Force sensing with a graphene nanomechanical resonator coupled to photonic crystal guided resonances

Achieving optimal force sensitivity with nanomechanical resonators requires the ability to resolve their thermal vibrations. In two-dimensional resonators, this can be done by measuring the energy they absorb while vibrating in an optical standing wave formed between a light source and a mirror. However, the responsivity of this method -- the change in optical energy per unit displacement of the resonator -- is modest, fundamentally limited by the physics of propagating plane waves. We present simulations showing that replacing the mirror with a photonic crystal supporting guided resonances increases the responsivity of graphene resonators by an order of magnitude. The steep optical energy gradients enable efficient transduction of flexural vibrations using low optical power, thereby reducing heating. Furthermore, the presence of two guided resonances at different wavelengths allows thermal vibrations to be resolved with a high signal-to-noise ratio across a wide range of membrane positions in free space. Our approach provides a simple optical method for implementing ultrasensitive force detection using a graphene nanomechanical resonator.