Theoretical Analysis of Resonant Frequency for Anisotropic Artificial Circular Dielectric Resonator Encapsulated in Waveguide

The analysis of resonant frequency for anisotropic artificial circular dielectric resonator (CDR) encapsulated in waveguide is investigated theoretically. The anisotropic permittivity of CDR is established by taking a relative permittivity value in one direction higher than the values of other directions in cylindrical coordinate system. By deriving Maxwell time-dependent curl equations for the CDR inside of a short-ended circular waveguide and then applying proper boundary conditions for the waveguide walls, mathematical formulation to calculate resonant frequencies for transverse electric (TE) and transverse magnetic (TM) wave modes as the function of material thickness and the anisotropic permittivity value are determined. For a comparison, the analysis is also performed for conventional CDR loaded in the same waveguide. In this case, the conventional CDR uses a natural dielectric material with isotropic permittivity. From the results, it shows that the anisotropic artificial CDR has resonant frequencies lower than the conventional CDR for the first of 3 successive TE and TM wave modes. The significant impact in lowering resonant frequencies for the TE and TM wave modes are shown by the anisotropic permittivity in ρand z-directions, respectively. The anisotropic permittivities are able to reduce the resonant frequencies of conventional CDR up to 13.77%, 4.19%, and 5.99% for TE11, TE21, and TE01 wave modes, respectively and 43.07%, 35.98%, 34.86% for the TM01, TM11, and TM21 wave modes, respectively. These results can be applicable for wave mode selection. The anisotropic permittivity in -direction has no effect in lowering the TE and TM wave mode resonant frequencies.