Many skew rays within a circular dielectric rod that geometric optics predicts are trapped by total internal reflection are in fact leaky. By finding the complex roots of the eigenvalue equation, we derive a concise analytic expression for the loss of all weakly attenuated rays. The solution is uniformly valid for leaky as well as those refracted rays that obey Fresnel’s laws. The results provide a unified theory of light transmission within fibers and represent the necessary generalization of Fresnel’s laws for cylindrical structures. A weakly leaky mode is formed by a family of leaky rays. The number of weakly leaky modes is determined.
© 1974 Optical Society of AmericaFull Article | PDF Article
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