Dispersion relation for electromagnetic waves in anisotropic media

Itin, Yakov

doi:10.1016/j.physleta.2009.12.071

Cited by 28 publications

(29 citation statements)

References 18 publications

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“…A purely real rotation that diagonalizes any one of these two tensors may not exist. A mathematically tractable dispersion relation for the most general case has been derived only recently [42], and we will use below one particular case of this result.…”

Section: Waves In Infinite Latticesmentioning

confidence: 99%

Homogenization of Maxwell's equations in periodic composites: Boundary effects and dispersion relations

Markel

Schotland

2012

Phys. Rev. E

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We consider the problem of homogenizing the Maxwell equations for periodic composites. The analysis is based on Bloch-Floquet theory. We calculate explicitly the reflection coefficient for a half-space, and derive and implement a computationally-efficient continued-fraction expansion for the effective permittivity. Our results are illustrated by numerical computations for the case of two-dimensional systems. The homogenization theory of this paper is designed to predict various physically-measurable quantities rather than to simply approximate certain coefficients in a PDE.

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Section: Waves In Infinite Latticesmentioning

confidence: 99%

Homogenization of Maxwell's equations in periodic composites: Boundary effects and dispersion relations

Markel

Schotland

2012

Phys. Rev. E

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“…For illustration, following [86,3], see also [41], we will display a classical example of such a surface. In Eqs.…”

Section: Fresnel Wave Surfacementioning

confidence: 99%

Axion and Dilaton + Metric Emerge Jointly from an Electromagnetic Model Universe with Local and Linear Response Behavior

Hehl

2016

Fundamental Theories of Physics

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We take a quick look at the different possible universally coupled scalar fields in nature. Then, we discuss how the gauging of the group of scale transformations (dilations), together with the Poincaré group, leads to a Weyl-Cartan spacetime structure. There the dilaton field finds a natural surrounding. Moreover, we describe shortly the phenomenology of the hypothetical axion field. -In the second part of our essay, we consider a spacetime, the structure of which is exclusively specified by the premetric Maxwell equations and a fourth rank electromagnetic response tensor density χ i jkl = −χ jikl = −χ i jlk with 36 independent components. This tensor density incorporates the permittivities, permeabilities, and the magneto-electric moduli of spacetime. No metric, no connection, no further property is prescribed. If we forbid birefringence (double-refraction) in this model of spacetime, we eventually end up with the fields of an axion, a dilaton, and the 10 components of a metric tensor with Lorentz signature. If the dilaton becomes a constant (the vacuum admittance) and the axion field vanishes, we recover the Riemannian spacetime of general relativity theory. Thus, the metric is encapsulated in χ i jkl , it can be derived from it.file CarlBrans80 08.This gauging of the P(1, 3) extends the geometrical framework of gravity. The 4 translational potentials e i α and the 6 Lorentz potentials Γ i αβ = −Γ i β α span a Riemann-Cartan spacetime, enriching the Riemannian spacetime of GR by the presence of Cartan's torsion; here α, β = 0, 1, 2, 3 are (anholonomic) frame indices. Whereas the translational potentials couple to the canonical energy-momentum ten-2 We skip here the plethora of scalar mesons, π ± , π 0 , η, f 0 (500), η ′ (958), f 0 (980), a 0 (980), ...,they are all composed of two quarks. Thus, the scalar mesons do not belong to the fundamental particles.

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“…(vi) The following argument, applied to the magnetoelectric parts (7) and (8) of the HO decomposition, is helpful here. The point group3m of Cr 2 O 3 forbids the time-even axial property tensor V i j in (7) and (8), and it requires the time-odd axial traceless W i j to have just one independent non-zero component. 2 Thus, if X = 0 then Cr 2 O 3 would have only one independent magnetoelectric modulus.…”

Section: Translational Invariance Of the Constitutive Tensor Tomentioning

confidence: 99%

“…Also, the propagation equation for transmission phenomena in linear dielectrics is conveniently expressed in terms of property tensors in (2) and (3)-see (66) and (91)-as is a dispersion relation. 8 The pseudoscalar observable X plays an unusual, even counter-intuitive, role in macroscopic electrodynamics. For homogeneous media, its contributions D = XB and H = −XE have no effect in the Maxwell equations,…”

Section: Introductionmentioning

confidence: 99%

Multipole theory and the Hehl–Obukhov decomposition of the electromagnetic constitutive tensor

Lange

Raab

2015

Journal of Mathematical Physics

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The Hehl-Obukhov decomposition expresses the 36 independent components of the electromagnetic constitutive tensor for a local linear anisotropic medium in a useful general form comprising seven macroscopic property tensors: four of second rank, two vectors, and a four-dimensional (pseudo)scalar. We consider homogeneous media and show that in semi-classical multipole theory, the first full realization of this formulation is obtained (in terms of molecular polarizability tensors) at third order (electric octopole-magnetic quadrupole order). The calculations are an extension of a direct method previously used at second order (electric quadrupole-magnetic dipole order). We consider in what sense this theory is independent of the choice of molecular coordinate origins relative to which polarizabilities are evaluated. The pseudoscalar (axion) observable is expressed relative to the crystallographic origin. The other six property tensors are invariant (with respect to an arbitrary choice of each molecular coordinate origin), or zero, at first and second orders. At third order, this invariance has to be imposed (by transformation of the response fields)-an aspect that is required by consideration of isotropic fluids and is consistent with the invariance of transmission phenomena in dielectrics. Alternative derivations of the property tensors are reviewed, with emphasis on the pseudoscalar, constraint-breaking, translational invariance, and uniqueness. C 2015 AIP Publishing LLC. [http://dx.

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Dispersion relation for electromagnetic waves in anisotropic media

Cited by 28 publications

References 18 publications

Homogenization of Maxwell's equations in periodic composites: Boundary effects and dispersion relations

Homogenization of Maxwell's equations in periodic composites: Boundary effects and dispersion relations

Axion and Dilaton + Metric Emerge Jointly from an Electromagnetic Model Universe with Local and Linear Response Behavior

Multipole theory and the Hehl–Obukhov decomposition of the electromagnetic constitutive tensor

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