Weakly guiding analysis of elliptical core step index waveguides based on the characteristic numbers of Mathieu's equation

A new weak guidance analysis for step index elliptical core optical fibers is developed. The method shows that weakly guiding, or linearly polarized (LP), modes are determined by and correspond uniquely to the characteristic numbers of Mathieu's equation. This is the first analysis of elliptical core weakly guiding modes which determines propagation constants and indexes modes by directly solving the underlying Mathieu's equation through the sole use of characteristic numbers. The resulting new analysis resolves an ambiguity in the standard literature concerning the classification of weakly guiding modes.