  We present a detailed study of mechanically compliant, photonic-crystal-based
microcavities featuring a quasi-bound state in the continuum. Such systems have
recently been predicted to reduce the optical loss in Fabry-Perot-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 quasi-bound state in the continuum. We find that a suspended
photonic-crystal slab facing a distributed Bragg reflector realizes an
optomechanical system with a quasi-bound 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.
