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论文范文
1. Introduction With the development of material science and fabrication techniques, the electromagnetic (EM) peculiarities of anisotropic media have attracted continued interests of both physics and engineering communities [1–7]. The effects of anisotropy or gyrotropy of the media must be taken into account in many practical applications, where a number of new devices with unique characteristics are designed by applying these effects [8, 9]. For studying the interactions of EM waves and gyrotropic media, the most important and challenging task is to solve the vector wave equation characterizing EM fields in gyrotropic media. In the last several decades, a few analytical approaches have been developed based on the Cartesian coordinate expression of permittivity and permeability tensors, such as the perturbation expansion method [10, 11], the method of expanding EM fields in gyrotropic media using a complete set of VSWFs [12], the method of adopting VSWFs combined with Fourier transform [13–15], dyadic Green’s functions method [16–18], and the -matrix method [19–23]. To study the spherical anisotropy, Qiu et al. have investigated the characteristics of radial anisotropic uniaxial and gyrotropic sphere, where the permittivity and permeability tensors are expressed in spherical coordinate [24–30]. Due to the completeness and noncoplanar properties of VSWFs, any three-dimensional vector function satisfying the vector Helmholtz equation can be expanded as a linear combinations of VSWFs [31]. In [20], Lin and Chui have developed a complete theory to solve Maxwell equations for gyromagnetic particles. This method has a good solution accuracy since it does not involve lengthy evaluations of complicated integrals. Li and Ong applied this method to study the EM scattering characteristics of a gyroelectric sphere in [21] and then generalized the scattering problem by considering both permittivity and permeability tensors in [22]. In [23], the homogeneous gyroelectric sphere considered in [20, 21] was extended to a multilayered gyroelectric sphere. In this paper, the method developed in [23] is further extended to the most general case: the gyrotropic sphere under consideration consists of multiple anisotropic layers, each of which is characterized by both permittivity and permeability tensors. A new -matrix formulation is proposed for the spherical multilayered scatterer. It is shown from numerical results that the proposed computation procedure is robust and accurate for a wide range of material parameters. In this method, the EM fields in each layer are first expanded as an infinite summation of VSWFs based on the Mie scattering theory [20, 32]. The expansion coefficients in each layer and the scattering coefficients are then determined recursively by matching the boundary conditions at all interfaces. To validate the derived formulation, we compare two specific RCS results with those obtained by the FEM simulation and the Fourier transform combined with VSWFs method [33] for gyrotropic and uniaxial cases, respectively. Excellent agreements can be observed. The formulation developed in this paper can be used as a reference for other analytical approaches or numerical methods relying on discretizations. Finally, we calculate the RCS for several specific cases to provide some physical insights and possibilities of optimized designs for suppressing or enhancing RCS based on multilayered gyrotropic structures. 
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