Modeling the Adsorption-Desorption Phase Noise in Optomechanical Oscillators

Optomechanical oscillators (OMOs) exhibit self-sustained mechanical oscillations, driven by optical pumping through radiation pressure or optical gradient force. Due to the lack of externally applied feedback, prior theoretical models and experiments have reported that such oscillators are free of 1/f³ (pink noise) and higher order slopes in the phase noise spectrum [Opt. Exp. 2011;19:24522-29]. However, most OMO results reported at sub-atmospheric temperatures and pressures exhibit significant 1/f⁴ phase noise (brown noise), that is not explained by conventional models. In this work, we study the impact of adsorption and desorption (of gas molecules on the resonator surface) on phase noise in OMOs, based on noise analysis in mechanical oscillators [IEEE TUFFC. 1989;36(4):452-8]. Experimental data recorded for a chip-scale silicon OMO (obtained in a liquid nitrogen cooled vacuum ambience) fits well with the theoretical prediction. An additional insight drawn from the model is that unlike phase noise originating from thermal noise sources, the brown phase noise is independent of the mechanical mode shape, as validated through observation of similar magnitude of 1/f⁴ noise in oscillations of a radial breathing mode at 70MHz and wineglass mode at 58MHz in the same device.