Second harmonic generation of high power laser beam in cold quantum plasma

Second harmonic generation of high power laser beam in cold quantum plasma (CQP) is investigated in present communication. In order to derive 2nd order differential equations governing the behavior of laser beam against normalized distance, paraxial theory and WKB approximation are adopted. There is self-focusing of beam on account of relativistic increase in mass of electron, which further results in production of intensity gradients in transverse direction. The electron plasma wave (EPW) gets excited due to these intensity gradients at pump wave frequency. Further, there is an interaction of EPW with pump beam thereby producing to second harmonics. In order to study the effect of various parameters of laser and plasma medium on self-focusing of pump beam and second harmonic yield, we have carried out numerical simulations. The comparison of present results is made with classical relativistic plasma (CRP).