Collective effect of preformed plasma channel and plasma density ramp on second harmonic generation of Laguerre-Gaussian laser beam in plasma

Present study demonstrates the relativistic optical guiding of Laguerre-Gaussian laser beam in preformed plasma channel with density ramp. Relativistic nonlinearity leads to electronic mass variation when the plasma electrons oscillate at high velocities close to the light's velocity. Focusing is always contradicted by the diffractive nature of the laser beam. Preformed plasma channel and an exponential density ramp have been used to overcome natural diffraction of laser and thus lead to arrest power loss. Studies have also been done on the incident laser beam's second harmonic generation. Laguerre-Gaussian profile of the laser beam is taken into account which is a non-uniform kind of irradiated intensity along the laser wavefront. Laser self-focusing has been detected from the differential equation which itself has been derived by the method of moments where different moments of the laser field signify different physical quantities. Numerical results have been obtained by Runge-Kutta 4th-order method. It has been determined that the density transition and the plasma channel both significantly increase the second harmonic yield of the incident laser beam. It is further observed that the different modes (Lmn)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(L_m<^>n)$$\end{document} of the LG laser beam are more productive for harmonic generation than the Gaussian beam.