“…In theory, such a birefringent microcavity can be approximately described by an effective Hamiltonian , where describes the intrinsic transverse-electric-transverse-magnetic (TE-TM) splitting of the cavity modes 45 , is the RD Hamiltonian 33 , 34 , 46 , giving rise to a spin-splitting along direction with the strength , and is the Hamiltonian representing the XY splitting 45 , i.e., the energy splitting ( at ) of the perpendicularly linearly polarized modes (X- and Y-polarizations) with opposite parity (here, we define it as β 0 = E X − E Y , where E X and E Y are the ground state energies of X and Y modes of opposite parity). The above effective Hamiltonian in the circular polarization basis can be written in the form of a 2 × 2 matrix: where is the energy of the ground state, is the effective mass of cavity photons, is the strength of the TE-TM splitting, and ( ∈[0, 2 ]) is the polar angle.…”