Optical surface waves along a toroidal metallic guide

An approximate analysis shows that rays guided inside a torus oscillate sinusoidally around the equator. Expressing the Helmholtz equation in toroidal coordinates yields the equivalent index of refraction. The equation can be solved, yielding Airy functions in the direction perpendicular to the surface. Along the surface the equation is similar to that for media with a quadratic index profile, the Hermite-Gaussian solutions of which follow sinusoidal trajectories while oscillating in width. Experimental verification of these features is presented.