Identification of whispering gallery mode radial mode number based on standing-wave pitch measurement

We propose a method to estimate the radial mode number of whispering gallery modes (WGMs) in microspheres with diameters of several tens of micrometers by analyzing the standing-wave pitch. By addressing the issues associated with measuring WGM intensity distributions on the microsphere surface, we experimentally validate the approach. We selectively excite equatorial modes ( m = l ) in a glass microsphere and measure the standing-wave pitch using a scanning near-field optical microscopy (SNOM) probe. From the measured pitch, we determine the radial mode number, which is then used to calculate the microsphere diameter via the WGM dispersion equation. The resulting diameter shows good agreement with independent measurements using a white-light interferometer, confirming the accuracy of the radial mode number estimation.