Dielectric tuning and coupling of whispering gallery modes using an anisotropic prism


Optical whispering gallery mode (WGM) resonators are a powerful and versatile tool in many branches of science. Fine-tuning of the central frequency and linewidth of individual resonances is, however, desirable in a number of applications, including frequency conversion, optical communications, and efficient light–matter coupling. To this end we present a detailed theoretical analysis of dielectric tuning of WGMs supported in axisymmetric resonators. Using the Bethe–Schwinger equation and adopting an angular spectrum field representation, we study the resonance shift and mode broadening of high-Q WGMs when a planar dielectric substrate is brought close to the resonator. Particular focus is given to use of a uniaxial substrate with an arbitrarily aligned optic axis. Competing red and blue resonance shifts (∼30  MHz), deriving from generation of a near-field material polarization and back action from the radiation continuum, respectively, are found. Anomalous resonance shifts can hence be observed depending on the substrate material, whereas mode broadening on the order of ∼50  MHz can also be realized. Furthermore, polarization-selective coupling with extinction ratios of textgreater104 can be achieved when the resonator and substrate are of the same composition and their optic axes are chosen correctly. Double refraction and properties of outcoupled beams are also discussed.