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Hindawi Publishing Corporation

International Journal of Antennas and Propagation

Volume 2011, Article ID 409764, 6 pages

doi:10.1155/2011/409764

Research Article

Scattering of a Plane Wave by an Anisotropic Plasma-Coated

Conducting Sphere

You-Lin Geng

Institute of Antenna and Microwaves, Hangzhou Dianzi University, Xiasha, Zhejiang Province, Hangzhou 310018, China

Correspondence should be addressed to You-Lin Geng, gengyoulin@yahoo.com.cn

Received 19 June 2011; Revised 18 August 2011; Accepted 24 August 2011

Academic Editor: Miguel Ferrando

which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

The electromagnetic ﬁeld in homogeneous plasma anisotropic medium can be expressed as the addition of the ﬁrst and second

spherical vector wave functions in plasma anisotropic medium. The tangential electromagnetic ﬁelds are continued in the

boundary between the homogeneous plasma anisotropic medium and free space, and the tangential electrical ﬁeld is zero in

the surface of conducting sphere. The coeﬃcients of electromagnetic ﬁelds in plasma anisotropic medium expanded in terms of

spherical vector wave functions in plasma anisotropic medium are derived, and then the coeﬃcients of scattering ﬁelds in terms of

spherical vector functions in free space can be obtained. Numerical results between this paper and hybrid ﬁnite element-boundary

integral-multilevel fast multipole algorithm (FE-BI-MLFMA) are given, and they are in agreement very well. Some new numerical

results of a plane wave scattering by an anisotropic plasma-coated conducting sphere are obtained.

1. Introduction

Plasma represents a medium of gas in highly ionized state,

and it is a neutral mixture of free ions, electrons, and mole-

cules. For example, when the ionosphere and the sheath of

satellite and missile come into atmosphere, the y are consider-

ed to be plasma in nature. When there is an externally applied

magnetic ﬁeld, a plasma exhibits anisotropic behavior and its

permittivity takes a tensor form. The elements of the permit-

tivity tensor are complex functions of wave, plasma, gyro and

collision frequencies [1–3]. Wave propagation in, and scatter-

ing by, an anisotropic medium is nonreciprocal, and its anal-

ysis becomes very diﬃcult even when the plasma is treated

as an incompressible gas [1–4].

The interaction between e lectromagnetic wave and an-

isotropic medium has attracted much interest. It is simply be-

cause there are many natural and artiﬁcial anisotropic mate-

rials, and they are frequently used in optical signal processing

(such as constructing signal processing elements at optical

frequencies), the radar cross-section control for various

objects or scatterers, antennas or airborne radomes, optical

ﬁbers, developments of certain types of radar absorbers, and

high-perfor m ance microstrip antenna designs where the

substrates of this nature are desirable.

One of the basic problems in investigating waves in aniso-

tropic media is to accurately and eﬃciently characterize elec-

tromagnetic scattering. Scattering by homogeneous aniso-

tropic objects has attracted considerable interests in recent

years. Numerical methods based on integral equations [5]as

well as diﬀerential equations [6] were developed, and the

analytical method based on eigen vector wave functions [7]

was also adopted to characterize this kind of problems. Al-

though the eﬀorts in the past were primarily spent on two-

dimensional (2-D) geometries, some progresses have been

made in the analysis of three-dimensional (3-D) anisotropic

scatterers using the method of moments (MoM) [8, 9], the

couple dipole approximation method [10], hybrid ﬁnite

element-boundary integral-multilevel fast multipole algo-

rithm (FE-BI-MLFMA) [11], integral equation method [12],

and Fourier transform, eigenvalue and eigen functions,

spherical vector wave functions solution [13–15]. In the pre-

sent study, the simple and eﬃcient method proposed in [13]

will be employed to tackle the scattering problem associated

with an anisotropic plasma-coated conducting sphere by a

plane wave.

Electromagnetic ﬁelds in plasma anisotropic medium

andfreespacecanbeexpandedintermsofsphericalvector

wave functions in plasma anisotropic medium and free space,

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