Non-linear and quantum optics of a type II OPO containing a birefringent element Part 1: Classical operation

We describe theoretically the main characteristics of the steady state regime of a type II Optical Parametric Oscillator (OPO) containing a birefringent plate. In such a device the signal and idler waves are at the same time linearly coupled by the plate and nonlinearly coupled by the $\chi^{(2)}$ crystal. This mixed coupling allows, in some well-defined range of the control parameters, a frequency degenerate operation as well as phase locking between the signal and idler modes. We describe here a complete model taking into account all possible effects in the system, \emph{i.e.} arbitrary rotation of the waveplate, non perfect phase matching, ring and linear cavities. This model is able to explain the detailed features of the experiments performed with this system.