Exact and Physical‐Optics analysis of the electromagnetic scattering by an elliptic cone

Abstract

Purpose

The purpose of this paper is to compare exact and Physical‐Optics‐approximated results of the electromagnetic field scattered by a perfectly conducting semi‐infinite elliptic cone illuminated by a plane wave. The results are important for judging the reliability of Physical‐Optics based field estimations of electrically large environments which include tip‐like structures (e.g. airport scenarios).

Design/methodology/approach

The spherical‐multipole analysis is applied to determine the exact total field outside a perfectly conducting semi‐infinite elliptic cone. The underlying boundary‐value problem is solved by a separation of variables of the Helmholtz equation in sphero‐conal coordinates leading to a two‐parametric eigenvalue problem with two coupled Lamé differential equations. The exact scattered far field is determined from the exact surface current on the cone using a bilinear expansion of the dyadic Green's function. The Physical‐Optics (PO) field is evaluated similarly starting from a surface current which is directly found from the incident magnetic field.

Findings

The diffraction coefficients of the exact scattered field and the PO scattered field are compared for different parameters (polarization and angle of incidence) of the plane wave. Reasonably well corresponding results are obtained for those angles of incidence of the plane wave where the entire cone is illuminated, otherwise the error of the PO approximation is increasing not just in the shadow region.

Originality/value

If carefully applied, the Physical‐Optics method can be useful and sufficient to obtain fields scattered by cone‐like structures.

Citation

Kijowski, M. and Klinkenbusch, L. (2013), "Exact and Physical‐Optics analysis of the electromagnetic scattering by an elliptic cone", COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, Vol. 32 No. 3, pp. 868-884. https://doi.org/10.1108/03321641311305809