Stability criterion of solitons in three wave mixing of chi((2)) nonlinear media

An analytical stability criterion of the fundamental soliton in general three wave mixing of chi((2)) nonlinear media is derived by operator theory for the (1 + 1)D case of spatial planar geometry or pulses, the (2 + 1)D case of circular geometry or pulsed planar waves, and for (3 + 1)D spatiotemporal bullets. The stability characteristics of the fundamental localized wave or soliton are shown to be in contrast with the corresponding CW eigenstates which are all stable. The regime for the stability of the fundamental soliton is found to vary with dimensionality; the low (high) dimensional solitons have a small (large) instability regime. Numerical simulations are also presented, showing the dissipative or oscillatory evolution of unstable localized waves. (C) 1997 Published by Elsevier Science B.V.