  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.
