Whispering gallery mode microspheres as open resonators

Optical whispering gallery mode resonators based on microspheres, microtoruses and crystalline disks may be used as chemi and biosensors and in QED experiments as interacting with single atoms and quantum dots. It is important for different applications to calculate accurately field distributions in microresonators both in classical and in quantum cases to use perturbation methods. Radiation losses, however, lead in open resonators to fundamental difficulties, caused by divergence of total energy integrals and nonorthogonality of modes. These problems characteristic for any type of open resonators may be neglected when the size of the cavity is large enough but with the shortening of the cavity and radical lowering of the radiative Q become significant. In this case traditionally used characteristic equations, determining the resonant frequencies become only approximate ones. Using dielectric microspheres as an example an accurate characteristic equations are found for the TE and TM modes and it is shown that earlier optimizations of the effective volume for the small microspheres and hence other types of microresonators are wrong due to incorrect accounting of external radiative field.