General Bianisotropic Media Research Articles

Analysis of gyrobianisotropic media effect on the input impedance, field distribution and mutual coupling of a printed dipole antenna

In this paper, we present an analytical study for the investigation of the effects of the magnetoelectric elements of a reciprocal and nonreciprocal bianisotropic grounded substrate on the input impedance, resonant length of a dipole antenna as well as on the mutual coupling between two element printed dipole array in three configuration geometries: broadside, collinear and echelon printed on the same material. This study examines also the effect of the considered bianisotropic medium on the electric and magnetic field distributions that has been less addressed in the literature for antenna structures. Computations are based on the numerical resolution, using the spectral method of moments, of the integral equation developed through the mathematical derivation of the appropriate spectral Green’s functions of the studied dipole configuration. Original results, for chiral, achiral, Tellegen and general bi-anisotropic media cases, are obtained and discussed with the electric and magnetic field distributions for a better understanding and interpretation. These interesting results can serve as a stepping stone for further works to attract more attention to the reciprocal and non-reciprocal Tellgen media in-depth studies.

Homogeneous Bianisotropic Medium, Dissipation and the Non-constancy of Speed of Light in Vacuum for Different Galilean Reference Systems

A procedure is developed which leads to a relation that can be used to argue the negation of the Special Relativity Theory when there exists a general homogeneous bianisotropic medium with dissipation. The unbounded general bianisotropic medium is interfaced with a perfectly conducting medium fllling a half space so that the interface is an inflnite plane. The perfectly conducting half space (medium (II)) is assumed to move uniformly and along the O 0 z 0 axis of the Galilean reference system K 0 which is attached to medium (II), and the interface plane with medium (I), the bianisotropic medium which is at rest and to which is attached the Galilean reference system K, is assumed to be perpendicular to the O 0 z 0 axis. The relation found is between constitutive parameters, the direction cosines with respect to Oxyz axes of the incident plane wave impingent on the inflnite plane interface, the incident wave parameters, v1 the relative speed of K 0 with respect to K and c the speed of light in vacuum. This relation is shown to be interpretable to falsify the Special Relativity Theory. On the other hand it is demonstrated also that when the same homogeneous bianisotropic medium without loss is considered no such relation can be obtained and the Special Relativity Theory cannot be contradicted. Three examples are presented. One for a lossless electrically uniaxially anistropic medium, one for a dissipative simple medium and another for a dissipative electrically uniaxially anistropic medium. While the flrst one does not lead to any contradiction of Maxwell's equations with Special relativity Theory, the other two are shown to lead to such relations.

Class of electromagnetic SD media

Applying the four-dimensional differential-form formalism the electromagnetic medium conditions can be represented in compact form through the medium dyadic mapping two-forms to two-forms. In the present paper one of the most basic classes of media is studied, the one defined by medium dyadics satisfying an algebraic equation of the second order (labeled as that of SD media). The general form of the medium dyadic in this class is derived and shown to involve 20 scalar medium parameters out of the 36 corresponding to the most general bi-anisotropic medium. Because each such medium dyadic defines two involutory linear transformations (called left- and right-hand duality transformations), in terms of which the medium dyadic is invariant (self-dual), the class can also be labeled as that of self-dual media. Further, the two eigen-two-forms of the medium dyadic are shown to be self-dual and anti-self-dual with respect to the two transformations. The eigenfields of the SD medium are shown to obey second-order differential equations. As a special case, the 10-parameter class of principal SD media is considered, which is shown to have no birefringence.

On interaction of electromagnetic waves with infinite bianisotropic layered slab

AbstractA stratified general bianisotropic medium is considered, consisting of several infinite slabs either between two half‐spaces filled with isotropic material, or grounded. The slab is illuminated by an incident plane wave from one of the half‐spaces. The excited electromagnetic field inside the bianisotropic slab and in the isotropic domains is described. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Efficient Modal Analysis of Bianisotropic Waveguides by the Coupled Mode Method

A modal analysis based on the coupled mode method is performed for the resolution of partially filled waveguides with a general bianisotropic medium. The calculation of the generalized telegraphist's equations can be made by using two different strategies: direct and indirect formulations. In this paper, the indirect formulation of the method is extended to bianisotropic materials and exposed in detail. The convergence of both formulations is compared and it is demonstrated that the indirect formulation converges much faster than the direct formulation, which means that fewer modes are required for a given precision. Results of some particular cases of the constitutive relationships, like dielectric, magnetic, ferrites, and omega materials are shown and compared with the bibliography or commercial electromagnetic simulators. Good agreement is found, which demonstrates the validity and reliability of the method

Optimization Approach to the Retrieval of the Constitutive Parameters of Slab of General Bianisotropic Medium

Optimization Approach to the Retrieval of the Constitutive Parameters of Slab of General Bianisotropic Medium

INVERSE FOR THE SKEWON MEDIUM DYADIC

In four-dimensional differential-form representation linear medium relations can be expressed in terms of a medium dyadic mapping the electromagnetic two-form involving the B and E fields to the two-form involving the D and H fields. There does not seem to exist a method to invert the medium dyadic in a coordinate-free manner for the general bi-anisotropic medium. Such an inversion is introduced here for the special class of skewon media which is a 15 parameter subclass of previously studied IB media. The resulting compact analytic expression is verified through two simple tests and an expansion in eigenvectors.

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.

