Multimode Sensing by Optical Whispering-gallery-mode Barcodes: A New Route to Expand Dynamic Range for High-resolution Measurement

Sensors play a vital role in detecting and quantifying various parameters relevant to the physical and biochemical aspects of the world. In the field of optical sensing, Whispering-Gallery-Mode (WGM) microresonators have emerged as promising candidates, offering the advantages of high sensitivity, high resolution, and small footprint. However, conventional sensing methods, which rely on tracking changes in a single mode, have a limited dynamic range of measurement. In this study, we develop a theoretical framework that offers comprehensive analytical insights for multimode-sensing techniques. We demonstrate an optical WGM barcode technique that enables simultaneous monitoring of the patterns of multiple modes that can provide over-FSR (Free spectral range) tracking with high resolution. By analyzing the Cramer–Rao bound (CRB) for resonance shift estimation, we assess the theoretical limits of measurement resolution and dynamic range, independent of specific sensing system and estimation algorithm. Comparative analysis of the CRBs for single-mode sensing and multimode sensing confirms the improvement in resolution and dynamic range achievable through the barcode technique based on the multimode spectrum. This work lays the foundation for developing a high-resolution sensor with superior sensitivity across a drastically expanded dynamic range.