Soliton Dynamics in a Grating-Assisted Semilinear Dual Core System with Dispersive Reflectivity

Abstract

Bragg grating solitons are investigated in a linearly coupled dual core system, in which one core exhibits Kerr nonlinearity and is equipped with a nonuniform Bragg grating with dispersive reflectivity, while the other core is linear and unperturbed. When relative group velocity in the linear core c is zero, the dispersion relation of the linearized system gives rise to two disjoint gaps in the upper and lower halves of the spectrum. When c ≠ 0, the central gap emerges in the linear spectrum. Soliton solutions do not exist in the central gap but they exist as a continuous family of solutions in the upper and lower gaps. The maximum velocity that solitons can possess in this system is limited by c. An interesting property of the soliton solutions is that the presence of dispersive reflectivity may induce sidelobes in solitons’ profile, however c tends to counteract the formation of sidelobes. The stability of solitons are determined through numerical simulations and vast stable regions are identified both in the upper and lower gaps. The general trend is that when c 0, as the value of coefficient of coupling between the cores increases, the stable region expands and also the stabilization effect of dispersive reflectivity becomes more prominent. However, soliton stability is affected as c and/or soliton velocity δ becomes larger. The interaction (collision) dynamics of stationary (counter-propagating) solitons are investigated by means of systematic numerical simulations and a variety of outcomes are identified. Of particular interest is the fusion of solitons into a quiescent one through in-phase interactions, which is more observed in the lower gap than in its upper counterpart. It is found that in the presence of sidelobes, interactions of solitons strongly depend on their initial separation. Another noteworthy finding is that solitons can merge into single zero velocity (slow moving) solitons as a result of low velocity in-phase (nearly in-phase) collisions.