  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.
