## Abstract

A polynomial expansion approach to the extraction of guided and leaky modes in layered structures including dielectric waveguides and periodic stratified media is proposed. To verify the method we compared the results of analysis of a typical test case with those reported in the literature and found good agreement. Polynomial expansion is a nonharmonic expansion and does not involve harmonic functions or intrinsic modes of homogenous layers. This approach has the benefit of leading to algebraic dispersion equations rather than to a transcendental dispersion equation; therefore, it will be easier to use than other methods such as the argument principle method, the reflection pole method, and the wave-vector density method, which solve the transcendental dispersion equation by means of integrals. Besides, an algebraic dispersion equation can be obtained without any problem of numerical instability, whereas an ordinary transcendental dispersion equation, which is usually derived by the transfer matrix method, is difficult to obtain because of instability in multiplying transfer matrices. A demonstration of the utility of the proposed method when the other methods mentioned are inferior or fail are also given.

© 2003 Optical Society of America

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