The Method of Lines: A Versatile Tool for the Analysis of Waveguide Structures

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Abstract
Algorithms for the determination of eigenmodes and for the analysis of longitudinally varying structures are presented. The media may be anisotropic and the devices may consist of an arbitrary number of layers or waveguide sections, respectively. Starting with generalized transmission line equations, suitable expressions are derived which are implemented in the method of lines, a semianalytical algorithm. To ensure the numerical stability, a transformation of the reflection coefficient is performed. Numerical results are presented for a Bragg-grating with a very high number of periods, for an electro-optical switch, and for an anisotropic groove waveguide. The results prove stability of the algorithm, and comparisons with other methods show the accuracy.