Electromagnetics and exotic media: a quest for the holy grail

During the past eight years, the authors have extensively studied the properties of linear homogeneous bianisotropic media. They have studied the Green's dyadics, the factorization of the Helmholtz determinant operator, the field and source decomposition, and plane-wave propagation in various classes of these media. We give an overview of our findings, and we place these findings in historical order. The results we found provide insight into the nature of Maxwell's equations, in general, and into the field propagation mechanisms in the different media, in particular. Finally, we mention that closed-form solutions are valuable as benchmarking results for numerical solutions     

New fast and accurate line parameter calculation of generalmulticonductor transmission lines in multilayered media

An enhanced method to calculate the C, L, and R of a multiconductor bus in a multilayered medium is presented. Different board technologies, conductors of complicated shape, and conductors embedded in different layers can be handled without loss of accuracy or substantial increase in CPU time compared with existing simulation techniques. Correct determination of skin effect losses is shown to depend critically on surface charge modeling. Surface charge discontinuities are explicitly taken into account which results in reduced computation time. A further reduction of computation time is obtained by a particular treatment of the calculation of the Green's function     

Analysis of cylindrical waveguide discontinuities using vectorialeigenmodes and perfectly matched layers

In this paper, we analyze the scattering at discontinuities in cylindrical waveguides, starting from a vectorial eigenmode expansion and by introducing perfectly matched layer (PML) boundary conditions. The structure under study is enclosed in a metal cylinder to discretize the radiative mode spectrum, while the coating of this cylinder with PML vastly reduces the influence of parasitic reflections at the metal. This allows for a model that is both faster and more accurate than previous models     

Comments on "Properties of and generalized full-wave transmission line models for hybrid (Bi)(an)isotropic waveguides" [and reply]

For the original paper see ibid., vol. 44, no. 11, p. 2064-2075 (1996). In this comment on the aforementioned paper, the problems of reciprocity, bidirectionality, and relation between the modal field patterns in waveguides with bianisotropic media are discussed. In addition to the three McIsaak's elements of symmetry, which determine bidirectionality in waveguides, two new elements of symmetry for this purpose are introduced. The author replies to this comment.     

The FE-BIE technique applied to some 2-D problems relevant toelectromagnetic compatibility: optimal choice of mechanisms to take intoaccount periodicity

A study of mechanisms to account for periodicity when modeling two-dimensional (2-D) structures with a hybrid finite-element boundary integral equation (FE-BIE) method is presented. These techniques are either based on the use of Green's functions or on the application of the Floquet-Bloch theorem as a periodic boundary condition. The described formalism can be used to model very diverse problem geometries as is demonstrated by means of some typical examples. For these configurations, it is shown how an optimal choice can be made between the mechanisms that impose periodicity     

Rigorous boundary integral equation solution for general isotropicand uniaxial anisotropic dielectric waveguides in multilayered mediaincluding losses, gain and leakage

Bounded and leaky eigenmodes of arbitrary shaped polygonal dielectric waveguides embedded in a multilayered medium are determined based on a rigorous full-wave analysis. The dielectric waveguides consist of isotropic or uniaxial anisotropic material. Losses and gain inside the layers and the waveguides are allowed. The eigenmodes are determined with a boundary integral equation technique in conjunction with the method of moments. Results for the propagation constants are presented for a number of waveguides and, where possible, compared with published data. Special attention is devoted to the transition from a dielectric waveguide to a perfectly conducting waveguide when the loss tangent of the waveguide material changes from zero to infinity     

The diaphanous wedge

Complete solutions for the scattering by a diaphanous wedge, meaning a wedge with identical wavenumbers inside and outside the wedge, are presented. The results are obtained from an integral equation for the fields on the wedge, which is solved by the Mellin and Kantorovich-Lebedev transforms in the static and dynamic cases, respectively. Pertinent formulations of Gegenbauer's addition theorems play an important part in the derivation of the results, which are presented in closed form     

Generalized decomposition of electromagnetic fields inbi-anisotropic media

TE/TM decomposition of electromagnetic fields, with respect to one special direction in space, is well known to be valid for fields in isotropic and uniaxially anisotropic media. The theory was recently generalized to bi-anisotropic media by defining the decomposition for linear combinations of electric and magnetic fields with respect to two vectors. In the present paper, the theory is further generalized by defining the decomposition with respect to four vectors (two six-vectors), which restrict the polarizations of the decomposed electromagnetic fields. It is shown that the class of bi-anisotropic media in which electromagnetic fields can be decomposed into two independent electromagnetic fields (a-field and b-field) is more general than in all previous decomposition theories. It is also shown that the decomposed a- and b-fields see the original bi-anisotropic medium as simpler equivalent ones (aand b-media) for which analytic Green dyadics were previously derived by these authors     

Comparative study of three methods for the simulation of two-dimensional photonic crystals

Three methods for the efficient simulation of two-dimensional photonic crystal structures are compared, namely, a semianalytical multiple-scattering technique; a vectorial eigenmode expansion technique; and a FDTD-ROM technique. The basic principles of each method are presented. For the semianalytical technique and for the vectorial eigenmode expansion technique, we show how reflections coming from abruptly terminated waveguides can be avoided. The main advantages and disadvantages of each method are discussed. Results from use of the three methods are compared for several photonic crystal structures.