effect of various laser and plasma parameters on the propagation dynamics of the pump beam and the conversion efficiency of second harmonics.