Effect of four-wave mixing on copropagating spatial solitons

It is known that in the absence of four-wave mixing, spatial solitons of two frequencies can copropagate stably in a Kerr-law nonlinear medium. We investigate the effect of including four-wave mixing. We show that when phase-matching conditions are satisfied, Stokes and anti-Stokes waves can be generated to produce a new steady-state solution consisting of four copropagating beams. On the other hand, if weak signal beams are injected along with the pump beams, then four-wave mixing can be used to amplify those side beams. When phase-matching conditions are not satisfied, the Stokes and anti-Stokes waves simply propagate as linear modes in the effective waveguides induced by the pump solitons.