Rays and modes on step-index multimode elliptical waveguides

Generalised geometric optics are applied to the classification of rays within an optical waveguide of elliptical cross-section. We find four classes of ray paths; (i) bound, (ii) tunnelling, (iii) refracting and (iv) paths that both tunnel and refract. The last class is not found on circular waveguides. The corresponding classes of modes are established from electromagnetic theory. A simple expression for the attenuation of each tunnelling mode is given in the weakly guiding approximation for slight eccentricity, and is shown to be analytically equivalent to the attenuation of the corresponding family of tunnelling rays, when ray-power loss is averaged over all reflections. This equivalence also justifies the use of local ray power-transmission coefficients in the description of ray attenuation.