Non-classical Properties of Non-degenerate Parametric Amplifiers and Oscillators with Pump Depletion and Non-homogeneous Losses Using the Wigner Representation

The squeezing properties of non-degenerate parametric amplification and oscillation with pump depletion and non-homogeneous absorption losses are studied. A method based in the Wigner representation is used which allows one, within a linearization scheme, to derive directly the Langevin equations for the involved optical fields from their quantum Heisenberg equations. Non-homogeneous absorption losses for the three beams are included in order to analyse the sensitivity of the squeezing spectra to the asymmetry of the losses. Intracavity squeezing spectra are calculated within this method both below- and above-threshold regimes. Special attention is given to the squeezing properties of the phase sum and amplitude difference of the correlated beams and amplitude of a single beam above threshold, where the role of loss asymmetry and pump losses is analysed in detail.