Abstract
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.
Highlights
The recent progress in the experimental and theoretical work with engineered optical media has made it possible to emulate, by means of the optical-beam propagation, a wide range of physical effects which were originally predicted or experimentally discovered in other areas of physics
Another noteworthy finding is that the spin-orbit coupling (SOC) terms stabilize 2D PT -symmetric solitons under the action of the cubic self-attraction, in spite of the simultaneous presence of two mechanisms driving the catastrophic instability in the 2D system: the possibility of the breakup of the PT symmetry, i.e., failure of the gain-loss balance [2, 10], and the onset of the critical collapse induced by the Kerr nonlinearity [14]
The systems are based on dual-core planar optical couplers with the Kerr nonlinearity in their cores
Summary
The recent progress in the experimental and theoretical work with engineered optical media has made it possible to emulate, by means of the optical-beam propagation, a wide range of physical effects which were originally predicted or experimentally discovered in other areas of physics. New dynamical features are revealed by the analysis of the combined models, such as a nonmonotonous dependence of the stability area of 1D PT -symmetric solitons on the SOC strength, δ: the area originally shrinks but strongly expands with the increase of δ Another noteworthy finding is that the SOC terms stabilize 2D PT -symmetric solitons under the action of the cubic self-attraction, in spite of the simultaneous presence of two mechanisms driving the catastrophic instability in the 2D system: the possibility of the breakup of the PT symmetry, i.e., failure of the gain-loss balance [2, 10], and the onset of the critical collapse induced by the Kerr nonlinearity [14] (the latter may take place in the presence of SOC [15]). Results for 2D solitons are reported in Section V, and the paper is concluded by Section VI
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