MODULATIONAL INSTABILITIES AND OPTICAL SOLITONS DUE TO COMPETITION OFCHI((2)) AND CHI((3)) NONLINEARITIES

Modulational instabilities and optical solitons are analyzed for dispe rsive (or diffractive) media with competing quadratic (chi((2))) and c ubic (chi((3))) nonlinearities. Such a competition between the nonline arities is expected for the parametric interaction between the fundame ntal and second harmonics that originates the so-called cascaded nonli nearity. It is shown that strong interplay between the nonlinearities can occur for both large and small values of the phase mismatch and, f or example, the influence of chi((2)) nonlinearities may have dramatic effect on modulational instability of continuous waves and properties of optical solitons. Solitons supported by such competing nonlinearit es are analyzed, and an exact analytical solution for bright solitons is presented for special relations between parameters. It is also demo nstrated that even a small contribution of quadratic nonlinearity brea ks degeneracy of optical solitons and also make some of them unstable.