Wave Equations for Bi-Anisotropic Media in Differential Forms

Differential-form formalism appears to be an ideal tool for electromagnetic analysis because it allows one to express the basic electromagnetic laws in a most compact and elegant form. In fact, the Maxwell equations for the two electromagnetic two-forms are represented by two differential equations of first-order in the simplest possible form. Connection between the two-forms in a homogeneous and time-invariant linear medium is given by a simple algebraic equation. However, constructing the wave equation for a single electromagnetic two-form through elimination appears to be cumbersome and such an equation corresponding to the general bianisotropic medium could not be found in the literature. The present paper gives one possibility for its derivation based on operations in multivector and dyadic algebra. Two special media are considered in more detail leading to wave equations with scalar second-order and factorized fourth-order operators.

Propagation in bianisotropic media — reflection and transmission

A systematic analysis for solving the wave propagation problem in a general bianisotropic, stratified medium is presented. The method utilises the concept of propagators, and the representation of these operators is simplified by introducing the Cayley–Hamilton theorem. The propagators propagate the total tangential electric and magnetic fields in the slab and only outside the slab do the up- and down-going parts of the fields need to be identified. This procedure makes the physical interpretation of the theory intuitive. The reflection and the transmission dyadics for a general bianisotropic medium with an isotropic (vacuum) half-space on both sides of the slab are presented in a co-ordinate-independent dyadic notation, as well as the reflection dyadic for a bianisotropic slab with perfectly electric backing (PEC). In the latter case the current on the metal backing is also given. Some numerical computations that illustrate the algorithm are presented.

Plane-Wave Propagation in Decomposable Bianisotropic Media

Plane-wave propagation is studied in the most general bianisotropic medium in which the electromagnetic wave can be split into two eigenwaves with certain polarizations depending on two arbitrary directions in space. Hence the whole problem splits into two parts. The dispersion dyadics of the materials seen by the eigenwaves are derived and the refractive indices are solved for arbitrary direction of propagation. Also, a general expression for the eigenpolarizations is found. The theory is applied to some cases fitting the requirements of the media.

Factorization of Helmholtz Determinant Operator for Decomposable Bi-Anisotropic Media

Conditions for the most general bi-anisotropic media in which the electromagnetic field can be decomposed in two components with respect to two six-vectors were recently derived by these authors. In the present paper it is shown that the fourth-order Helmholtz determinant operator, which appears in the basic scalar Helmholtz equation for electromagnetic fields, can be expressed in factorized form as a product of two second-order operators. These two operators are shown to correspond to the decomposition of the field. Finally, because of the factorization, the scalar Green function corresponding to the Helmholtz determinant is shown to take a numerically tractable form in terms of two finite integrations.

Coordinate-independent dyadic formulation of the dispersion relation 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.

Electromagnetic Source Decomposition in Bi-Anisotropic Media

Conditions for the most general bi-anisotropic medium in which any electromagnetic field can be decomposed into two uncoupled partial fields were recently introduced by one of the present authors. In the present paper it is shown that any electromagnetic source in this class of media can be decomposed into two sources creating uncoupled partial fields. Further, it is shown that for each of the problems the original bi-anisotropic medium can be replaced by a simpler equivalent medium for which an analytic Green dyadic can be found. This makes it possible to solve both decomposed problems in integral form.

Magnetoelectric Interactions in Bi-Anisotropic Media

Classification of bi-anisotropic media based on the structure of magnetoelectric coupling dyadics is proposed. It appears that the most general bi-anisotropic media can be modeled as composites of only a few basic idealized elements: for reciprocal materials, these elements are uniaxial helices and "hats," and in the case of non-reciprocal media, the fundamental particles are Tellegen elements (coupled electric and magnetic dipoles). In particular, it is shown that some composites with omega-shaped conductive inclusions embedded in an isotropic dielectric matrix can be considered as media with equivalent phantom chiral particles. Also, the mechanism is analyzed of the bi-anisotropic material based on magnetostatic-wave resonators.

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.

General Optimization Approach To a Frequency-Domain Inversie Problem of a Stratified Bianisotropic Slab

An inverse problem for a stratified slab of a general bianisotropic medium is considered in the frequency domain. Considering obliquely impinging plane waves, imbedding equations and Green's functions equations for the reflection and transmission coefficient matrices and the internal fields are derived through the concept of wave-splitting. Two different optimization approaches, based on the imbedding method and the Green's functions method respectively, are applied to reconstruct the constitutive parameters as functions of the position using band-limited reflection and/or transmission data from different angles of illumination. Exact and explicit expressions for the gradients are derived, which result in a one order faster computation compared with numerical perturbations of the objective functionals. The reconstruction algorithm (based upon a conjugate gradient method) is tested with both clean and noisy data.

Electromagnetic field behaviour at edges in general bianisotropic media

A semianalytical approach for the determination of the singular behaviour of electromagnetic fields near a perfectly (electrically and/or magnetically) conducting wedge is presented. The surrounding medium is assumed to consist of several general bianisotropic wedges. Explicit formulas are provided and the numerical implementation is outlined. The applicability of the method is demonstrated with sample results.

Time-harmonic two- and three-dimensional Green's dyadics for general 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. >

Six-vector formalism in electromagnetics of bi-anisotropic media

Notation using six-vectors and six-dyadics appears very applicable for describing electromagnetic problems in general bi-anisotropic media, because with normal three-vector notation analytic expressions often tend to be very complicated. Introducing some operations, recourse to the three-vector and three-dyadic notation during the analysis can be avoided. A number of theorems and concepts of electromagnetic fields in bi-anisotropic media are given as examples.