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.
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