Abstract

Collisions between solitons are perhaps the most fascinating features of soliton phenomena because the interacting self-trapped wavepackets exhibit many particle-like features [1]. Solitons collisions have been extensively studied theoretically, both for the integrable (1+1)D Kerr case [2] and for the more general case in saturable nonlinearities (see [1] and references therein). Soliton collisions can be classified into two categories: coherent and incoherent interactions. Coherent interactions occur when the nonlinear medium responds to interference effects taking place where the beams overlap. Such collisions occur for all nonlinearities with an extremely fast time response (the optical Kerr effect and the quadratic nonlinearity). In materials with a long response time x (e.g., photorefractives, liquid crystals, and thermal nonlinearity), coherent collisions occur only if the relative phase between the beams is stationary for a time longer than τ [3]. In such media, if the relative phase between the beams varies much faster than τ, then the contribution of the interference terms is averaged out and the surviving terms (in the nonlinear change of the refractive index, Δn) depend only on the sum of the intensities of the beams [4]. This latter case is generally referred to as incoherent collisions [1,4]. The interaction between two solitons can be described through the "Newtonian forces" they exert on one another. For coherent interactions, this force depends on the relative phase between the solitons. For example, two solitons launched in parallel attract (repel) each other if the relative phase between them is zero (π) [1,2,5]. For incoherent interactions, on the other hand, the interference terms do not contribute to Δn (as the relative phase between solitons varies much faster than τ). Thus, the incoherent force between bright solitons in self-focusing media is always attractive, is independent of the relative phase between the solitons, and is weaker than the force in a coherent interaction [4,6]. Thus far, all studies on optical soliton collisions have dealt with solitons propagating in the same general direction.

© 2002 Optical Society of America