Energy-Exchange Interactions between Colliding Vector Solitons

Abstract

We demonstrate experimentally collisions between vector ( Manakov-like) solitons that involve energy exchange at large collision angles, for which scalar solitons pass through one another practically unaffected. PACS numbers: 42.65.Tg, 05.45.Yv Vector solitons consist of two (or more) components that mutually self-trap in a nonlinear medium. They were first suggested by Manakov [1] for the Kerr nonlinearity, which is proportional to the intensity. The Manakov system leads to two coupled cubic nonlinear Schrödinger equations and is integrable and soluble analytically. Temporal Manakov-like solitons were proposed [2] and demonstrated in single mode optical fibers [3], and spatial ones were demonstrated in planar waveguides [4]. Vector solitons were also suggested [5] and observed [6] in a dark-bright form: when one of the components is a bright soliton and the other dark. Following the discovery of photorefractive spatial solitons, vector (Manakov-like) solitons were also suggested in photorefractives. In contrast to the Kerr nonlinearity, the photorefractive nonlinearity is saturable, but coincides with the Kerr nonlinearity in the limit of very low intensities [7]. One form of vector solitons found in photorefractives is of particular interest, because it applies to any noninstantaneous nonlinearity and allows more than two components: vector solitons based on mutual incoherence between the vector constituents [8]. Observations of such two-component vector solitons followed soon thereafter in three realizations: bright-bright, dark-dark, and dark-bright coupled pairs [9]. Finally, vector solitons can be realized as multimode [2,10] and multihump solitons which were recently demonstrated experimentally using the mutual-incoherence method [11].Interactions between solitons are fascinating, since in many aspects solitons interact like particles: they pass through one another [12], undergo elastic collisions [13], and, in saturable nonlinearities [14], undergo fusion [15], fission and annihilation [16], and can even spiral about each other [17]. Soliton interactions depend on the number of soliton components. Thus far, interactions between vector solitons were studied theoretically only [1,18,19], with the exception of one experiment demonstrating a bound state between two dark-bright solitons [20].Here, we demonstrate experimentally interactions between vector solitons, highlighting features that are nonexistent for scalar solitons in the same regime: energy exchange at large collision angles, that is, in the regime where scalar solitons simply pass through each other [12].Consider the coupled nonlinear wave equations for the slowly varying amplitudes of two EM fields, A͑x, z͒ and B͑x, z͒, in a ͑1 1 1͒D system in which x and z are the transverse and longitudinal coordinates, respectively, µ ≠ ≠z 2 i 2k ≠ 2 ≠x 2

Novel energy sharing collisions of multicomponent solitons

“…This interesting collision behaviour has also been experimentally verified in birefringent fibers [28] and in photorefractive media [29]. The most important application of the energy sharing collision property is a theoretical possibility for constructing logic gates for optical computer.…”

Exact Soliton Solutions, Shape Changing Collisions, and Partially Coherent Solitons in Coupled Nonlinear Schrödinger Equations

“…Firstly, the Manakov spatial solitons have been observed in AlGaAs planar waveguides [14] and their collisions involving energy exchange of precisely the type discussed here has been experimentally demonstrated [15]. Also collisions between PCS's of shape changing type as treated here were observed in a photorefractive strontium barium niobate crystal using screening solitons [16].…”

Bright N-Soliton Solutions to the Vector Hirota Equation from Nonlinear Optics with Symbolic Computation

“…Such collisions have some potential applications in nonlinear optics such as the all-optical switching, logic and computation [16,17]. In this paper, we have applied the method used in [18,19] to the VH equation, i.e., (2), which models the m interacting femtosecond soliton pulses simultaneously propagating in a certain type of coupled optical waveguides [20].…”

“…Bright VNLS solitons can exhibit the amplitude-preserving collisions with no energy exchange among all the components and amplitude-changing collisions along with energy exchange among the components, depending on the pre-collision soliton parameters [12 -15]. Recently, amplitude-changing collisions have been observed for c 2012 Verlag der Zeitschrift für Naturforschung, Tübingen · http://znaturforsch.com the spatial Manakov-like solitons in the Kerr and Kerrlike media [16] and temporal ones in the linearly birefringent optical fibers [4]. Such collisions have the potential applications in implementing the all-optical digital computation by virtue of some virtual logic gates [16,17].…”

“…Recently, amplitude-changing collisions have been observed for c 2012 Verlag der Zeitschrift für Naturforschung, Tübingen · http://znaturforsch.com the spatial Manakov-like solitons in the Kerr and Kerrlike media [16] and temporal ones in the linearly birefringent optical fibers [4]. Such collisions have the potential applications in implementing the all-optical digital computation by virtue of some virtual logic gates [16,17]. Based on the work of [12 -14, 17], an indirect method of analyzing the collisions of bright VNLS solitons can be summarized as follows: (i) An N-soliton collision can be decomposed into N(N − 1)/2 pairwise collisions because the multi-soliton collision process has been proved to be pairwise and independent of the order in which the collisions occur [12]; (ii) As (1) admits an SU(m) symmetry, the pairwise soliton collisions with m > 2 components can be reduced to those in the two-component case by a unitary transformation [14]; (iii) Two-soliton collisions of the two-component VNLS solitons are described by a couple of linear fractional transformations (LFTs), by which the operators defined can form a Möbius transformation group [17].…”