Dispersion relations and bending losses of cylindrical and spherical shells, slabs, and slot waveguides

TL;DR

This paper derives formulas for whispering gallery mode resonances and bending losses in cylindrical and spherical shells, revealing effects of shell proximity and structural resonances on radiation losses.

Contribution

It introduces a WKB-based derivation of resonance and loss formulas applicable to multiple concentric shells, including the novel analysis of shell proximity effects and slot waveguide behavior.

Findings

Formulas applicable to cylindrical and spherical shells and bent waveguides.

Identification of structural resonances affecting radiation losses.

Analysis of close-shell limit leading to slot waveguide behavior.

Abstract

We derive formulas for Whispering Gallery Mode resonances and bending losses in infinite cylindrical dielectric shells and sets of concentric cylindrical shells. The formulas also apply to spherical shells and to sections of bent waveguides. The derivation is based on a WKB treatment of Helmholtz equation and can in principle be extended to any number of concentric shells. A distinctive limit analytically arises in the analysis when two shells are brought at very close distance to one another. In that limit, the two shells act as a slot waveguide. If the two shells are sufficiently apart, we identify a structural resonance between the individual shells, which can either lead to a substantial enhancement or suppression of radiation losses.