  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 Schroedinger 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.
