Mathieu functions and their applications to scattering by a coated strip

The elliptic-cylinder harmonics, known as Mathieu (1868) functions, are reviewed. These functions are then used to describe EM scattering by confocal elliptic cylinders where each cylinder´s dielectric constant is different. A peculiarity of this problem is that the Mathieu functions in different regions are not orthogonal at regional boundaries. Hence, each boundary couples all harmonics from both sides together, and infinite sets of coefficients must be simultaneously evaluated. Numerical results are given for the special case where the innermost region is a perfect conductor. The authors consider both TE and TM illumination. Only normal incidence is actually treated, although oblique generalization is conceptually easy