Abstract

A method presented previously [ J. Opt. Soc. Am. A 3, 116 ( 1984)] for the determination of the number of guided modes in layered structures is extended to the case of graded-index waveguides. It is shown that the recursion relation that connected the phase of the wave function in adjacent layers is transformed into a form of nonlinear, first-order differential equation for this phase. Mathematical properties of this equation are discussed, and examples of applications are presented.

© 1987 Optical Society of America

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