Pairwise mode-locking of coupled parametric oscillators

The canonical example of coherent interaction between oscillators is a system of coupled pendulums — where due to the coupling, energy is transferred slowly from one oscillator to the other and back at a beat frequency that reflects the coupling strength. A system of coupled pendulums is an idealization of coherent transfer of energy, that cannot be directly observed in steady-state — a real system will eventually lose coherence due to dissipation and unwanted couplings to the environment. Parametric amplifiers offer a method to coherently amplify the oscillation in a way that conserves the coherent dynamics between the coupled oscillators. An optical parametric oscillator (OPO) relies on coherent amplification of light to generate coherent radiation, but the dynamics and coherence properties of an OPO are fundamentally different from those of a standard laser, the amplification mechanism in an OPO relies on a coherent parametric coupling of energy from the strong pump field (ω p ) to a pair of frequencies, signal (ω s ) and idler (ω i ) such that the energy and momentum of light are conserved (ω p = ω s + ω i , k p = + k i ). An OPO therefore always generates pairs of correlated coherent fields, conserving the beat coherence.