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      Electromagnetic Media with no Dispersion Equation

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          Abstract

          It has been known through some examples that parameters of an electromagnetic medium can be so defined that there is no dispersion equation (Fresnel equation) to restrict the choice of the wave vector of a plane wave in such a medium, i.e., that the dispersion equation is satisfied identically for any wave vector. In the present paper, a more systematic study to define classes of media with no dispersion equation is attempted. The analysis makes use of coordinate-free four-dimensional formalism in terms of multivectors, multiforms and dyadics.

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          Causal structure and algebraic classification of area metric spacetimes in four dimensions

          Area metric manifolds emerge as a refinement of symplectic and metric geometry in four dimensions, where in numerous situations of physical interest they feature as effective matter backgrounds. In this article, this prompts us to identify those area metric manifolds that qualify as viable spacetime backgrounds in the first place, in so far as they support causally propagating matter. This includes an identification of the timelike future cones and their duals associated to an area metric geometry, and thus paves the ground for a discussion of the related local and global causal structure in standard fashion. In order to provide simple algebraic criteria for an area metric manifold to present a consistent spacetime structure, we develop a complete algebraic classification of area metric tensors up to general transformations of frame. Remarkably, a suitable coarsening of this classification allows to prove a theorem excluding the majority of algebraic classes of area metrics as viable spacetimes.
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            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.
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              A restatement of the normal form theorem for area metrics

              An area metric is a (0,4)-tensor with certain symmetries on a 4-manifold that represent a non-dissipative linear electromagnetic medium. A recent result by Schuller, Witte and Wohlfarth provides a pointwise normal form theorem for such area metrics. This result is similar to the Jordan normal form theorem for (1,1)-tensors, and the result shows that any area metric belongs to one of 23 metaclasses with explicit coordinate expressions for each metaclass. In this paper we restate and prove this result for skewon-free (2,2)-tensors and show that in general, each metaclasses has three different coordinate representations, and each of metaclasses I, II, ..., VI, VII need only one coordinate representation.
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                Author and article information

                Journal
                2013-03-22
                2013-03-25
                1303.5535

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

                Custom metadata
                Progress in Electromagnetics Research PIER B, vol. 51, pp. 269 - 289, 2013
                math-ph math.MP

                Mathematical physics, Mathematical & Computational physics

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