  The plane-wave dynamics of 3*omega => (2*omega, omega) subharmonic optical
parametric oscillators containing a second harmonic generator of the idler wave
omega is analyzed analytically by using the meanfield approximation and
numerically by taking into account the field propagation inside the media. The
resonant Chi(2):Chi(2) cascaded second-order nonlinearities induce a mutual
injection-locking of the signal and idler waves that leads to coherent self
phase-locking of the pump and subharmonic waves, freezing the phase diffusion
noise. In case of signal-and-idler resonant devices, largely detuned
sub-threshold states occur due to a subcritical bifurcation, broadening out the
self-locking frequency range to a few cavity linewidths.
