Medium Dyadics Research Articles

Plane-Wave Propagation in Extreme Magnetoelectric Media

The extreme magnetoelectric medium (EME medium) is defined in terms of two medium dyadics, $\alpha$, producing electric polarization by the magnetic field and $\beta$, producing magnetic polarization by the electric field. Plane-wave propagation of time-harmonic fields of fixed finite frequency in the EME medium is studied. It is shown that (if $\omega\neq 0$) the dispersion equation has a cubic and homogeneous form, whence the wave vector $k$ is either zero or has arbitrary magnitude. In many cases there is no dispersion equation ("NDE medium") to restrict the wave vector in an EME medium. Attention is paid to the case where the two medium dyadics have the same set of eigenvectors. In such a case the $k$ vector is restricted to three eigenplanes defined by the medium dyadics. The emergence of such a result is demonstrated by considering a more regular medium, and taking the limit of zero permittivity and permeability. The special case of uniaxial EME medium is studied in detail. It is shown that an interface of a uniaxial EME medium appears as a DB boundary when the axis of the medium is normal to the interface. More in general, EME media display interesting wave effects that can potentially be realized through metasurface engineering.

Decomposable Medium Conditions in Four-Dimensional Representation

The well-known TE/TM decomposition of time-harmonic electromagnetic fields in uniaxial anisotropic media is generalized in terms of four-dimensional differential-form formalism by requiring that the field two-form satisfies an orthogonality condition with respect to two given bivectors. Conditions for the electromagnetic medium in which such a decomposition is possible are derived and found to define three subclasses of media. It is shown that the previously known classes of generalized Q-media and generalized P-media are particular cases of the proposed decomposable media (DCM) associated to a quadratic equation for the medium dyadic. As a novel solution, another class of special decomposable media (SDCM) is defined by a linear dyadic equation. The paper further discusses the properties of medium dyadics and plane-wave propagation in all the identified cases of DCM and SDCM.

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.

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.

Generalized Helmholtz Decomposition and Static Electromagnetics

The well-known decomposition of vector fields to solenoidal and irrotational parts, known as the Helmholtz decomposition, is generalized in terms of more general linear operators involving two arbitrary symmetric, positive-definite and complete (non-singular) dyadics. It is seen that, in terms of the generalized decomposition, potential expansions for the static electric and magnetic fields in anisotropic media can be formed in a straightforward manner. The decomposition theorem is further generalized in a form applicable to the static electromagnetic fields in the most general linear medium (bi-anisotropic medium) characterized by four medium dyadics. In this case, the decomposition theorem and potential expressions are presented in a compact form in terms of six-vectors.

Plane Waves in Decomposable Bi-Anisotropic Media

The class of decomposable bi-anisotropic media was recently defined to consist of media in which any electromagnetic field can be decomposed in two individual electromagnetic fields satisfying certain conditions for the electromagnetic fields. Also it was shown that, for a medium in this class, the fourth-order Helmholtz determinant operator governing the basic electromagnetic fields can be factorized, i.e., expressed as a product of two second-order operators. In the present paper, plane-wave propagation in the general decomposable medium is studied. Analytical solutions are derived for the dispersion equation and the polarizations of the eigenwaves are also determined in analytic form. As a check the expressions are applied to a medium with previously known solutions. In an appendix, conditions for the medium dyadics of the decomposable bi-anisotropic medium are derived for the case when the medium is lossless.

Reply to comments by W. S. Weiglhofer on “Green's dyadics for bi‐anisotropic media with similar medium dyadics”

Microwave and Optical Technology LettersVolume 18, Issue 6 p. 440-440 Reply to comments by W. S. Weiglhofer on “Green's dyadics for bi-anisotropic media with similar medium dyadics” F. Olyslager, Corresponding Author F. Olyslager Department of Information Technology, University of Ghent, B-9000 Ghent, Belgium Department of Information Technology, University of Ghent, B-9000 Ghent, BelgiumSearch for more papers by this authorI. V. Lindell, I. V. Lindell Electromagnetics Laboratory, Helsinki University of Technology, FIN-02015 HUT, Espoo, FinlandSearch for more papers by this author F. Olyslager, Corresponding Author F. Olyslager Department of Information Technology, University of Ghent, B-9000 Ghent, Belgium Department of Information Technology, University of Ghent, B-9000 Ghent, BelgiumSearch for more papers by this authorI. V. Lindell, I. V. Lindell Electromagnetics Laboratory, Helsinki University of Technology, FIN-02015 HUT, Espoo, FinlandSearch for more papers by this author First published: 07 December 1998 https://doi.org/10.1002/(SICI)1098-2760(19980820)18:6<440::AID-MOP21>3.0.CO;2-1AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinked InRedditWechat No abstract is available for this article. Volume18, Issue620 August 1998Pages 440-440 RelatedInformation

Comments on ?Green's dyadics for bi-anisotropic media with similar medium dyadics? By F. Olyslager and I. V. Lindell

Comments on ?Green's dyadics for bi-anisotropic media with similar medium dyadics? By F. Olyslager and I. V. Lindell

Reply to comments by W. S. Weiglhofer on ?Green's dyadics for bi-anisotropic media with similar medium dyadics?

Reply to comments by W. S. Weiglhofer on ?Green's dyadics for bi-anisotropic media with similar medium dyadics?

Green's dyadics for bi‐anisotropic media with similar medium dyadics

The Green's dyadics are constructed for a bi-anisotropic medium in which the four medium dyadics are proportional to the same dyadic. Since this dyadic is not symmetric, it is not possible to derive the Green's dyadics from the Green's dyadics for a bi-isotropic medium by an affine transformation. If one scalar material condition is satisfied it is possible to derive the Green's dyadics in closed form; otherwise, a one-dimensional integral representation is obtained. © 1998 John Wiley & Sons, Inc. Microwave Opt Technol Lett 17: 45–47, 1998.

Green's dyadics for bi-anisotropic media with similar medium dyadics

The Green's dyadics are constructed for a bi-anisotropic medium in which the four medium dyadics are proportional to the same dyadic. Since this dyadic is not symmetric, it is not possible to derive the Green's dyadics from the Green's dyadics for a bi-isotropic medium by an affine transformation. If one scalar material condition is satisfied it is possible to derive the Green's dyadics in closed form; otherwise, a one-dimensional integral representation is obtained. © 1998 John Wiley & Sons, Inc. Microwave Opt Technol Lett 17: 45–47, 1998.