Cavity optomechanics with arrays of thick dielectric membranes

Optomechanical arrays made of structured flexible dielectrics are a promising system for exploring quantum and many-body optomechanical phenomena. We generalize investigations of the optomechanical properties of periodic arrays of one-dimensional scatterers in optical resonators to the case of vibrating membranes whose thickness is not necessarily small with respect to the optical wavelength of interest. The array optical transmission spectrum and its optomechanical coupling with a linear Fabry-Perot cavity field are investigated both analytically and numerically.