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