Determining the geometric parameters of microbubble resonators from their spectra

Abstract

A method for determining the diameters and shell thicknesses of microbubble resonators is presented; it entails simulating whispering gallery mode (WGM) spectra using a newly developed finite-difference time-domain (FDTD)-based toolkit. Spectra for a range of shell thicknesses are simulated using FDTD, assuming a linear dependence of the free spectral range on the diameter, and the free spectral ranges and positions of the prominent modes are matched to those of the measured spectrum. This method improves upon existing techniques for extracting the diameter and thickness, such as SEM imaging, which typically require the microbubble to be dissected or otherwise rendered unusable for subsequent use. The model allows a variety of methods of mode excitation to be simulated. Dye coatings are simulated by placing a layer of dipole sources on the surface of the resonator, yielding mode couplings comparable to those measured in experiments. The model is tested for a small-diameter silica glass microbubble, with the free spectral range being simulated for a range of diameters and shell thicknesses. The numerically simulated spectra are then compared to the experimentally measured spectrum. The ability to determine the geometric parameters of such resonators directly from their WGM spectra represents a step forward in the characterization of microbubble resonators. Furthermore, the model opens the way to previously unstudied spectral behavior of microbubbles with small diameters and thin shell thicknesses.