The Electromagnetic (EM) fields of a concentric, mismatched-material, elliptical system are studied when excited by an interior or exterior electric surface current. The interior or exterior surface current is assumed to be proportional to a single, angular Mathieu mode. It is shown that despite the fact that the system is concentric, that a single Mathieu mode surface current excites EM Mathieu-mode fields of all orders. A derivation of the EM fields due a single mode electric surface in an infinite, homogeneous media is given, as well as the matrix formulation from which the EM fields of the mismatched-material, elliptical system may be determined. Validation of numerical results and comparison with other research work is given for both interior and exterior single-mode, current sources. Detailed numerical examples of the EM fields that result for a single-mode, exterior source excitation are given for the first time. Discussion of the EM mode coupling that results by single-mode excitation on a mismatched elliptical system is given.
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