Modulational instability in vector exciton-polariton condensates with photonic spin-orbit coupling

The paper demonstrates the existence of modulational instability (MI) in nonlinear exciton-polariton condensates (EPCs). A set of coupled two-dimensional (2D) driven-dissipative Gross-Pitaevskii equations describing the spin-up and spin-down polaritons, containing the photonic spin-orbit (SO) coupling and the rate equations describing the density of incoherent excitonic reservoir density, is reduced to a system of two coupled 2D complex Ginzburg-Landau (2DCGL) equations, with saturable nonlinearities for complex polariton order parameters, thanks to the adiabatic approximation and small density fluctuations approximation. The analytical approach relies on the linear stability analysis of continuous waves (CWs) to derive an expression for the growth rate and conduct a parametric study of MI. The effect of different parameters on the growth rate spectrum is discussed with an emphasis on the photonic SO coupling and the pumping power. The predictions are verified against a direct simulation of the 2DCGL equations, and excellent agreement is found. The emergence of solitonic clusters manifests the evolution of MI. Phase diagrams on a MI spectrum for the CWs are presented against the magnetic field (B) and SO coupling strength (σ), based on which the dynamical behaviors of the emerging structures are debated, along with their response to changing σ and B. The results suggest that the photonic SO coupling and the magnetic field constitute efficient tools for nonlinear mode selection and characterization via the MI process and are equally important in any eventual experimental realization of such a process in the studied EPC system.