Dyadic eigenfunctions and natural modes for hybrid waves in planar media

A new formulation for studying electromagnetic wave propagation in an open, planarly layered medium is presented based on eigenfunctions of the Hertzian potential dyadic Green's function operator. Due to the complicated coupling of scalar components of potential at material interfaces, elevation of the usual vector eigenfunction problem to dyadic level is found to lead to a convenient, compact representation of wave propagation phenomena. Although we study the source-free problem here, the three columns of the eigenfunction dyadics represent (up to an excitation-dependent amplitude) the vector fields excited by a given three-dimensional source. The general theory of dyadic eigenfunctions is presented, including orthogonality and the possibility of associated functions (root functions) at modal degeneracies, and an example of propagation in a grounded dielectric slab environment is provided.     

Reciprocity relationships for bianisotropic media

Reciprocity relationships for electromagnetic fields with general time dependence in bianisotropic media are derived and discussed. Constitutive relations of complementary media are defined to warrant a modified reciprocity relationship. As a consequence, the magnetoelectric media, the Tellegen media, and the moving media are all nonreciprocal. The complementary media to uniformly moving media with symmetrical permeability and permittivity tensors in their rest frames of reference are the same ones moving in the opposite direction.     

Full-wave analysis of planar stratified media with inhomogeneouslayers

In this paper, the dyadic Green's functions for an inhomogeneous isotropic grounded slab embedded in an unbounded isotropic half-space fed by an electric three-dimensional (3-D) point-source based on the equivalent two-port circuit representation along the axis normal to the stratification is presented. The working case is extensively investigated by deriving important information on the radiation of the structure and on how to control the radiation on the horizon plane. Numerical results are also presented showing the effects of the electromagnetic parameters on radiation pattern of the integrated structure     

Theorems of bianisotropic media

Theorems concerning electromagnetic fields in linear nonconducting bianisotropic media are investigated. After establishing their symmetry properties, the constitutive relations are examined under time reversal and spatial inversion transformations. Conditions under which the image method and the reciprocity relationships can be applied are discussed. Dyadic Green's functions and duality relations are also derived. With a postulated Lagrangian density, Maxwell's equations are obtained from Hamilton's principle, and energy momentum tensors are obtained from Noether's theorem. Introducing a quantum postulate in addition to the Maxwell's equations, electromagnetic fields in bianisotropic media are quantized.     

Passbands of bianisotropic and waveguide bianisotropic metamaterials based on planar double split rings

The transmission properties of a bianisotropic composite material based on regular gratings of planar double split rings (PDSRs) and a waveguide bianisotropic composite material of waveguide structures loaded with such gratings are studied theoretically and experimentally. The tensors of effective permittivity, permeability, and chirality of the PDSR medium are calculated with allowance for the diagonality of the tensors relating the local-average field differences to the PDSR dipole moments, and the dispersion equation is solved. Frequency dependences of the effective refractive indexes of both composite materials are studied. Their pass-bands are determined, the conditions for the existence of forward and backward waves are formulated, and the respective regions of existence (left and right passbands) are found. It is shown that a medium containing only similarly oriented PDSRs at a low concentration has a frequency band in which the permittivity and permeability are both negative, but the squared refractive index is negative there as well and, hence, the waves do not propagate. The positional relationship between the overforbidden bands and passbands of the waveguide bianisotropic material with PDSRs is studied theoretically and experimentally for different excitation conditions of the PDSR system.     

Covariant descriptions of bianisotropic media

It is suggested that a medium it which the field vectors D and H depend on both E and B but are parallel to neither be described as bianisotropic. A moving medium, even if it is isotropic it its rest frame, then appears bianisotropic to the laboratory observer. This paper gives the transformation formulas for the constitutive relations of a bianisotropic medium between inertial frames in relative motion. It circumvents the necessity of knowing the constitutive relations of the medium in its rest frame. As an application of the general formulation, the dispersion relations for plane waves in a bianisotropic medium are derived.     

On surface integral representations: validity of Huygens' principleand the equivalence principle in inhomogeneous bianisotropic media

Here we provide the mathematical foundation for general inhomogeneous (even discontinuous) media for the principle that Huygens devised with ingenious foresight over three hundred years ago (1690). We also validate the associated (and often used without a proof) equivalence principle as a natural extension of the isotropic formalism     

Coordinate-independent dyadic formulation of the dispersionrelation for bianisotropic media

This paper presents a coordinate-independent dyadic formulation of the dispersion relation for general bianisotropic media. The dispersion equation is expanded with the aid of dyadic operators including double-dot, double-cross and dot-cross or cross-dot products. From the dispersion relation, the Booker quartic equation is derived in a form well-suited for studying multilayered structures. Several deductions are made in conjunction with the bianisotropic media satisfying reciprocity and losslessness conditions. In particular, for reciprocal bianisotropic media, the dispersion equation is biquadratic in wave vector while for lossless bianisotropic media, all dispersion coefficients are of real values. As an application example, the dispersion equation for gyrotropic bianisotropic media is considered in detail     

General form of the reciprocity relationship for bianisotropic media

In this letter, the reciprocity relationship of electromagnetic theory is established for the bianisotropic media. The result is applied to the particular case of a uniformly moving medium, even when it has anisotropic properties in its rest frame.     

