Spontaneous symmetry breaking in continuous waves, dark solitons, and vortices in linearly coupled bimodal systems

We introduce a model governing the copropagation of two components which represent circular polarizations of light in the optical fiber with relative strength $g=2$ of the nonlinear repulsion between the components, and linear coupling between them. A more general system of coupled Gross–Pitaevskii (GP) equations, with $g\ne 2$ and the linear mixing between the components, is considered too. The latter system is introduced in its one- and two-dimensional (1D and 2D) forms. A new finding is the spontaneous symmetry breaking (SSB) of bimodal CW (continuous-wave) states in the case of $g>1$ (in the absence of the linear coupling, it corresponds to the immiscibility of the nonlinearly interacting components). The SSB is represented by an exact asymmetric CW solution. An exact solution is also found, in the case of $g=3$, for stable dark solitons (DSs) supported by the asymmetric CW background. For $g\ne 3$, numerical solutions are produced for stable DSs supported by the same background. Moreover, we identify a parameter domain where the fully miscible (symmetric) CW background maintains stable DSs with the inner SSB (separation between the components) in its core. In 2D, the GP system produces stable vortex states with a shift between the components and broken isotropy. The vortices include ones with the inter-component shift imposed by the asymmetric CW background, and states supported by the symmetric background, in which the intrinsic shift (splitting) is exhibited by vortical cores of the two components.