Optically driven limit cycle oscillations in MEMS

We examine the dynamics of nanoscale bridge resonators fabricated from SOI wafers. When illuminated within an interference field, resonators are seen to self-oscillate due to feedback between heating and displacement. They are driven in high vacuum and their motion transduced with laser interferometry. Analysis of Maxwell’s equations indicates that laser heating is not confined to the resonator’s top surface. A finite element model is built to study thermo-mechanical coupling. Analysis shows that feedback is strongest in barely post-buckled beams, leading to low power self-oscillation. A theoretical model is built starting with the continuum description of the temperature and displace-ment fields and a Galerkin projection is used to obtain a set of coupled ordinary differential equations. These equations are analyzed using numerical contin-uation and perturbation theory. Analysis of the model suggests that a Hopf bifurcation leads to limit cycle oscillations and that multiple stable limit cycles may be possible due to periodicity in the interference field. The threshold power for self-oscillation as well as the amplitude, frequency, and frequency noise are measured experimentally. Measured amplitude-frequency relationships verify the predicted softening/hardening nature of first and second mode vibrations in pre- and post-buckled beams. Experimental results suggest that frequency noise in self-oscillating beams is due to instability in the power of the laser drive. Fluctuations in the laser power result in fluctuations of the resonant fre-quency via the power-amplitude-frequency relationship. Self-resonant beams are also driven inertially and regions of sub- and superharmonic entrainment are measured, where the resonator response frequency is a whole multiple or sub-multiple of the drive frequency