A solution to the problem of three-dimensional scattering by an infinite homogeneous anisotropic elliptic cylinder for an obliquely incident plane wave of an arbitrary linear polarization is proposed. The axial components of the electromagnetic fields inside an anisotropic elliptic cylinder are represented as two coupled integrals of suitable eigenfunctions in elliptic coordinates in terms of Mathieu functions. Scattering by an anisotropic elliptic cylinder is different from scattering by a sphere or a circular cylinder because of the nonorthogonality properties of Mathieu functions at the interface between two different media. In order to solve this problem, Galerkin’s method is applied to the boundary conditions to solve the unknown coefficients. Numerical results are presented, discussed, and compared with available data.
© 2009 Optical Society of America
Original Manuscript: April 9, 2009
Revised Manuscript: August 30, 2009
Manuscript Accepted: September 4, 2009
Published: October 8, 2009
Shi-Chun Mao, Zhen-Sen Wu, and Hai-Ying Li, "Three-dimensional scattering by an infinite homogeneous anisotropic elliptic cylinder in terms of Mathieu functions," J. Opt. Soc. Am. A 26, 2282-2291 (2009)