Quantitatively Predicting Third Harmonic Generation for Gaussian Pulses Propagating in Kerr Nonlinear Media

Abstract

Strictly speaking, it is almost impossible to quantitatively predict the third harmonic generation (THG) for high peak power pulses propagating through Kerr nonlinear media, although a theoretical formula has been deduced for a harmonic plane wave. In this paper, we try to quantitatively evaluate the nonlinear effects for the Gaussian pulse by multiply a correction factor to the formula of the harmonic plane wave. Numerical simulations have been performed to measure the THG by using the nonlinear finite-difference time-domain method to simulate the nonlinear propagations of the Gaussian pulses. It is found that the correction factor multiplied to THG changes obviously with the variation of the pulse parameters such as the pulse width and amplitude. However, interestingly, the other factor multiplied to the THG conversion efficiency, which is defined as the intensity ratio of the third harmonic wave to the fundamental wave, is nearly independent of these parameters of the Gaussian pulse. Our results may offer a method to calculate the THG for the nonlinear propagation of Gaussian pulses.