Optimal optomechanical cavity setups with highly reflecting membranes

Highly reflecting mechanically compliant membranes based on photonic-crystal patterns have recently gained increasing attention within cavity optomechanics due to their prospects of reaching high coupling rates in membrane-in-the-middle experiments. Here, we present an analysis and comparison of four different setups in which highly reflecting membranes can be employed for cavity optomechanics and discuss optimal choices with respect to the figures of merit: cooperativity and efficiency-weighted cooperativity. The analysis encompasses three different types of membrane-in-the-middle setups (membrane at the edge, membrane in the actual middle, and membrane at the back), as well as the simple Fabry-Pérot cavity. Interestingly, we identify and propose the membrane-at-the-back setup as an optimal choice in the limit of negligible membrane parasitic loss, which can reach enormous enhancements of optomechanical cooperativity and, if implemented with a low-loss membrane, would pave the way to nonlinear optomechanics in the quantum regime.