Forward and Backward Four-wave Mixing of Non-classical Light with Pump Depletion

Abstract
Photon statistics and non-classical behaviour of forward and backward four-wave mixing are examined including the coupling of modes in the approximation of small fluctuations around a stationary point, which is analytically determined and conditions for its stability are obtained. The depletion of pump modes is involved and effects of nonlinear dynamics, non-classical behaviour of input radiation, external noise and losses are included.