In this paper we study the properties of microring resonator structures fabricated with high-index-of-refraction dielectric material. These structures concentrate light and can produce very strong optical potential gradients. They are of great interest for the trapping, manipulation and transport of cold atoms near surfaces. The study consists of two parts: in the first part we investigate the symmetry properties of the resonator response for simple models of the microring structures. In the second part we present detailed numerical calculations of the actual spectra for realistic microfabricated structures. We employ the direct space integral equation method (DSIEM). This method, based on a volume integral solving procedure, has already been found to cope successfully with nonresonant dielectric nanostructures. Such ab initio investigations of the optical near-field distributions only require a specification of the frequency-dependent dielectric constant and the precise shape of the fabricated structures. Consequently, these calculations can stand alone, or complement and inform anticipated experimental studies.
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