Class Of Bi-anisotropic Media Research Articles

Generalized Q-media and Field Decomposition in Differential-form Approach

Differential-form formalism in four dimensions gives the simplest possible representation to the Maxwell equations. The constitutive equation for the general linear (bi-anisotropic) medium is a relation between the two electromagnetic two-forms through a medium dyadic of the Hodge type. In a previous paper a class of bi-anisotropic media labeled as that of Q-media was studied in four-dimensional formalism. It was shown to correspond to a known class of media in the classical three-dimensional formalism allowing one to solve the Green dyadic in analytical form. The present paper is a continuation where the similar problem is solved for a class of bi-anisotropic media, previously labeled as that of generalized Q-media. It is shown that the simple four-dimensional definition of this class of media corresponds to a three-dimensional definition of a class of bi-anisotropic media which has been previously labeled as that of decomposable media. To see this explicitly, it is shown that fields of a plane wave are decomposed in two sets each satisfying a certain polarization condition.

Differential-Form Electromagnetics and Bi-Anisotropic Q-Media

It is known that differential-form formalism in four dimensions gives the simplest possible representation to the Maxwell equations. The constitutive equation for the general linear (bi-anisotropic) medium is a relation between the two electromagnetic two-forms through a medium dyadic of the Hodge type. It was previously shown that when the medium dyadic satisfies a certain simple condition, the wave equation for the electromagnetic two-form reduces to one with a second-order scalar operator. The corresponding class of bi-anisotropic media ('Q-media') allows one to solve the basic electromagnetic problem analytically. In this paper we find the corresponding conditions for the four three-dimensional medium dyadics familiar in the Gibbsian vector analysis. Repeated use of multivector and dyadic identities is made in deriving the conditions which can be identified with those recently defined for time-harmonic problems in the literature. As an example, the solution for the potential of an impulsive point source in a Q-medium is given.

Antisymmetric Six-Dyadics and Bi-Anisotropic Media

Novel analytical methods are introduced for antisymmetric six-dyadics which form a linear space of 15 dimensions. By defining new multiplication operations analogous to those of the classical Gibbsian dyadics, algebraic handling of equations is greatly simplified. As an application, time-harmonic electromagnetic fields expressed in concise six-vector form are considered. A certain class of bi-anisotropic media, labeled as A media, is defined for which the six-dyadic Maxwell operator can be expressed in terms of an antisymmetric operator. It is shown that, applying six-dyadic identities, the corresponding antisymmetric six-dyadic Green function can be straightforwardly expressed in explicit form.

Factorization and Green Dyadics for a New Class of Bi-Anisotropic Media Using Duality

In this paper we will study the Green dyadics and the factorization of the Helmholtz determinant operator for a new class of homogeneous bianisotropic media. That new class of media is derived from previously studied media using a rotational duality transformation. The new class of media is very general and contains many other, previously studied classes, as special cases. The Green dyadics are expressed in a form that contains a one-dimensional inverse Fourier transformation that, in general, cannot be evaluated in closed form.

Electromagnetic Source Decomposition for Generalized Decomposable Bi-Anisotropic Media

The classical TE/TM decomposition theory, valid for isotropic and uniaxially anisotropic media, has recently been generalized to a class of bi-anisotropic media. In such a decomposable medium any electromagnetic field can be decomposed into two individual electromagnetic fields, an a-field and a b-field, satisfying certain polarization conditions. The natural continuation of the theory is to decompose the electromagnetic sources that is the topic of the present paper. The differential equations for the a- and b-sources are derived and seen to generalize the previous results. Also one example of possible source decomposition is suggested.

Green dyadic for a class of nonreciprocal bianisotropic media

The possibility of finding an analytic Green dyadic expression for a class of bianisotropic media, defined by the relations , , and between the medium parameter dyadics, is studied. It is shown that the determinant of the dyadic Helmholtz operator, an operator of fourth order, can be expressed as a product of two second-order operators. A method for finding the solution for the Green dyadic in the form of infinite series in terms of powers of the dimensionless parameter ξζ/μoϵo is given. For small values of the parameter, a two-term approximation is seen to take a simple analytic form. As an Appendix, another approach through the Fourier transformation is briefly discussed. Dyadic formalism is applied throughout in the analysis. © 1998 John Wiley & Sons, Inc. Microwave Opt Technol Lett 19: 216–221, 1998.

Generalized decomposition of electromagnetic fields in bi-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.

Radiation of an electric point-source in a homogeneous omega medium

In recent years, new materials, such as chiral, nonreciprocal, nonlinear, gyrotropic, high T c superconducting and omega materials, have attracted special attention for their potential applications in microwave and millimetre wave engineering, as well as in the infrared and optical regime. This paper attempts to present a rigorous formulation of the problem of the radiation of an electric point-source embedded in an unbounded omega medium. The omega medium which falls into the class of bi-anisotropic media can be, from an electromagnetic point of view, thought of as a composite medium composed of an isotropic host material within which a large number of Ω-shaped metallic microstructures are embedded. Spectral and spatial Green dyads are introduced to express the spatial radiated electric field. Eventually, numerical computations of the electric radiated field are shown, in the case of an electric x ̂ - and z ̂ - oriented point-source.

Duality transformations, Green dyadics and plane-wave solutions for a class of bianisotropic media

Duality transformations are defined as linear transformations between pairs of vector fields and sources. A class of bianisotropic media is defined so that a pair of duality transformations can be found which leave the media invariant (self dual). It is seen that for such media the permittivity, permeability and nonreciprocity parameters must be multiples of the same dyadic while the chirality parameter may be an arbitrary dyadic. Any source and field in such a medium can be decomposed in a pair of self-dual components which see the bianisotropic medium as two equivalent anisotropic media of affine-isotropic type. The Green dyadics in these two media can be solved through affine transformations and the Green dyadics of the original bianisotropic medium can be written in explicit analytic form. The plane-wave dispersion equation can be solved through a similar self-dual decomposition of fields.