Self-focusing of q-Gaussian beam in unmagnetized plasma and its impact on second harmonic generation

Self-focusing of q-Gaussian beam in unmagnetized plasma and its impact on second harmonic generation (SHG) is explored in present work. Here, relativistic nonlinearity is taken in to consideration. The charge carriers get redistributed on account of relativistic nonlinearity. Further, the intensity gradients are generated in transverse direction to propagation of beam. Electron plasma wave (EPW) gets excited at frequency of input wave as a result of these intensity gradients. Excited EPW and input beam interacts nonlinearly thereby producing second har-monics (SHG). The second order ODE for beam width and expression for yield of SHG are derived by adopting WKB & paraxial ray approximations. The established laser and plasma parameters are used for acquiring numerical solutions for these equations. The beam's ability to focus and SHG yield gets improved with increment in intensity of beam, beam radius, plasma density and q -values.