Stability of Bragg Grating Solitons in a Semilinear Dual Core System With Dispersive Reflectivity

The existence and stability of quiescent Bragg grating solitons in a linearly coupled dual core system, where one core has the Kerr nonlinearity and is equipped with a Bragg grating with dispersive reflectivity and the other core is a linear uniform waveguide, are investigated. When the group velocity in the linear core is zero, the linear spectrum of the system possesses two genuine bandgaps. It is found that soliton solutions exist throughout the bandgaps. When the group velocity in the linear core is nonzero, the linear spectrum contains three gaps, a genuine central gap and an upper and lower gaps that overlap with one branch of continuous spectrum. It is found that solitons do not exist in the central gap. On the other hand, the lower and upper gaps are completely filled with soliton solutions. It is also found that above a certain value of dispersive reflectivity parameter, sidelobes appear in the soliton´s profile. We have found exact analytical expressions for the tails of solitons that agree very well with the numerical solutions. The stability of solitons have been analyzed by means of systematic numerical stability analysis. we have considered the effects and interplay of coupling coefficient, group velocity in the linear core and dispersive reflectivity on the stability of solitons. Vast stable regions have been found in the upper and lower gaps. A key finding is that stronger coupling coefficient tends to enhance the stabilizing effect of dispersive reflectivity. In the vicinity of the stability border, unstable solitons initially radiate some energy and subsequently evolve to a single moving soliton. In some cases, when the group velocity in the linear core is nonzero, the unstable soliton breaks up into two moving solitons. These results demonstrate that stable moving solitons exist in this model.