Abstract

We introduce a set of coupled nonlinear Helmholtz equations that include four-wave mixing in a χ(3) medium. A geometric explanation of phase matching for four-wave mixing with self-phase modulation is presented. The nonlinear phase-matching condition provides a two-dimensional parameterization for stationary four-wave-mixing modes. Using physical constants corresponding to a GaAs sample with a central-frequency mode at 1.55 µm and two sidebands with 0.1% frequency detuning, we calculate a two-parameter set of fundamental stationary field profiles. In addition, a higher-order stationary mode is presented. Classical conserved quantities are derived from a Lagrange density. In particular, the Hamiltonian, power, and a skew power related to contributions from each sideband for stationary solutions are described by contour plots over a continuous two-dimensional parameter space.

© 1997 Optical Society of America

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