Electromagnetic coupling to centimeter-scale mechanical membrane resonators via RF cylindrical cavities

Abstract

We present experimental and theoretical results for the excitation of a mechanical oscillator via radiation pressure with a room-temperature system employing a relatively low-( Q ) centimeter-size mechanical oscillator coupled to a relatively low- Q standard three-dimensional radio-frequency (RF) cavity resonator. We describe the forces giving rise to optomechanical coupling using the Maxwell stress tensor and show that nanometer-scale displacements are possible and experimentally observable. The experimental system is composed of a 35 mm diameter silicon nitride membrane sputtered with a 300 nm gold conducting film and attached to the end of a RF copper cylindrical cavity. The RF cavity is operated in its ${\mathrm{TE}}_{011}$ mode and amplitude modulated on resonance with the fundamental drum modes of the membrane. Membrane motion is monitored using an unbalanced, non-zero optical path difference, optically filtered Michelson interferometer capable of measuring sub-nanometer displacements.

Keywords

• RF cavity
• optomechanics
• Maxwell stress tensor
• interferometry
• thin membrane
• mechanical modes