Correction Due to a Finite Permittivity for a Ring Resonator in Free Space

To better determine the resonant fields of a dielectric resonator with high permittivity epsilon_r, the asymptotic theory with1/√epsilon₃ as a small parameter is extended by adding higher order terms in 1/√epsilon _r in the fields, the resonant wavenumber, and radiation Q. Extensive data are shown for the Phi independent "nonconfined" mode of a ring resonator, which radiates as a magnetic dipole. Some results are added for the "magnetic quadruple" mode.