Mechanical resonators based on two-dimensional materials have gained attention for their interesting optical and mechanical properties, which translate into versatile applications such as ultrasensitive force detection and pressure sensing. Optical reflectometry is a technique of choice to measure the flexural vibrations of these resonators. The latter consists in sending normally incident monochromatic light on the resonator and measuring the intensity of reflected light, which varies as the distance d between the resonator and a nearby mirror varies. In this work we consider resonators based on suspended membranes of graphene, molybdenum disulfide and tungsten diselenide, and theoretically investigate the dependence of the reflectance R(d) of the resonator on the angle of incidence θ of the probing light. The optical response of these membranes is accounted for by their complex refractive indices. For s-polarized light, we find that R oscillates as a function of d with an amplitude that increases as theta increases. These results may help enhance the optical readout accuracy of these two-dimensional resonators.
Mechanical resonators based on suspended two-dimensional membranes are promising systems for developing sensitive detectors of mass, charge and force. To measure the flexural vibrations of the membrane, it is important to employ a technique capable of resolving tiny fluctuations of vibration amplitude. To this end, researchers have been developing optical detection methods based on Fabry-Perot interferences of light between the membrane and a mirror-like substrate, which relate the intensity of light reflected by the device to the distance between the membrane and the substrate. In this work, we calculate the membrane-to-substrate distances that maximize the optical responsivity of the resonator, which we define as the derivative of the resonator’s reflectivity with respect to membrane’s displacement. In addition, we examine how various substrates with different refractive indices affect this optical responsivity, including bare silicon, silicon coated with silicon oxide, dissipative metal mirrors, and non-dissipative Bragg reflectors. Our calculation method is based on the transfer matrix method for propagating electromagnetic fields. Our results are consistent with earlier theoretical and experimental results, and offer perspectives to enhance the optical responsivity of these mechanical resonators.