Propagation constants for linearly polarized modes of arbitrarily shaped optical fibers or dielectric waveguides

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Abstract
A simple, approximate formula (valid for modes not too close to cutoff) is given for the propagation constants of linearly polarized modes on a step-index, weakly guiding optical fiber with a core of arbitrary shape. The formula requires only knowledge of the value of a Dirichlet eigenvalue of a similarly shaped region; not only is it significantly more accurate than previously obtained approximate formulas, but it also has a particularly intuitive physical explanation in terms of the depth-of-field penetration into the cladding region.

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