Analysis of laser power threshold for self oscillation in thermo-optically excited doubly supported MEMS beams

An optically thin MEMS beam suspended above a substrate and illuminated with a CW laser forms an interferometer, coupling out-of-plane deflection of the beam to absorption within it. In turn, laser absorption creates thermal stresses which drive further deflection. This coupling of motion to thermal stresses can cause limit cycle oscillations in which the beam vibrates in the absence of periodic external forcing. Prior work has modeled such thermal-mechanical systems using ad-hoc coupled ordinary differential equations, with finite element analysis (FEA) used to fit model parameters. In this paper we derive a first principles model of such oscillations from the continuum description of the temperature and displacement field. A bifurcation analysis of the model is performed, allowing us to easily estimate the threshold power for self-oscillation as a function of geometric and optical constants of the beam.