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.

Plasma represents a medium of gas in highly ionized state, and it is a neutral mixture of free ions, electrons, and molecules. For example, when the ionosphere and the sheath of satellite and missile come into atmosphere, they are considered 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 permittivity tensor are complex functions of wave, plasma, gyro and collision frequencies [

The interaction between electromagnetic wave and anisotropic medium has attracted much interest. It is simply because there are many natural and artificial anisotropic materials, 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-performance microstrip antenna designs where the substrates of this nature are desirable.

One of the basic problems in investigating waves in anisotropic media is to accurately and efficiently characterize electromagnetic scattering. Scattering by homogeneous anisotropic objects has attracted considerable interests in recent years. Numerical methods based on integral equations [

Electromagnetic fields in plasma anisotropic medium and free space can be expanded in terms of spherical vector wave functions in plasma anisotropic medium and free space, respectively. Applying the continued boundary conditions of electromagnetic fields on the interfaces between the free space and a coated-plasma anisotropic medium, and the vanishing of the tangential field in the surface of the conducting sphere, the coefficients of electromagnetic fields in plasma anisotropic medium and scattered fields in free space can be obtained. Then, radar cross-sections of an anisotropic plasma-coated conducting sphere scattered by a plane wave can be derived. The theoretical analysis shows that the present method can be reduced to these of the homogeneous plasma anisotropic medium when the radius of conducting sphere approaches zero. This analytical solution to electromagnetic scattering by an anisotropic plasma-coated conducting sphere can be used to characterize the targets and their radar cross-sections and also to understand wireless communication channels and radio wave propagation mechanisms.

Consider the geometry depicted in Figure

The geometry of scattering of a plane wave by an anisotropic plasma-coated conducting sphere.

The electric field vector wave equation in such a source-free plasma anisotropic medium can be written in the following form [

Equation (3) are the spherical vector wave functions in plasma anisotropic medium, which is different to that in isotropic medium which are shown in (4a) and (4b),

first, spherical vector wave functions in plasma anisotropic medium is an integral expression comparing to that in isotropic medium, and

second, the eigenvalues (

The spherical vector wave functions in plasma anisotropic medium is more complex than that in isotropic medium, and electromagetic fields in plasma anisotropic medium can be expressed by that in anisotropic medium.

To characterize the scattering properties of the plasma-coated conducting sphere, the incidence wave (designated by the superscript inc) and the scattered wave (designated by the superscript

From (3), it shows that when the radius

By applying continuous boundary conditions of tangential electromagnetic field components on the interface between the plasma anisotropic medium and free space (where

firstly, there are six equations and six unknown coefficients, namely

then, the radar cross-section of an anisotropic plasma-coated conducting sphere by a plane wave can be derived.

In the last section, we have presented the necessary theoretical formulation of the electromagnetic fields of a plane wave scattered by an anisotropic plasma-coated conducting sphere. To gain more physical insight into the problem, we will provide, in this section, some numerical solutions to the problem of a plane electromagnetic wave scattered by an anisotropic plasma-coated conducting sphere.

To demonstrate the accuracy of the solutions achievable by using the present method, we compare bistatic radar cross-sections (RCSs) in

Radar cross-sections (RCSs) versus scattering angle

After the validation studies, we obtain some new results unavailable elsewhere in literature. Three examples are considered herein, and their radar cross-sections are plotted in Figures

Radar cross-sections (RCSs) versus scattering angle

Radar cross-sections (RCSs) versus scattering angle

Radar cross-sections (RCSs) versus scattering angle

Figure

To illustrate further applicability of the solution to electromagnetic scattering by an electrically large-sized anisotropic plasma-coated conducting sphere (e.g., in its resonance region), the radar cross-sections of a coated sphere of relatively large electric size with

From the above discussions, it is seen and concluded that

the radar cross-sections (RCS’s) (

for a medium-sized anisotropic plasma-coated conducting sphere, the RCS’s in both the

as the large-size for out radius of an anisotropic plasma-coated conducting sphere, the RCS’s in the

The spherical vector wave functions expansion technique is successfully applied in the present work for an analytical solution to the problem of plane wave scattering by an anisotropic plasma-coated conducting sphere in this paper. The solution has only one-dimensional integral which can be easily evaluated. The theoretical analysis shows that when the radius of conducting sphere approaches zero, the results of present formulation can be reduced to those of a single plasma anisotropic sphere. In addition, the general numerical results, including the lossy plasma-coated conducting sphere and resonance region, are given.

The author is greatly indebted to Professor Sheng X. Q. and Dr. Peng Z. in Beijing Institute of Technology for sending us their data. This work is partially supported by Grant no. 60971047 of National Natural Science Foundation of China (NSFC), and Grant no. Y1080730 of Natural Science Foundation of Zhejiang Province of China.