Synchronization of two indirectly coupled singly resonant optical parametric oscillators

We analyse a system of a singly resonant optical parametric oscillator for a second order nonlinear material. First, we show that the dynamics of the resonating cavity signal mode can be expressed by a Stuart–Landau oscillator, for a certain pumping powers close to the threshold. Second, we couple two optical parametric oscillators indirectly via a cold resonator. When the condition of a weak coupling is satisfied, the limit-cycle of each oscillator is unaltered, and the system is described by a coupled phase oscillator model (Kuramoto model), where a frequency synchronization of the two oscillators occurs at a critical coupling constant.