Third harmonic generation of a relativistic self-focusing laser in plasma under exponential density ramp

Present study focuses on self-focusing and its effect on third harmonic generation (THG) of a Gaussian laser beam in plasma under the influence of exponential density ramp. Relativistic nonlinearity has been taken into account which is aroused due the modification of electron’s mass in the presence of high intensity laser. Under strong ponderomotive force, electrons acquire very high quiver velocity and mass variation takes place. Equations for beam width parameter of incident laser and the amplitude of THG have been derived under WKB and paraxial ray approximation, and solved them numerically. It is found that the presence of exponential plasma density ramp results strong self-focusing of laser which further leads to enhance the efficiency of THG. Wiggler magnetic field adds an additional momentum to the photons of third harmonic due to which appreciable gain is observed in the normalized amplitude of THG. Significant enhancement in the THG amplitude has been reported in the presence of exponential density ramp for optimum values of intensity of incident laser, wiggler magnetic field and plasma frequency.