Transmissive optomechanical platforms with engineered spatial defects

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.