  We investigate the optomechanical photon-phonon coupling of a single light
mode propagating through an array of vibrating mechanical elements. As recently
shown for the particular case of a periodic array of membranes embedded in a
high-finesse optical cavity [A. Xuereb, C. Genes and A. Dantan, Phys. Rev.
Lett., \textbf{109}, 223601, (2012)], the intracavity linear optomechanical
coupling can be considerably enhanced over the single element value in the
so-called \textit{transmissive regime}, where for motionless membranes the
whole system is transparent to light. Here, we extend these investigations to
quasi-periodic arrays in the presence of engineered spatial defects in the
membrane positions. In particular we show that the localization of light modes
induced by the defect combined with the access of the transmissive regime
window can lead to additional enhancement of the strength of both linear and
quadratic optomechanical couplings.
