Highly nonlinear dynamics of third-harmonic generation by focused beams

Abstract

Beams that experience third-harmonic generation (THG) also experience Kerr effects. With Kerr effects, beams do not take simple Gaussian shapes, but exhibit nonlinear dynamics. These nonlinear dynamics have an effect on the THG accumulated by focusing and then diverging beams. We formulate a self-consistent and complete set of nonlinear Schr\"odinger equations for a pair of coupled beams---a fundamental and its third-harmonic. Numerical simulations show that the Kerr nonlinearities allow some third harmonic to propagate to the far-field even for zero or negative phase mismatch. This is because the nonlinear dynamics break the beams' reflection symmetry about the focal plane and therefore increases far-field THG by changing some of the interference from destructive to constructive. THG conversion efficiencies are computed as functions of several beam parameters.