# Scattering by rotationally symmetric anisotropic spheres: Potential formulation and parametric studies

## Abstract

Vector potential formulation and parametric studies of electromagnetic scattering problems of a sphere characterized by the rotationally symmetric anisotropy are studied. Both {epsilon} and {mu} tensors are considered herein, and four elementary parameters are utilized to specify the material properties in the structure. The field representations can be obtained in terms of two potentials, and both TE (TM) modes (with respect to r) inside (outside) the sphere can be derived and expressed in terms of a series of fractional-order (in a real or complex number) Ricatti-Bessel functions. The effects due to either electric anisotropy ratio (A{sub e}={epsilon}{sub t}/{epsilon}{sub r}) or magnetic anisotropy ratio (A{sub m}={mu}{sub t}/{mu}{sub r}) on the radar cross section (RCS) are considered, and the hybrid effects due to both A{sub e} and A{sub m} are also examined extensively. It is found that the material anisotropy affects significantly the scattering behaviors of three-dimensional dielectric objects. For absorbing spheres, however, the A{sub e} or A{sub m} no longer plays a significant role as in lossless dielectric spheres and the anisotropic dependence of RCS values is found to be predictable. The hybrid effects of A{sub e} and A{sub m} are considered for absorbing spheres as well, but it is foundmore »

- Authors:

- Department of Electrical and Computer Engineering, National University of Singapore, Kent Ridge, Singapore 119260 (Singapore)
- (France)

- Publication Date:

- OSTI Identifier:
- 21072389

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics; Journal Volume: 75; Journal Issue: 2; Other Information: DOI: 10.1103/PhysRevE.75.026609; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ANISOTROPY; BESSEL FUNCTIONS; DIELECTRIC MATERIALS; ELECTROMAGNETIC RADIATION; PARAMETRIC ANALYSIS; PERMITTIVITY; POTENTIALS; SCATTERING; SPHERES; VECTORS

### Citation Formats

```
Qiu, C.-W., Li, L.-W., Yeo, T.-S., Zouhdi, Saied, and Laboratoire de Genie Electrique de Paris, Ecole Superieure D'Electricite, Plateau de Moulon 91192, Gif-Sur-Yvette, Cedex.
```*Scattering by rotationally symmetric anisotropic spheres: Potential formulation and parametric studies*. United States: N. p., 2007.
Web. doi:10.1103/PHYSREVE.75.026609.

```
Qiu, C.-W., Li, L.-W., Yeo, T.-S., Zouhdi, Saied, & Laboratoire de Genie Electrique de Paris, Ecole Superieure D'Electricite, Plateau de Moulon 91192, Gif-Sur-Yvette, Cedex.
```*Scattering by rotationally symmetric anisotropic spheres: Potential formulation and parametric studies*. United States. doi:10.1103/PHYSREVE.75.026609.

```
Qiu, C.-W., Li, L.-W., Yeo, T.-S., Zouhdi, Saied, and Laboratoire de Genie Electrique de Paris, Ecole Superieure D'Electricite, Plateau de Moulon 91192, Gif-Sur-Yvette, Cedex. Thu .
"Scattering by rotationally symmetric anisotropic spheres: Potential formulation and parametric studies". United States.
doi:10.1103/PHYSREVE.75.026609.
```

```
@article{osti_21072389,
```

title = {Scattering by rotationally symmetric anisotropic spheres: Potential formulation and parametric studies},

author = {Qiu, C.-W. and Li, L.-W. and Yeo, T.-S. and Zouhdi, Saied and Laboratoire de Genie Electrique de Paris, Ecole Superieure D'Electricite, Plateau de Moulon 91192, Gif-Sur-Yvette, Cedex},

abstractNote = {Vector potential formulation and parametric studies of electromagnetic scattering problems of a sphere characterized by the rotationally symmetric anisotropy are studied. Both {epsilon} and {mu} tensors are considered herein, and four elementary parameters are utilized to specify the material properties in the structure. The field representations can be obtained in terms of two potentials, and both TE (TM) modes (with respect to r) inside (outside) the sphere can be derived and expressed in terms of a series of fractional-order (in a real or complex number) Ricatti-Bessel functions. The effects due to either electric anisotropy ratio (A{sub e}={epsilon}{sub t}/{epsilon}{sub r}) or magnetic anisotropy ratio (A{sub m}={mu}{sub t}/{mu}{sub r}) on the radar cross section (RCS) are considered, and the hybrid effects due to both A{sub e} and A{sub m} are also examined extensively. It is found that the material anisotropy affects significantly the scattering behaviors of three-dimensional dielectric objects. For absorbing spheres, however, the A{sub e} or A{sub m} no longer plays a significant role as in lossless dielectric spheres and the anisotropic dependence of RCS values is found to be predictable. The hybrid effects of A{sub e} and A{sub m} are considered for absorbing spheres as well, but it is found that the RCS can be greatly reduced by controlling the material parameters. Details of the theoretical treatment and numerical results are presented.},

doi = {10.1103/PHYSREVE.75.026609},

journal = {Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics},

number = 2,

volume = 75,

place = {United States},

year = {Thu Feb 15 00:00:00 EST 2007},

month = {Thu Feb 15 00:00:00 EST 2007}

}