Properties of the signal mode in the polariton optical parametric oscillator regime

Theoretical analyses of the polariton optical parametric oscillator (OPO) regime often rely on a mean-field approach based on the complex Gross-Pitaevskii equations in a three-mode approximation, where only three momentum states, the signal, pump, and idler, are assumed to be significantly occupied. This approximation, however, lacks a constraint to uniquely determine the signal and idler momenta. In contrast, multimode numerical simulations and experiments show a unique momentum structure for the OPO states. In this work we show that an estimate for the signal momentum chosen by the system can be found from a simple analysis of the pump-only configuration. We use this estimate to investigate how the chosen signal momentum depends on the properties of the drive.