Plane-wave expansion of elliptic cylindrical functions

• We apply an integral representation of Mathieu functions available in the literature.
• We show analytical derivation of plane-wave spectrum of Elliptic Cylindrical Waves.
• We reduce the plane-wave spectrum to a simple analytic form.
• We test numerical accuracy and reliability of the proposed spectrum.

Elliptic Cylindrical Waves (ECW), defined as the product of an angular Mathieu function by its corresponding radial Mathieu function, occur in the solution of scattering problems involving two-dimensional structures with elliptic cross sections. In this paper, we explicitly derive the expansion of ECW, along a plane surface, in terms of homogeneous and evanescent plane waves, showing the accuracy of the numerical implementation of the formulas and discussing possible applications of the result.