Optimal Optomechanical Coupling Strength in Multi-Membrane Systems

We calculate the optomechanical coupling strength for a multi-membrane in a cavity system. The optimal configuration for an array of $N$ membranes placed near the center of a cavity is identified. This results in a coupling strength much greater than previously proposed multi-membrane configurations. We find that the coupling strength scales exponentially with the number of membranes until saturating due to complete localization of the field within the array. Furthermore we explore two sources of loss, those due to light absorption within the membrane(s) and leakage through the cavity's end-mirrors, and evaluate how they affect the possibility of achieving strong coupling.