(Invited) Quiescent solitary waves in dual-core systems with separated Bragg grating and cubic–quintic nonlinearity

Abstract

The existence and stability of zero-velocity solitons in a dual-core optical fiber, where one core possesses cubic–quintic nonlinearity and the other core is linear with a Bragg grating, are investigated. The frequency spectrum for the model consists of three bandgaps, of which only the central band gap is a genuine one. There are no soliton solutions in the central gap. On the other hand, the upper and lower gaps are filled with two distinct and disjoint families of soliton solutions, termed Type-1 and Type-2 solitons, that differ in their shapes and phase characteristics. When the relative group velocity in the linear core is zero, implicit analytical solutions for Type-1 and Type-2 quiescent solitons are found. For nonzero values of the relative group velocity, soliton solutions can only be found using numerical techniques. The stability of solitons has been analyzed systematically by means of numerical stability analysis. It is found that Type-2 solitons are always unstable. In the case of Type-1 solitons, stability regions are identified in the upper and lower bandgaps. The effects and interplay of the relative group velocity and the Bragg grating-induced linear coupling coefficient on the stability of the solitons are also analyzed.