Electromagnetic excitation of a solid oblate spheroid in a lossless medium by a low-frequency magnetic dipole
摘要
The current contribution is associated with the electromagnetic wave scattering of an impenetrable oblate spheroidal object, which is embedded within a lossless medium (e.g., air) and it is illuminated by an arbitrarily orientated time-harmonic magnetic dipolar source that operates at considerably low frequencies, since it is assumed to be located in a far distance from the solid body. The physical situation admits a classical Maxwell-type boundary value problem and it is processed by expanding the involved magnetic and electric fields via positive integral powers of the wave number of the medium, which is linearly connected to the implied frequency. The Rayleigh static term of zeroth order and the three first dynamic terms of the series sufficiently describe the fields, because higher-order terms are neglected due their minor contribution in the low-frequency regime. Evidently, the electromagnetic components of each remaining order constitute the fields under evaluation that comprise solutions of elliptic-type partial differential equations, which are accompanied by the appropriate boundary and limiting conditions. Implying the proper oblate spheroidal geometry, conveniently set at the center of the scatterer, the mathematical problem itself is readily solved, providing the spatial low-frequency electromagnetic fields in an analytical compact fashion as infinite series in terms of standard oblate spheroidal harmonic eigenfunctions and their counterparts. The validity of the presented analytical approach is demonstrated by including the reduction procedure for recovering the separate cases of a prolate spheroidal and a complete isotropic spherical target, hence a reliable benchmark is given.