Cấu trúc sóng chức năng trong điện lý thuyết P3

Dyadic Green’s Functions in Spheroidal Systems3.1 DYADIC GREEN’S FUNCTIONS To analyze the electromagnetic radiation from an arbitrary current distribution located in a layered inhomogeneous medium, the dyadic Green’s function (DGF) technique is usually adopted. If the geometry involved in the radiation problem is spheroidal, the representation of dyadic Green’s functions under the spheroidal coordinates system should be most convenient. If the source current distribution is known, the electromagnetic fields can be integrated directly from where the DGF plays an important role as the response function of multilayered dielectric media....
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Cấu trúc sóng chức năng trong điện lý thuyết P3 Spheroidal Wave Functions in Electromagnetic Theory Le-Wei Li, Xiao-Kang Kang, Mook-Seng Leong Copyright  2002 John Wiley & Sons, Inc. ISBNs: 0-471-03170-4 (Hardback); 0-471-22157-0 (Electronic) 3Dyadic Green’s Functions in Spheroidal Systems3.1 DYADIC GREEN’S FUNCTIONSTo analyze the electromagnetic radiation from an arbitrary current distribu-tion located in a layered inhomogeneous medium, the dyadic Green’s function(DGF) technique is usually adopted. If the geometry involved in the radiationproblem is spheroidal, the representation of dyadic Green’s functions underthe spheroidal coordinates system should be most convenient. If the sourcecurrent distribution is known, the electromagnetic fields can be integrated di-rectly from where the DGF plays an important role as the response functionof multilayered dielectric media. If the source is of an unknown current distri-bution, the method of moments [87], which expands the current distribution into a series of basis functions with unknown coefficients, can be employed. Inthis case, the DGF is considered as a kernel of the integral; and the unknowncoefficients of the basis functions can be obtained in matrix form by enforcing the boundary conditions to be satisfied. Dyadic Green’s functions in various geometries, such as single stratified planar, cylindrical, and spherical structures, have been formulated [ 14,88-901. In multilayered geometries, the DGFs have also been constructed and their coefficients derived. Usually, two types of dyadic Green’s functions, electro- magnetic (field) DGFs and Hertzian vector potential DGFs, were expressed. Three methods that are common and available in the literature: the Fourier transform technique (normally, in planar structures only), the wave matrix operator and/or transmission line (frequently, in planar structures) method, and the vector wave eigenfunction expansion method (in regular structures 6162 DYADIC GREEN’S FUNCTIONS IN SPHEROIDAL SYSTEMSwhere vector wave functions are orthogonal). In general, two domains areassumedin formulations of the DGFs: i.e. the time domain and the spectral(or frequency) domain, where the spatial variables T and T’ are still in use.However, it must be noted that the spectral domain has a different meaningin the derivation of the DGFs for planar stratified media. This is becausethe Fourier transform is frequently utilized there to transform part of thespatial components from the conventional spectral domain to a Fourier trans-form domain. The conventional spectral (or frequency) domain in this caseis referred to a~ the spatial domain and the Fourier transform domain as thepartial spectral domain, where spectral components such as k, associated withthe discontinuity along the direction are considered. In a planar stratified geometry [ 141, Lee and Kong [91] in 1983 employed theFourier transform to deduce the DGFs in an anisotropic medium; Sphicopouloset al. [92] in 1985 used an operator approach to derive the DGFs in isotropicand achiral media; Das and Pozer [93] in 1987 utilized the Fourier transformtechnique; Vegni et al. [94] and Nyquist and Kzadri [95] in 1991 made use ofwave matrices in the electric Hertz potential to obtain DGFs and their scat-tering coefficients in isotropic and achiral media; Pan and Wolff [96] employedscalarized formulas, and Dreher [97] used the Fourier transform and methodof lines to rederive the DGFs and their coefficients in the same medium; Mesaet al. [98] applied the equivalent boundary method to obtain the DGFs andtheir coefficients in two-dimensional inhomogeneous bianisotropic media; Aliet al. [99] in 1992 used the Fourier transform, and Li et al. [loo] in 1994employed vector wave eigenfunction expansion to formulate the DGFs andformulated their coefficients in isotropic and chiral media; Bernardi and Cic-chetti [loll again employed Fourier transform and operator technique to thesame medium but with backed conducting ground plane; Barkeshli utilizedthe Fourier transform technique in 1992 and 1993 to express the DGFs andtheir coefficients in anisotropic uniaxial [102] media, dielectric/magnetic media [103], and gyroelectric media [104]; Habashy et al. [105] in 1991 applied theFourier transform technique to work out the DGFs in arbitrarily magnetizedlinear plasma. For the casesof a free space (or unbounded space), a single-layered medium, or a multilayered structure, many references exist, such asvarious representations by Pathak [lOS], C avalcante et al. [107], Engheta andBassiri [108], Chew [go], Gl isson and Junker [1091, Krowne [l lo], Lakhtakia [ill-1131, Lindell [114], T oscano and Vegni [1151, and Weiglhofer [116-1201.Since a large number of publications are available, it is impractical to list allof them here. In a multilayered cylindrical geometry [14], the DGFs in the chiral media and the specific coefficients were given in 1993 by Yin and Wang [121]. Later in 1995, the unified DGFs in chiral media and their scattering coefficients in general form were formulated by Li et al. [122]. In a multilayered spherical geometry [14,123,124], the DGFs in achiral media and their scattering coefficients were generalized in 1994 by Li et al. FUNDAMENTAL FORMULATION 6311251. This work was then extended in 1995 to the DGFs in chiral media, andtheir scattering c ...