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Canonical Four-Wave-Mixing occurs in a resonator with only the requirednumber of modes, thereby inhibiting competing parametric processes. Theproperties of the recently introduced photonic crystal parametric oscillator,Marty et al. Nat. Photonics, 15, 53 (2021), are discussed extensively. Wecompare the bichromatic design with other geometries of photonic crystalresonators. Based on a statistical study over more than 100 resonators and 10parametric oscillators, robustness against fabrication tolerances is assessed,performances are evaluated in terms of average values and their dispersion, andthe dependence on the main parameters is shown to follow the theoreticalscaling. The lowest pump power at threshold is $\approx$ 40 $\mu$W and we showthe existence of a minimum value of the cavity photon lifetime as a conditionfor parametric oscillation, which is related to three photon absorption.

Canonical Four-Wave-Mixing in Photonic Crystal Resonators: tuning, tolerances and scaling