Field decomposition and factorization of the Helmholtz determinantoperator for bianisotropic media

The paper generalizes the class of media for which the electromagnetic (EM) fields can be decomposed in two independent components. Each of the two components see the medium as a simpler, so called, equivalent medium. This generalization was possible because it was realized that the plane-wave fields satisfy E·D-H·B=0. This discovery allows us to come to a consistent structure for the class of decomposable and factorizable bianisotropic media encompassing all previously studied media as special cases. The class of media of the present paper is shown to be closed with respect to duality transformations. We dare to say that the present paper puts the crown on a long quest for always more general classes of media that allow decomposition and factorization. The equivalent media yield a new class of media that allow a closed form representation of the Green dyadics     

TE-TM decoupling for guided propagation in bianisotropic media

The most general bianisotropic or magneto-electric medium is considered. Necessary and sufficient conditions are established for guided propagation in such a medium to be described in terms of the superposition of TE and TM fields. An additional condition ensures TE-TM decoupling independently of the direction of propagation in the medium. The field components for TE and TM fields are given     

Some properties of lossless bianisotropic media

Conditions for the constitutive dyadic parameters of a lossless bianisotropic medium are derived. Applying these conditions it is shown that a conservation relation, previously shown to hold for lossless anisotropic media, also holds for lossless bianisotropic media. Further, it is shown that a lossless bianisotropic medium set in motion remains lossless.     

Comments on "Theorems of bianisotropic media"

The conditions for electromagnetic reciprocity can be satisfied or not by a given anisotropic medium, depending on the particular choice of a complex reference frame. Consequently, when statements are made on an anisotropic medium being reciprocal or not, polarization of the wave should be specified.     

Far-field approximations to the Kirchoff-Helmholtz representations of scattered fields

The standard far-field approximation to the Kirchhoff formula for the field scattered by a flat metallic plateSof arbitrary shape is given by a certain surface (double) integral. This double integral can be reduced to a line integral evaluated around the boundary of S. Moreover, ifSis a polygon, this line integral can be reduced to a closed form expression involving no integrations at all. The use of such line integral representations can easily reduce the costs of numerical calculation by orders of magnitude. If the integrands are to be sampledptimes per wavelength to achieve an acceptable degree of precision, and ifAis the area ofS, then the numerical evaluation of the double integral requiresp^{2}A/lambda^{2}functional evaluations whereas the line integral only requirespsqrt{A/lambda^{2}}. IfSis a polygon withNvertices, then only2Nfunctional evaluations are required to evaluate the closed form expression with no quadrature error at all.     

Time-harmonic two- and three-dimensional Green's dyadics forgeneral uniaxial bianisotropic media

A rigorous study of the Green's dyadics in two and three dimensions for general uniaxial bianisotropic media is made. The Green's dyadics are derived in the time-harmonic regime. A general uniaxial bianisotropic medium is described by eight parameters. In general, it is impossible to derive a closed-form representation of the Green's dyadics in three dimensions. In one important special case, however, where one relation is satisfied between the eight parameters, it is possible to obtain a closed-form representation     

时域物理光学后向散射近场线积分表达式

提出了一种计算偶极子源照射时理想导体平板后向散射近场的时域物理光学（Time-Domain Physical-Optics,TDPO）线积分表达式.利用并矢分析中的面梯度定理和面散度定理,将TDPO面积分表达式化为线积分表达式.该表达式消除了积分中的奇异性,适用于偶极子天线处在任意位置处的情形.计算了导体平板和复杂目标的瞬态后向散射场,与其他方法结果吻合良好.数值结果表明,该方法在保证计算精度的前提下,可以大大提高计算效率.     

Extended method of line procedure for the analysis of microwave components with bianisotropic inhomogeneous media

Method of line (MoL) procedure is very useful in the analysis of radiative and transmissive microwave components, but its standard version does not allow for the study of elements with complex substrates. In this work, we first show that components integrated into materials exhibiting the magneto-electric effect (biisotropic and general bianisotropic media) cannot be analyzed following a standard MoL algorithm. Next, we derive an extended MoL numerical tool, which allows for the analysis of components in the presence of any linear medium (even inhomogeneous, bianisotropic and lossy). Such an extension is based on the generalization of the transmission-line equations for a general linear medium, which, in the case in point, are not necessarily decoupled. Furthermore, we present the full coincidence of this new method with the standard MoL in the case of simpler media (i.e., not exhibiting the magneto-electric effect) and, finally, we show some numerical results, obtained analyzing microwave antennas and resonators with bianisotropic and chiral substrates.     

Dyadic Green's function for a multilayered planar medium-a dyadic eigenfunction approach

A new formulation of the dyadic Green's function for a planarly layered medium is presented, based on dyadic eigenfunctions of the Green's function operator. The general development of the dyadic Green's function is shown, resulting in a three-dimensional purely spectral representation. The spectral form is converted to a Hankel-function form using standard techniques, analogous to the sum-of-residues plus branch-cut representation often obtained from the Sommerfeld Green's function. Advantages and disadvantages of both the eigenfunction and Hankel function forms are outlined, and compared to other Green's function representations. Examples of the Green's dyadic for free space and for a grounded dielectric slab environment are provided, and the role of the continuous and discrete spectrum is discussed.     

Closed-form Green's functions for cylindrically stratified media

A numerically efficient technique is developed to obtain the spatial-domain closed-form Green's functions of the electric and magnetic fields due to z- and φ-oriented electric and magnetic sources embedded in an arbitrary layer of a cylindrical stratified medium. First, the electric- and magnetic-field components representing the coupled TM and TE modes are derived in the spectral domain for an arbitrary observation layer. The spectral-domain Green's functions are then obtained and approximated in terms of complex exponentials in two consecutive steps by using the generalized pencil of function method. For the Green's functions approximated in the first step, the large argument behavior of the zeroth-order Hankel functions is used for the transformation into the spatial domain with the use of the Sommerfeld identity. In the second step, the remaining part of the Green's functions are approximated on two complementary parts of a proposed deformed path and transformed into the spatial domain, analytically. The results obtained in the two consecutive steps are combined to yield the spatial-domain Green's functions in closed forms