Solitary waves in systems with separated Bragg grating and nonlinearity

Abstract

The existence and stability of solitons in a dual-core optical waveguide, in which one core has Kerr nonlinearity while the other one is linear with a Bragg grating written on it, are investigated. The system's spectrum for the frequency omega of linear waves always contains a gap. If the group velocity c in the linear core is zero, it also has two other, upper and lower (in terms of omega) gaps. If c not equal to 0, the upper and lower gaps do not exist in the rigorous sense, as each overlaps with one branch of the continuous spectrum. When c=0, a family of zero-velocity soliton solutions, filling all the three gaps, is found analytically. Their stability is tested numerically, leading to a conclusion that only solitons in an upper section of the upper gap are stable. For c not equal to 0, soliton solutions are sought for numerically. Stationary solutions are only found in the upper gap, in the form of unusual solitons, which exist as a continuous family in the former upper gap, despite its overlapping with one branch of the continuous spectrum. A region in the parameter plane (c,omega) is identified where these solitons are stable; it is again an upper section of the upper gap. Stable moving solitons are found too. A feasible explanation for the (virtual) existence of these solitons, based on an analytical estimate of their radiative-decay rate (if the decay takes place), is presented.

Spatial solitons in a medium composed of self-focusing and self-defocusing layers

“…1 shows the hyperbola L + γ + = 1/2, along which the average Kerr coefficient (9) exactly vanishes. The finite separation between the lower stability boundary and the dashed curve can be measured by the average value γ of the Kerr coefficient (9). The smallest value for γ found on the lower boundary is approximately 0.3.…”

“…It has been demonstrated that a part of the family is stable, and another part is unstable [6,7]. Exact gap-soliton solutions can also be found, and their stability can be investigated, in generalized versions of the model (1), (2), which describe a system of parallelcoupled nonlinear and linear fibers with BG written on both of them [8], including also an especially interesting case when BG is written only on the linear core, so that the nonlinearity and BG are separated [9].…”

Interactions of solitons in Bragg gratings with dispersive reflectivity in a cubic-quintic medium

“…To date, solitons with a velocity of 23% of the speed of light in the medium have been experimentally observed [22]. Gap solitons have also been predicted in more sophisticated nonlinear systems such as dual-core fibers equipped with Bragg gratings [23,24], waveguide arrays [25], quadratic nonlinearity [26][27][28], photonic crystals [29][30][31], and cubic-quintic nonlinearity [32,33].…”

Interaction dynamics of Bragg grating solitons in a semilinear dual-core system with dispersive reflectivity

“…It has theoretically been shown that inhomogeneity within BGs such as local defects and apodization may CONTACT Javid Atai javid.atai@sydney.edu.au also be utilized to generate slow or quiescent solitons (14)(15)(16). BG solitons have also been studied in more sophisticated photonic bandgap materials such as waveguide arrays (17), photonic crystals (18,19), dual-core systems (20)(21)(22)(23)(24)(25)(26) as well as diverse nonlinear media such as quadratic nonlinearity (27,28), sign-changing Kerr nonlinearity (29) and cubic-quintic nonlinearity (30)(31)(32)(33) and more recently matter-wave structures such as Bose-Einstein condensate (34,35). In the case of nonuniform gratings, the standard model of BG solitons must be modified to take into account the effect of nonuniformity.…”