Predicting the whispering gallery mode spectra of microresonators
The whispering gallery modes (WGMs) of optical resonators have prompted intensive research efforts due to their usefulness in the field of biological sensing, and their employment in nonlinear optics. While much information is available in the literature on numerical modeling of WGMs in microspheres, it remains a challenging task to be able to predict the emitted spectra of spherical microresonators. Here, we establish a customizable Finite- Difference Time-Domain (FDTD)-based approach to investigate the WGM spectrum of microspheres. The simulations are carried out in the vicinity of a dipole source rather than a typical plane-wave beam excitation, thus providing an effective analogue of the fluorescent dye or nanoparticle coatings used in experiment. The analysis of a single dipole source at different positions on the surface or inside a microsphere, serves to assess the relative efficiency of nearby radiating TE and TM modes, characterizing the profile of the spectrum. By varying the number, positions and alignments of the dipole sources, different excitation scenarios can be compared to analytic models, and to experimental results. The energy flux is collected via a nearby disk-shaped region. The resultant spectral profile shows a dependence on the configuration of the dipole sources. The power outcoupling can then be optimized for specific modes and wavelength regions. The development of such a computational tool can aid the preparation of optical sensors prior to fabrication, by preselecting desired the optical properties of the resonator.