Scattering of electromagnetic waves from a multilayer elliptic cylinder moving in the axial direction Matteo Pastorino * Mirco Raffetto † December 20, 2012 Abstract A new exact solution to the problem of scattering of electromagnetic waves from multilayer elliptic cylinders moving in the axial direction is proposed. The homogeneous media of the different layers are assumed to be linear and isotropic in their rest frames. All media which are not at rest with respect to the host medium are, moreover, supposed to have an electric conductivity equal to zero (in their rest frames). Starting from the fact that a moving medium can be treated as a stationary bianisotropic one we deduce the series expansions in terms of Mathieu functions for the electromagnetic fields in the different layers. Then an efficient recursive procedure for the computation of the solutions is developed. Some numerical results show the reliability of the solution and the efficiency of the recursive procedure proposed. Keywords: electromagnetic scattering; time-harmonic electromagnetic fields; bianisotropic media; moving media; inhomogeneous elliptic cylinders; multilayer elliptic cylinders; recursive analytical procedure; series solution. 1 Introduction The electromagnetic scattering by canonical objects has been widely studied in the framework of the electromagnetic theory. Canonical scatterers are very important also in practical applications, since, as it is well known, they allow to find field solutions for targets that can approximate con- figurations encountered in real applications. Moreover, they can be adopted for testing numerical methods of interest in many specific situations (e.g., imaging applications). The scientific litera- ture about the scattering by canonical targets is wide and the reader can refer, for example, to the comprehensive book by Bowman et al [1]. Among the various possible solutions, the authors proposed in [2] a recursive solution for the scattering by multilayer elliptic dielectric cylinders, which was an extension of the Yeh solution for a single homogeneous elliptic cylinder [3], [4]. The solution for this scatterer shape is important since the multilayer elliptic cylinder can simulate several coated targets (e.g., tunnels and pipes [5], airplane fuselages [6], simplified models of parts of the human body [7], etc.). The algorithm proposed in [2], which has been extended to cylinders with perfect electric conductors cores in [8] and to other dielectric materials in [9], [10], [11], is computationally efficient and allowed to solve problems which were considered to be “relatively intractable” by Richmond [12]. It should be noted that other solutions for configurations involving elliptic cylinders have been developed in several papers (see, for example [13], [14], [15]). In the field of canonical objects, great interest has also been focused on the study of moving media, which needs the introduction of relativistic concepts, at least when the moving velocity * Department of Telecommunication, Electrical, Electronics, and Naval Engineering, University of Genoa, Via Opera Pia 11a, I–16145, Genoa, Italy, email: pastorino@dibe.unige.it † Department of Telecommunication, Electrical, Electronics, and Naval Engineering, University of Genoa, Via Opera Pia 11a, I–16145, Genoa, Italy, email: raffetto@dibe.unige.it 1