A unified approach to mode splitting and scattering loss in high-Q whispering-gallery-mode microresonators

Current theoretical treatment of mode splitting and scattering loss resulting from sub-wavelength scatterers attached to the surface of high-quality-factor whispering-gallery-mode microresonators is not satisfactory. Different models have been proposed for two distinct scatterer regimes, i.e., a-few- and many-scatterers. In addition, many experimental results seem difficult to understand within the existing theoretical framework. Here we develop a unified approach that applies to an arbitrary number of scatterers, which reveals the applicable conditions and the limits of the existing theoretical models. Moreover, many new understandings on mode splitting and scattering loss have been achieved, which are supported by numerical and experimental evidences. Such a unified approach is essential for the fundamental studies as well as the practical applications of mode splitting and scattering loss in high-quality-factor whispering-gallery-mode microresonators.