Synchronization in Coupled Opto-thermal Silicon MEMS Limit Cycle Oscillators

Abstract

Micro- and nano-scale oscillators exhibit nonlinear phenomena such as limit cycle oscillations, self-synchronization, and frequency entrainment to an external drive. In this work, we chart the behavior of silicon MEMS oscillators that are nominally 40 µm long and 205 nm thick, mechanically coupled, and opto-thermally driven by a continuous-wave helium-neon laser. Experimentally, we demonstrate synchronization in pairs of coupled oscillators which result in reduced frequency fluctuations in the devices. Irregular oscillations are observed at higher input laser powers and are explained by the existence of bistable states and sensitive dependence on initial conditions in the corresponding lumped-parameter mathematical model. The key parameters studied in this work are frequency detuning, coupling level, and the input laser power. Using numerical and analytical perturbation methods, we extend the analysis to an array of eight coupled oscillators and study self-synchronization and frequency entrainment to an external inertial drive. Key contributions include the mapping of the dynamical behavior of clamped-clamped silicon structures widely used in MEMS sensors, actuators, and time-keeping devices, and the use of a third-order model to give numerical and theoretical boundaries for self-synchronization, entrainment, and bistability.