Study on planar whispering gallery dielectric resonators. I. General properties

Several basic properties of homogeneous planar Whispering Gallery dielectric resonators are investigated through a general approach. In particular the values for the minimum and maximum allowed radius, defined by irradiation and dielectric losses, respectively, are obtained in terms of the complex dielectric constant of the involved media. The same approach is employed in the analysis of the limit allowed frequencies of a fixed family of mode, leading to the definition of the "ideal" frequency band. The role of the transverse mode is then discussed, and the "effective" frequency band is introduced and determined both in simple disc and circular ring resonators. The extension of the effective band is limited at least by a factor 3, in terms of decades, in comparison to the extension of the ideal one; this limitation, due to the presence of transverse modes, can be overcome using suitably designed non-homogeneous resonators, as discussed in a following companion paper.