Application Of Spherical Vector Wave Function To Electromagnetic Scattering By Anisotropic Media

From the source-free Maxwell equations, using the Fourier transform and plane wave factors expansion with spherical vector wave functions in three-dimensional isotropic medium, the analytical solution of electromagnetic fields in anisotropic medium in terms of spherical vector wave functions can be derived. With the spherical vector wave functions in isotropic medium, the solution to electromagnetic scattering by spherical uniaxial anisotropic medium and plasma anisotropic medium with spherical vector wave functions have been obtained in this paper. The results of this dissertation are as follows:First, using the source-free Maxwell's equations in uniaxial anisotropic media and making the Fourier transform of the field quantities, the electromagnetic fields in spectral domain in uniaxial anisotropic media are assumed to have the similar form to the plane wave expanded also in terms of the spherical vector wave functions. Applying the continuous boundary conditions of electromagnetic fields on the surface between the air region and uniaxial anisotropic sphere, the coefficients of scattered fields in free space and the transmitted fields in uniaxial anisotropic medium can be obtained analytically in the expansion form of spherical vector wave eigenfunctions. Numerical results for some special cases are obtained, and compared with those of the classical Mie theory and the Method of Moments (MoM) accelerated with the Conjugate-Gradient Fast-Fourier-Transform (CG-FFT) approach. We also present some new numerical results for the more general uniaxial dielectric material media.Second, based on the spherical vector wave function in uniaxial anisotropic medium (part one), and the first, second, third and fourth spherical Bessel functions satisfy the same differential equation and recursive formula. The scattering fields in terms of spherical vector wave function from a uniaxial anisotropic spherical shell and an anisotropic uniaxial-coated conducting sphere by a plane wave are derived. The electromagnetic fields in uniaxial anisotropic medium and free space can be expressed in terms of spherical vector wave functions in uniaxial anisotropic media and isotropic medium. Applying the boundary condition in the interface between the uniaxial anisotropic medium and free space, the surface of the conducting sphere, the expansion coefficients of electromagnetic fields in terms of spherical vector wave function in uniaxial anisotropic medium are obtained, and then the expansion coefficients of scattering fields and radar cross sections can be obtained. Numerical results between this method and Mie theory are in good agreement as we expect. Some new numerical results have been given in the end of this part.Third, an analytical solution of electromagnetic fields in homogeneous plasma anisotropic media is obtained in this part. In the source-free plasma anisotropic media, the source-free Maxwell's equations are utilized, where the expansion of plane wave factors is made in terms of the spherical vector wave functions in isotropic media, and the Fourier transformation is then applied. As a result, the field expressions in terms of spherical vector wave functions in plasma anisotropic medium represented using eigenfunctions are obtained in spectral domain. Applying boundary conditions on the spherical interface between air and plasma anisotropy, the electromagnetic fields of the plane wave scattered by a plasma anisotropic sphere are derived. Numerical results for the very general plasma dielectric material media are obtained and those in a special case are compared between the present method and the Method of Moments (MoM) speeded up with the Conjugate-GradientFast-Fourier-Transform (CG-FFT) approach. Some new numerical results have been given in later of this part.Fourth, on the base of the analytical solution of electromagnetic fields in terms of spherical vector wave functions in source-free plasma anisotropic medium (part three), the first, second spherical vector wave functions in source-free plasma anisotropic medium satisfy the same Maxwell's equations, and the electromagnetic fields in plasma anisotropic spherical medium can be expressed as an addition of the first and the second spherical vector wave functions. Applying the continue boundary conditions of electromagnetic fields in the interface of plasma anisotropic spherical medium, the coefficients of electromagnetic fields in terms of spherical vector wave function can be derived in stratified plasma anisotropic medium. Two concentric plasma anisotropic spheres and multilayer anisotropic spheres have been discussed in detail. Some numerical results has been given, the theory and numerical results show that the present method can be degenerated to a single plasma anisotropic sphere when the two plasma anisotropic media nearly have the same parameter of medium.Fifth, we apply the formula of electromagnetic scattering of three-dimensional uniaxial anisotropic medium to the scattering of left-handed materials (LHMs), or negative index of refraction (NIR) materials uniaxial sphere and spherical shell, and some numerical results have been given in this part.In the end, some works which will be done are given.