Instability of Solitons Governed by Quadratic Nonlinearities

Stability of two-wave solitons supported by resonant parametric interactions in a diffractive (or dispersive) optical quadratic medium is investigated analytically and numerically. It is found that the solitons can become unstable when the phase matching between the fundamental and second harmonics is not exactly satisfied. The analytical criterion for the linear instability is presented, and it is revealed that the instability leads to two possible scenarios of the soliton dynamics, either large-amplitude in-phase oscillations of two harmonics or the soliton decay.