Generation of photon pairs by spontaneous four-wave mixing in linearly uncoupled resonators

We present a detailed study of the generation photon pairs by spontaneous four-wave mixing in structure composed two linearly uncoupled resonators, where energy can be transferred from one resonator to another only through nonlinear interaction. Specifically, we consider case racetrack-shaped resonators connected coupler designed guarantee that resonance comb each tuned independently and allow interaction between modes belong different combs. show such realized at least ways: A directional or Mach-Zehnder interferometer. For these scenarios, derive analytic expressions for pair-generation rate via single-pump compare results with achievable single-ring resonator.