Unusual scenarios in four-wave-mixing instability

Abstract

A pump carrier wave in a nonlinear dispersive system may decay by giving birth to blue- and redshifted satellite waves due to modulation or four-wave mixing instability. We analyze situations where the satellites are so different from the carrier wave, that the redshifted satellite either changes its propagation direction $(k<0,$ $\ensuremath{\omega}>0)$ or even gets a negative frequency $(k,\ensuremath{\omega}<0)$. Both situations are beyond the envelope approach and require application of the Maxwell equations.