Optical galleries of dielectric rings: antipode to whispering gallery modes

TL;DR

This paper explores the unique photonic eigenmodes of rectangular dielectric rings, revealing a spectrum of galleries with distinct resonances and modes, differing fundamentally from whispering gallery modes, supported by both theory and experiments.

Contribution

It introduces a new understanding of optical modes in dielectric rings with rectangular cross sections, highlighting the structure of galleries and their resonances, which is a novel perspective compared to traditional whispering gallery modes.

Findings

Optical spectrum consists of infinite galleries with Fabry-Pérot and longitudinal modes.

Transverse radial and axial modes show periodic line contours due to cylindrical harmonic periodicity.

Theoretical predictions match experimental results perfectly.

Abstract

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.