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Modulational instability and excitations in circular-symmetry exciton-polariton condensates

We investigate the stability and excitations of two-dimensional circular-symmetry exciton-polariton condensates. The system is described by the circular-symmetry dissipative Gross-Pitaevskii (GP) equation based on the meanfield theory. The excitation properties around the steady-state is analytically calculated by means of the standard Bogoliubov-de Gennes (BdG) approach. We discuss the stability and modulational instability conditions which are determined by the parameters of the system and the parameters that characterize the Gaussian steady-state. We find that, the square of a parameter ¯ι plays a crucial role in characterizing the stability criterion and the excitaion spectrum.