Visual Detection of Arbitrary Mode Shape of Optomechanical Resonant Sensor Based on Silicon Nitride Membrane

Optomechanical resonant sensors based on membrane are widely used in fundamental effects and sensing. As the applications of resonators evolve toward high-order modes, where significant overlap of modes occurs. Therefore, it poses some challenges to effectively identify arbitrary high-order modes of the membrane resonant sensor. In this work, we propose a multi-interface interferometric structure and systematically test the first 30 modes of a nano optomechanical resonant sensor based on Si3N4 membrane. The experimental results are in good agreement with the theoretical results. The resonator vibrates in the high-frequency range of 0.4–2 MHz. The thermomechanical resonance signal excited by thermomechanical noise is analyzed and the best displacement resolution reaches 5.02 fm/<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\surd $ </tex-math></inline-formula>Hz. Through establishing a systematic testing method consisting of theoretical models, thermomechanical resonance spectra, and mode shapes, the driving, detection, and visualization of any given mode can be achieved. The test of the mode shapes can not only accurately determine the mode sequence but also check the frequency splitting of degenerate modes caused by structural defects. It also lays foundation for multimodal signal processing and displacement detection of resonant sensors.