Analysis of splitting direction for coupling WGM resonators

Opposite splitting directions in mode splitting are observed in whispering gallery mode resonators, composed of asymmetrically coupled bispheres. To interpret this phenomenon, we introduce a “virtual ellipsoid” model, which establishes a direct correlation between the optical behavior of bispheres and that of ellipsoidal resonators. The splitting characteristics, including intensity difference and wavelength separation, are systematically investigated through theoretical analysis and experimental validation. These findings demonstrate that the splitting direction is governed by the relative positions of the fundamental and azimuthal modes within the splitting peaks. Experimental results further confirm that an increase in the diameter of Sphere D₂ leads to a redshift in the resonant wavelength, attributed to the extended optical path in the whispering gallery mode. Additionally, we propose an optical barcode approach based on the transmission spectra to intuitively characterize the optical features of splitting peaks, offering potential applications in size measurement of microspheres or ellipsoids, as well as optical information identification.