Emulation of spin-orbit coupling for solitons in nonlinear optical media

We design a framework based on the spatial-domain copropagation of two light beams with mutually orthogonal polarizations and opposite transverse components of carrier wave vectors in a nonlinear waveguide with randomly varying birefringence, the averaging with respect to which introduces an effective Manakov nonlinearity in the system. The corresponding two-component system of nonlinear Schrödinger equations is derived, being similar to the system of coupled one-dimensional Gross-Pitaevskii equations for a binary spin-orbit-coupled Bose-Einstein condensate. The system may also include an effective Rabi coupling (direct linear mixing of the components) and a periodic potential, representing a photonic-crystal structure in the underlying waveguide. For self-focusing and self-defocusing signs of nonlinearity, soliton solutions of several symmetry types are obtained by means of numerical methods, and their stability is investigated, including gap solitons in the case when the periodic potential is present.