  We present a theoretical study of optomechanical systems in which the
mechanical resonator modulates both the resonant frequency (dispersive
coupling) and the decay rates (dissipative coupling) of the optical cavity. We
extend the generic dispersive framework to a more general case in which the
dissipative coupling is split between its external and intrinsic contribution.
We report a complete analysis of the influence of each kind of optical losses
(intrinsic and external) on the three coupling mechanisms and highlight the
interest of each external decay rate regime. The basic tools to experimentally
identify the three couplings and their relative influence on the optical
response are presented. We demonstrate the general expression of the optical
spring effect and optomechanical damping. Comparison between experimental
measurements in photonic crystal systems from the literature and our
theoretical modal yields good agreement.
