One- and two-dimensional solitons in P T -symmetric systems emulating spin–orbit coupling

We introduce a two-dimensional (2D) system which can be implemented in dual-core planar optical couplers with the Kerr nonlinearity in its cores, making it possible to blend the effects of symmetry, represented by the balanced linear gain and loss in the two cores, and spin–orbit coupling (SOC), emulated by a spatially biased coupling between the cores. Families of 1D and 2D solitons and their stability boundaries are identified. In the 1D setting, the addition to the SOC terms leads, at first, to shrinkage of the stability area for -symmetric solitons, which is followed by its rapid expansion. 2D solitons have their stability region too, in spite of the simultaneous action of two major destabilizing factors, viz., the collapse driven by the Kerr nonlinearity, and a trend towards the spontaneous breakup of the gain–loss balance. In the limit of the SOC terms dominating over the intrinsic diffraction, the 1D system gives rise to a new model for gap solitons, which admits exact analytical solutions.