Radial mode number identification on whispering gallery mode resonances for diameter measurement of microsphere

A novel method for measuring the diameter of a microsphere by using whispering gallery mode (WGM) resonances is proposed. This measurement method mainly requires one to measure the WGM resonant wavelength and estimate the propagation mode numbers of the WGM. In this work, methods are proposed for estimating the radial mode number using a phase-matching condition. Numerical analysis was implemented to confirm the relationship between the coupling strengths and the matching of the propagation constants. Then, the proposed method was verified experimentally. According to the phase matching, candidates for the radial mode number of excited WGMs could be obtained using the propagation constant of the fiber, which was estimated from the diameter of the fiber. Among the candidates, the radial mode number was determined uniquely using data fitting. Finally, the accuracy of the proposed method was evaluated through a comparison with measurements by using scanning electron microscopy.