Quasibound states in the continuum in photonic crystal based optomechanical microcavities

We present a detailed study of mechanically compliant, photonic crystal based microcavities featuring a quasibound state in the continuum. Such systems were recently predicted to reduce the optical loss in Fabry-P\'erot-type optomechanical cavities. However, they require two identical photonic crystal slabs facing each other, which poses a considerable challenge for experimental implementation. We investigate how such an ideal system can be simplified and still exhibit a quasibound state in the continuum. We find that a suspended photonic crystal slab facing a distributed Bragg reflector realizes an optomechanical system with a quasibound state in the continuum. In this system, the radiative cavity loss can be eliminated to the extent that the cavity loss is dominated by dissipative loss originating from material absorption only. These proposed optomechanical cavity designs are predicted to feature optical quality factors in excess of ${10}^{5}$.