Enhanced second harmonic generation of dark hollow Gaussian laser beam in collisionless magneto-plasma

This paper presents an analysis and subsequent discussion of self-focusing and second harmonic generation (SHG) of a dark hollow Gaussian (dhG) laser beam in a magneto plasma, considering ponderomotive non-linearity. As a result of collisionless non-linearity, non-uniform distribution of plasma electrons takes place due to non-uniform irradiance of intensity along the wavefront of the laser beam which leads to the self-focusing of laser beam and production of density gradient in the transverse direction. As a result of density gradient, an electron plasma wave is excited at pump frequency that interacts with the pump beam to produce its second harmonics of frequency twice that of latter. To envision the spot size and dynamics of propagation of dhG laser beam, moment theory in Webtzel-Kramers-Brillouin (WKB) approximation has been used. The nature of self-focusing and second harmonic yield (SHY) is highlighted through critical curves as a plot of dimensionless beam width parameter and power of second harmonic radiation versus the dimensionless distance of propagation. The effect of magnetic field on self-focusing and SHY of various orders of dhG laser beam has also been explored.