Solitons in PT-symmetric nonlinear dissipative gratings

We investigate the soliton behaviors of laser beams in two types of two coupled PT-symmetric dissipative gratings which contain different coupling forms (constant coupling and periodic coupling). The dynamics of such systems is governed by coupled nonlinear time-dependent Schrodinger-like equations and the corresponding soliton solutions are obtained. Long-time soliton oscillations are observed in the case of constant coupling, but absent in the case of periodic coupling. The stable regions of the parameters for gain or loss strength and modulation frequency are estimated by the variational method and numerical simulation. It is interesting that the stable region in the parameter space in the periodic-coupling case is wider than that in the constant coupling case.