## 1. Introduction

[2] Electromagnetic and acoustic scattering by semi-infinite cones with a circular cross section have often been treated in the literature [*Siegel et al.*, 1955; *Felsen*, 1955, 1957a, 1957b] (for an overview, see *Bowman et al.* [1987]). The interest in this canonical structure is mainly motivated by the fact that it possesses a tip which is associated to a field- and current singularity, and the related tip diffraction coefficient could be a further element to complete asymptotic methods such as the Geometrical Theory of Diffraction [*Keller*, 1962]. In this context, the (not that often investigated) elliptic cone (that is, a cone with an elliptic cross section) is of particular interest as it provides a large variety of different geometries and corresponding tips, particularly including the circular cone and the plane angular sector.

[3] The diffraction of a plane electromagnetic wave by an electrically perfectly conducting (PEC) semi-infinite elliptic cone can be investigated by evaluating the corresponding dyadic Green's function, which is given by sums of dyads each consisting of vector multipole functions in sphero-conal coordinates. In work by *Blume et al.* [1993] [see also *Blume and Klinkenbusch*, 1999], methods have been represented how the outwardly traveling spherical waves of the total field can be used to calculate radar cross sections and diffraction coefficients of the elliptic cone. The main advantage of this method is that it automatically preserves the correct boundary conditions as it is purely based on the eigenfunction expansion of the elliptic cone. However, the outwardly traveling spherical waves do also include a part of the incident plane wave, in particular, they contain the transmitted field. These singular parts influence the behavior of the resulting series at all other directions as well, and nonlinear series summation techniques had to be applied to come to stable solutions with the disadvantage that the consistency of such nonlinear methods have not be proven for the cases in question [*Blume and Krebs*, 1998].

[4] The present paper describes a different approach to solve this scattered-field problem. First, from the dyadic Green's function of the elliptic cone we derive the exact surface current on the cone's surface for an incident plane wave by using a dipole source in the far-field and by employing an appropriate transformation [*Klinkenbusch*, 1993]. Next, we apply the equivalence principle, replace the PEC cone by this electric surface current, and obtain by means of the bilinear form of the free-space dyadic Green's function in sphero-conal coordinates the isolated scattered far-field. The corresponding limiting-value process which is necessary to obtain the scattered far-field has been successfully validated by the identically treatable half-plane problem [*Klinkenbusch*, 2006], which numerically yields the well-known *Keller* [1962] GTD results.

[5] The mathematical key to that solution is given by integrals which represent the coupling between the two (cone and free space) field expansions. In particular, all of these integrals are solved completely analytically, moreover, they explicitly provide quantitative rules about the “relative convergence” between the two expansions. Nevertheless, the attempt to simply summing up the final expansion (given in terms of free-space multipole functions) fails. That is expected since we are trying to represent the scattered far field which contains singularities by means of a multipole expansion which does not explicitly contain such singularities. However, useful numerical results can be obtained by employing suitable sequence transformation techniques, where, unlike the method mentioned above, a very simple linear (consistent) scheme, namely the Cesàro transform, is sufficient to come to physically meaningful asymptotic results. A comparison with available Physical Optics data for the bistatic scattering cross section of the nose-on illuminated circular cone yields a good agreement. Moreover, the numerical evaluation includes the scattering coefficients of semi-infinite circular and elliptic cones for non–nose-on-incident plane waves.