Theory of self-phase-locked optical parametric oscillators

The plane-wave dynamics of 3→ω2ω,ω subharmonic optical parametric oscillators containing a second-harmonic generator of the idler-wave {ω} is analyzed analytically by using the mean-field approximation and numerically by taking into account the field propagation inside the media. The resonant ${{χ}}⁽²⁾({-}3{ω};2{ω},{ω}):{{χ}}⁽²⁾({-}2{ω};{ω},{ω})$ 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 subthreshold states occur due to a subcritical bifurcation, broadening out the self-locking frequency range to a few cavity linewidths.