Third-order three-wave mixing in single-mode fibers: exact solutions and spatial instability effects

Abstract

Exact solutions are presented to the steady-state coupled-mode equations that govern the nonlinear parametric interaction of a central-frequency wave with a pair of upshifted and downshifted sidebands in isotropic single-mode optical fibers. This solution accounts for pump depletion as well for as a possible phase mismatch among the waves. The existence is predicted of eigensolutions propagating unchanged along the fiber, which may be either spatially stable or spatially unstable, depending on the total power and the propagation-constant mismatch. The presence of spatially unstable eigensolutions dramatically affects the power exchange among the three waves. The physical implications of this instability for the frequency-conversion process, as well as its potential application to all-optical switching, are discussed.