Analytical solutions to Maxwell's equations in homogeneous media.

摘要

The coupled differential equations that dictate the behavior of electromagnetic phenomena are known collectively in the literature as Maxwell's equations. Analytical solutions to these equations are notoriously difficult to obtain and, in general, can only be obtained for problems possessing a great deal of symmetry. Numerical methods are used for solving problems involving more complicated geometries.; In this thesis, exact analytical solutions to Maxwell's equations are presented for the case of homogeneous media. The solutions are obtained using a novel mathematical approach. Detailed derivations are provided for a lossless homogeneous medium in one, two, and three dimensions. In addition, the newly obtained one-dimensional solutions are converted to discrete form apt for use in computer programs. Several examples of transmission lines and one-dimensional propagating waves using these discrete solutions are presented and the results discussed.