A geometrical optics treatment shows that whispering-gallery waves following twisted trajectories can be in eigenstates of polarization if σ = (radius of curvature × torsion) is a constant. The Jones vectors of these eigenpolarizations are calculated, along with their propagation constants and power attenuation constants. The curve representing the evolution of an arbitrary input polarization makes a constant angle with the circles passing through the points corresponding to the eigenpolarizations, on the Poincaré sphere or in any one of the equivalent complex-plane representations. Experiments carried out with a cylindrical glass tube give results in good agreement with theoretical conclusions. The theory predicts that the smallest attenuation constant for three-dimensional trajectories in infrared and far-infrared guides should be about (1 + σ2) times larger than that for TE waves along two-dimensional trajectories of the same curvature, providing a practical criterion for the design of guides exhibiting twisted trajectories.
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