The field solution to the electromagnetic scattering of a plane wave by a uniaxial anisotropic sphere is obtained in terms of a spherical vector wave function expansion form. Using the source-free Maxwell's equations for uniaxial anisotropic media and making the Fourier transform of the field quantities, the electromagnetic fields in the spectral domain in uniaxial anisotropic media are assumed to have a form similar 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 transmitted fields and the scattered fields in uniaxial anisotropic media can be obtained analytically in the expansion form of vector wave eigenfunctions. Numerical results for some special cases are obtained and compared with those of the classical Lorenz-Mie theory and the method of moments accelerated with the conjugate-gradient fast-Fourier-transform approach. We also present some new numerical results for the more general uniaxial dielectric material media.

[1] An analytical solution of electromagnetic fields in homogeneous plasma anisotropic media is obtained in this paper. In the source-free plasma anisotropic media, the sourcefree 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 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-Gradient Fast-Fourier-Transform (CG-FFT) approach. The formulations in this paper can be generalized to those of more complex cases, such as layered plasma anisotropic sphere, plasma sheath, as well as plasma anisotropic material coated conducting sphere.

Until now, the expressions of the anisotropic energy barriers Δξ and ΔA, using the uniaxial magnetic anisotropy D, the intrachain coupling strength J, and the high-spin ground state S for single-chain magnets (SCMs) in the intermediate region between the Ising and the Heisenberg limits, were unknown. To explore this relationship, we used density functional theory and ab initio methods to obtain expressions of Δξ and ΔA in terms of D, J, and S of six R4Fe(II)-Re(IV)Cl4(CN)2 (R = diethylformamide (1), dibutylformamide (2), dimethylformamide (3), dimethylbutyramide (4), dimethylpropionamide (5), and diethylacetamide (6)) SCMs in the intermediate region. The ΔA value for compounds 1-3 was very similar to the magnetic anisotropic energy of a single Fe(II), while the value of Δξ was predicted using the exchange interaction of Fe(II) with the neighboring Re(IV), which could be expressed as 2JSReSFe. Similar to compounds 1-3, the anisotropy energy barrier ΔA of compounds 4 and 5 was also equal to (Di - Ei)SFe(2), but the correlation energy Δξ was closely equal to 2JSReSFe(cos 98.4 - cos 180) due to the reversal of the spins on the opposite Fe(II). For compound 6, one unit cell of Re(IV)Fe(II) was regarded as a domain wall since it had two different Re(IV)-Fe(II) couplings. Thus, the Δξ of compound 6 was expressed as 4J″SRe1Fe1SRe2Fe2, where J″ was the coupling constant of the neighboring unit cells of Re1Fe1 and Re2Fe2, and ΔA was equal to the anisotropic energy barrier of one domain wall given by DRe1Fe1(S(2)Re1Fe1 - 1/4).

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The scattering fields from 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 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 numerical results are given in this paper.