Generation of second harmonics of relativistically self-focused q-Gaussian laser beams in underdense plasma with axial density ramp

An investigation on frequency doubling of intense laser beams through the phenomenon of second harmonic generation (SHG) in underdense plasmas has been presented. In order to increase the efficiency of S.H.G the density profile of plasma has been considered in the shape of upward ramp. When laser beam with frequency omega 0 propagates through plasma, it makes the plasma electrons to oscillate at pump frequency. These oscillations of plasma electrons in the presence of thermal velocity generate a plasma wave at frequency omega 0. The generated plasma wave beats with the pump beam to double its frequency. Variational theory has been adopted to find semi analytical solution of the wave equation for the slowly varying envelope of the laser beam. By using hydrodynamic fluid model of plasma, nonlinear current density for 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 the power of generated second harmonics.