Spin-orbital effect on polariton state in traps

I discuss similitude and differences of spin-orbital effects for electrons in quantum wells with the Rashba coupling and for polaritons in semiconductor microcavities with TE-TM splitting. Contrary to the case of electron, the ground state of polariton in the trap can be non-degenerate and can possess specific polarization structure. For the case of azimuthally symmetric trap and sufficiently strong spin-orbital coupling, the ground state is either radial or azimuthal vortex, depending on the sign of the coupling constant. The effect is strongly enhanced for polaritons trapped in a ring, where even weak TE-TM splitting results in formation of vorticity and definite polarization of the ground state. The Hamiltonian for quasi-1D motion of polaritons in the ring is derived and it is shown the the dispersion of polaritons depend qualitatively on the curvature of the ring.