Optical control and sensing of high-quality nonlinear micromechanical resonance and macroscopic displacement

Abstract

Light can be used for high-precision control and measurement of the properties of physical systems through light-matter interactions, as its intensity, polarization, frequency, and phase can be adjusted and detected with high accuracy. In this dissertation, I present two experimental studies in the context of optical control and sensing. First, I investigate the nonlinear coupling of mechanical modes of a high-quality micromechanical resonator by using optical means. A mechanical mode of a 30-nm-thick 250×250-$\mu$ $m^2$-wide silicon nitride clamped square membrane is excited by intensity-modulated laser light via radiation pressure. Energy transfer from the optically driven mode to others is then observed by spatially-resolved interferometric measurements of the vibration profiles. In sharp contrast to the one-dimensional resonators such as nanobeams and microcantilevers exclusively used in many previous works, the clamped square membrane features almost frequency-commensurate relations among many mechanical modes. This unique frequency relation allows for the high-efficiency nonlinear coupling of multiple mechanical modes – 3 modes with pN-scale optical forces and 5 modes with piezoelectric ones in my case – via mechanical third-harmonic generation and cascaded four-wave mixing arising from third-order mechanical nonlinearity. These results pave a way towards the implementation of a small-footprint massive optomechanical array that may yield enhanced optomechanical coupling. Second, I demonstrate the optical detection of macroscopic displacements much larger than the optical wavelength by employing a combination of a free-space Fabry-Pérot optical cavity and a wedge prism pair. This scheme permits high-sensitivity measurement of large displacements up to 7 mm without $2\pi$ ambiguity, which surpasses the measurable range of conventional interferometers by a factor of 9,000. Moreover, a large-capacity high-resolution optomechanical mass sensor is developed by combining the cavity-based displacement detector and a load cell. By incorporating the null-method-based scheme of mass measurement, I achieve a resolution higher than 5000:1, a capacity beyond 1 kg, and excellent linearity.