Simple model for the mode-splitting effect in whispering-gallery-mode resonators

In this paper, we present a model describing the mode-splitting effect in a whispering-gallery (WG)-mode resonator. The WG mode is represented by an equivalent transmission-line ring resonator in which a localized perturbation is introduced. This perturbation induces a coupling between the two counter propagating waves, which, in turn, lifts the degeneracy of the WG modes. This simple model explains almost all the line shapes experimentally observed. It shows in a straightforward way how the coupling on the two twin modes are affected by changing the coupling probe and the perturbation angular positions. In that sense, it is useful to make the resonator adjustment easier. Moreover, the same approach can be used to simulate any microstrip ring resonator with localized perturbation.