High-accuracy analytic characterization of whispering gallery modes based on modified quantum potential

Several approaches have been proposed for the modal analysis of whispering gallery mode (WGM) microcavities, however, all of these modal analysis schemes have their limitations in applicability and simplicity. In this work, we develop a universal WKB-approximation-based analytic modal analysis approach applicable for the microresonators integrated with negative permittivity materials as well as their counterparts made of positive permittivity medium. For the microcavities with negative permittivity coating, the calculation results in terms of the resonance frequency show good accordance with the FDTD simulation results for low-order modes. And for those based on positive permittivity medium, the calculation results of resonance wavelength using WKB-approximation approach show trivial deviations on an angstrom level in comparison with the eigenequation solutions. Moreover, mode selection at specific resonance wavelengths has been studied based on quasi-quantum description of light field, which would be valuable for mode-switching applications of WGM microresonators. The analytic modal analysis method proposed in this study is also applicable for the microresonators made of inhomogeneous medium, where specific mode properties can be achieved by optimizing the potential function, which paves a new way toward developing WGM photonic devices with versatile functionalities.