A prism-based non-linear optical readout method for MEMS cantilever arrays

This paper demonstrates the use of a single right-angle prism for the optical readout of micro-electro-mechanical systems (MEMS) cantilever arrays. The non-linear reflectivity arisen from the internal reflection at the right-angle prism's hypotenuse plane enables the measurement of cantilever deflections. The cantilever arrays used in the experiments are made of electroplated nickel structures and actuated at resonance by an external electro-coil. A laser beam illuminates multiple cantilevers, and then it is partially reflected by the prism. The prism reflectivity changes with the cantilever deflection and modulates the laser intensity at the photodetector. The detection sensitivity of the optical readout system is determined by the initial angle of incidence at the prism's hypotenuse plane, numerical aperture of the illumination system and the polarization of the laser beam. In this paper, we showed both theoretically and experimentally that self-sustained oscillations of two MEMS cantilevers with simple rectangular geometry is achievable using only one actuator and one photodetector. The gain saturation mechanism for the oscillators was provided by the optical non-linearity in the prism readout, which eliminates the requirement for separate sensing electronics for each cantilever. Based on our analytical and experimental data, we found that the prism incident angle around 41.2° is desirable in the closed-loop system due to high responsivity. Finally, we demonstrated simultaneous self-sustained oscillations of two cantilevers in closed-loop with resonant frequencies in the range 25–30 kHz. It was shown that multiple oscillations are obtainable if the cantilever resonant frequencies are separated from each other by at least 3 dB bandwidth.