  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.
