Optical galleries of dielectric rings: antipode to whispering gallery modes

A general picture of photonic eigenmodes of dielectric rings with a rectangular cross section is presented, which is fundamentally different from those of whispering gallery modes of the disc. The optical spectrum of a rectangular dielectric ring consists of an infinite set of individual galleries, each starting with broad transverse radial or axial Fabry-P\'erot resonances due to two pairs of side faces. Each gallery continues with a set of equidistant longitudinal modes with exponentially increasing quality factors. Transverse radial and axial modes exhibit strict periodicity of line contours in the Fano-Lorentz-Fano-Lorentz... sequence due to the periodicity of cylindrical harmonics. Theoretical and experimental results are in perfect agreement.