Phase-dependent collisions of (211)-dimensional spatial solitons

The possibility of using spatial solitary waves for implementation of optical logic and switching has led to a number of experimental and theoretical investigations of the interactions between spatial solitons.1–8 An extensive discussion of geometrical and material alternatives for implementing optical soliton switches was given in Ref. 9. Initial experimental work in this area centered on Kerr or saturable Kerr-type nonlinearities in which phasedependent attraction and repulsion of one-dimensional, planar soliton beams was observed in media with a selffocusing nonlinearity.2,3 Related studies of dark soliton dynamics in self-defocusing media have also been reported.7 During the past few years steady-state self-focusing and formation of spatial solitons in photorefractive media have been reported by several groups.10–12 Interest in photorefractives in the context of spatial switching stems in part from the possibility of soliton propagation at relatively low levels of optical power. Self-focusing effects, and convergence to solitary profiles, have been observed for beams at the microwatt-power level, which is significantly lower than that required in traditional Kerr-type media. The interaction of both mutually coherent13–15 and mutually incoherent16,17 solitons has been studied. Mutually coherent beams exhibit attractive or repulsive forces, depending on their relative phase. For particular initial conditions excitation of a higher-order bound dipole state consisting of a pair of beams with p relative phase shift has been demonstrated.18 The interaction of incoherent beams in self-focusing-type media is qualitatively different from that in the coherent case. In the former