Transformations of gap solitons in linearly coupled Bragg gratings with a mismatch

An optical model based on two linearly coupled Bragg gratings, with equal periodicities and a phase shift 9 between them (mismatch) is considered. For θ = 0, the symmetry-breaking bifurcation of gap solitons (GSs) in this model was investigated before. The objective of the present work is to study an effect of the mismatch on families of symmetric and asymmetric GSs, and bifurcation between them. It is found that the system's bandgap is always completely filled with solitons. The largest velocity of moving solitons, c _max, is found as a function of θ and coupling constant. The mismatch transforms symmetric GSs into quasi-symmetric (QS) ones, in which the two components are not identical, but their peak powers and energies are equal. The QS solitons are stable against symmetry-breaking perturbations as long as asymmetric (AS) solutions do not exist. In addition, the mismatch breaks the spatial symmetry of the GSs, separating peaks in the two components of the soliton, and giving rise to side hump(s) in them. If θ is small, stable AS solitons emerge from their QS counterparts through a supercritical bifurcation. However, for a larger mismatch, the bifurcation may become subcritical. A condition for the stability against oscillatory perturbations is essentially the same as in the ordinary grating: both QS and AS solitons are stable, in this sense, if their intrinsic frequency is positive, i.e., they are stable in a half of the bandgap.