Bi-Isotropic and Bi-Anisotropic Media

Bolioli, S.

doi:10.1007/978-94-011-5734-6_3

Cited by 2 publications

(2 citation statements)

References 42 publications

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“…In the latter case, the theory predicts that the electric displacement is coupled with the magnetic field, and that the magnetic induction is coupled with the electric field [75]. Thereby, Willis theory agrees with what is already known in the photonics community as bianisotropic materials, described by the so-called magnetoelectric tensor [7,23,36,57].…”

Section: Introductionsupporting

confidence: 79%

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Homogenization of piezoelectric planar Willis materials undergoing antiplane shear

et al. 2022

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Homogenization theories provide models that simplify the constitutive relations of heterogeneous media while retaining their macroscopic features. These theories have shown how the governing fields can be macroscopically coupled, even if they are microscopically independent.A prominent example is the Willis theory which predicted the strain-momentum coupling in elastodynamic metamaterials. Recently, a theory that is based on the Green's function method predicted analogous electro-momentum coupling in piezoelectric metamaterials. Here, we develop a simpler scheme for fibrous piezoelectric composites undergoing antiplane shear waves.We employ a source-driven approach that delivers a unique set of effective properties for arbitrary frequency-wavevector pairs. We numerically show how the resultant homogenized model recovers exactly the dispersion of free waves in the composite. We also compute the effective properties in the long-wavelength limit and off the dispersion curves, and show that the resultant model satisfy causality, reciprocity and energy conservation. By contrast, we show how equivalent models that neglect the electromomentum coupling violate these physical laws.

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Section: Introductionsupporting

confidence: 79%

“…By construction, the equivalent description recovers the dispersion relation without using W, however it violates the energy conservation and reciprocity conditions 7 Ãii (-X-) (X-) (-X-) (X-)…”

Section: Free Wavesmentioning

confidence: 99%

Homogenization of piezoelectric planar Willis materials undergoing antiplane shear

et al. 2022

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Constitutive tensor in the geometrized Maxwell theory

Korolkova

2022

Discrete and Continuous Models

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It is generally accepted that the main obstacle to the application of Riemannian geometrization of Maxwell’s equations is an insufficient number of parameters defining a geometrized medium. In the classical description of the equations of electrodynamics in the medium, a constitutive tensor with 20 components is used. With Riemannian geometrization, the constitutive tensor is constructed from a Riemannian metric tensor having 10 components. It is assumed that this discrepancy prevents the application of Riemannian geometrization of Maxwell’s equations. It is necessary to study the scope of applicability of the Riemannian geometrization of Maxwell’s equations. To determine whether the lack of components is really critical for the application of Riemannian geometrization. To determine the applicability of Riemannian geometrization, the most common variants of electromagnetic media are considered. The structure of the dielectric and magnetic permittivity is written out for them, the number of significant components for these tensors is determined. Practically all the considered types of electromagnetic media require less than ten parameters to describe the constitutive tensor. In the Riemannian geometrization of Maxwell’s equations, the requirement of a single impedance of the medium is critical. It is possible to circumvent this limitation by moving from the complete Maxwell’s equations to the approximation of geometric optics. The Riemannian geometrization of Maxwell’s equations is applicable to a wide variety of media types, but only for approximating geometric optics.

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Bi-Isotropic and Bi-Anisotropic Media

Cited by 2 publications

References 42 publications

Homogenization of piezoelectric planar Willis materials undergoing antiplane shear

Homogenization of piezoelectric planar Willis materials undergoing antiplane shear

Constitutive tensor in the geometrized Maxwell theory

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