Electromagnetic excitation of dielectric concentric elliptical cylinders

Elliptically symmetric surface current sources excite respectively an infinite, materially uniform (permittivity and permeability) region and dielectric concentric elliptical cylinders. Electromagnetic fields are expanded in Mathieu functions and found by using the method of moments and imposing boundary conditions. Orthogonality of angular Mathieu functions in the uniform case simplifies the expansion coefficients' linear system and the modes decouple. Mode coupling occurs when the excitation source is interior and exterior to the concentric elliptical cylinders because the system is inhomogeneous. For the interior source, power conservation and electromagnetic field matching on the interfaces validate the computational method. Electromagnetic fields are obtained for excitation due to the zero and second order modes respectively of the exterior source. On the interfaces, these exhibit structure with the angular coordinate and many more modes are necessary for convergence for the exterior source than for the interior source.