The attenuation of rays within lossless dielectric structures is determined by two in-principle-exact methods: (a) solution of the appropriate eigenvalue equation, and (b) Poynting’s vector theorem. The methods are applied to cylinders and spheres. There are no trapped rays within the circle or sphere, or any finite structure; however, many rays are only very weakly attenuated.
Allan W. Snyder and D. J. Mitchell, "Ray attenuation in lossless dielectric structures," J. Opt. Soc. Am. 64, 956-963 (1974)