SOLITARY 4-WAVE-MIXING STATES IN CHI((3)) MEDIA

We introduce a set of coupled nonlinear Helmholtz equations that inclu de four-wave mixing in a chi((3)) medium. A geometric explanation of p hase matching for four-wave mixing with self-phase modulation is prese nted. The nonlinear phase-matching condition provides a two-dimensiona l parameterization for stationary four-wave-mixing modes. Using physic al constants corresponding to a GaAs sample with a central-frequency m ode at 1.55 mu m and two sidebands with 0.1% frequency detuning, we ca lculate a two-parameter set of fundamental stationary field profiles. In addition, a higher-order stationary mode is presented. Classical co nserved quantities are derived from a Lagrange density. In particular, the Hamiltonian, power, and a skew power related to contributions fro m each sideband for stationary solutions are described by contour plot s over a continuous two-dimensional parameter space. (C) 1997 Optical Society of America.