Energy exchange during third harmonic generation in multi-mode optical fibers

Abstract

In this paper, analytical solutions in the form of Jacoby functions are found for the first time of the nonlinear set of short-cut equations describing the generation of third harmonics. Additionally, the short-cut equations are extended to a set of equations, where the influences of self-phase modulation and cross-phase modulation on the process of third harmonics generation is taken into account. This nonlinear set correctly describes the processes of energy exchange between two laser beams propagating in multi-mode fibers. We solved this new set and the solutions are again in the form of Jacobi functions. The difference is in the elliptical period present in the new set, where the influence of the intensities of both waves is significant. The three nonlinear processes work simultaneously in cubic media. Thus, the new set of equations describes more precisely the period of energy transfer in the process of third harmonic generation.