Current-driven metamaterial homogenization

Fietz, Chris; Shvets, Gennady

doi:10.1016/j.physb.2010.01.006

Cited by 73 publications

(79 citation statements)

References 11 publications

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“…The formulation picked up on a recent observation by Fietz & Shvets (2010) that effective relations can be uniquely defined only if some additional driving force is introduced. In the electromagnetic context, Fietz and Shvets proposed the introduction of magnetic monopole current.…”

Section: Discussionmentioning

confidence: 99%

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Effective constitutive relations for waves in composites and metamaterials

2011

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Definitions of ‘effective fields’ for a randomly inhomogeneous material are offered, which guarantee automatic satisfaction of the equations of motion. The important case of a medium with periodic microstructure is included. In this special case, the definitions are completely explicit and can be applied without reference to random media. The presentation is mostly expressed in terms of electromagnetic waves. The reasoning is applicable also to other types of waves and its realization for elastodynamics is briefly outlined towards the end. Some of the effective fields are defined directly as ensemble averages, ensuring the exact satisfaction of the equations of motion, but the effective ‘kinematic’ fields to which they are related are defined more generally, as weighted averages. The main result of this work is an explicit formula for the tensor of effective properties. The important issue of uniqueness (or not) of the effective properties is explained and resolved. Self-adjointness of the original problem is not assumed. An attractive feature of the formulation is that self-adjointness at the local level implies self-adjointness at the level of the ‘effective medium’.

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Section: Discussionmentioning

confidence: 99%

“…A significant observation, recently made by Fietz & Shvets (2010), that the effective response cannot be uniquely defined without the introduction of some 'driving force' additional to the usual electric current, is taken on board here. The extra driving force is needed to ensure that two fields can be generated independently.…”

Section: Introductionmentioning

confidence: 99%

Effective constitutive relations for waves in composites and metamaterials

2011

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“…The function Σ(ω, q) arises in various physical contexts [27][28][29] and is sometimes interpreted as the nonlocal permittivity tensor of the medium due to its explicit dependence on q. We have shown 20 that the knowledge of Σ(ω, q) for all values of its arguments is insufficient for solving boundary value problems in finite samples.…”

Section: General Considerationsmentioning

confidence: 99%

“…In heterogeneous periodic media, the derivation is more involved. Sometimes (1) is derived for such media by employing an external excitation in the form of an "impressed" current that overlaps with the medium and has the mathematical form of a plane wave [27][28][29] . However, this approach is not necessary and introduction of such currents into the model is not physically justified 30 .…”

Section: General Considerationsmentioning

confidence: 99%

Applicability of effective medium description to photonic crystals in higher bands: Theory and numerical analysis

Markel

Tsukerman

2016

Phys. Rev. B

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We consider conditions under which photonic crystals (PCs) can be homogenized in the higher photonic bands and, in particular, near the Γ-point. By homogenization we mean introducing some effective local parameters eff and µ eff that describe reflection, refraction and propagation of electromagnetic waves in the PC adequately. The parameters eff and µ eff can be associated with a hypothetical homogeneous effective medium. In particular, if the PC is homogenizable, the dispersion relations and isofrequency lines in the effective medium and in the PC should coincide to some level of approximation. We can view this requirement as a necessary condition of homogenizability. In the vicinity of a Γ-point, real isofrequency lines of two-dimensional PCs can be close to mathematical circles, just like in the case of isotropic homogeneous materials. Thus, one may be tempted to conclude that introduction of an effective medium is possible and, at least, the necessary condition of homogenizability holds in this case. We, however, show that this conclusion is incorrect: complex dispersion points must be included into consideration even in the case of strictly non-absorbing materials. By analyzing the complex dispersion relations and the corresponding isofrequency lines, we have found that two-dimensional PCs with C4 and C6 symmetries are not homogenizable in the higher photonic bands. We also draw a distinction between spurious Γ-point frequencies that are due to Brillouin-zone folding of Bloch bands and "true" Γ-point frequencies that are due to multiple scattering. Understanding of the physically different phenomena that lead to the appearance of spurious and "true" Γ-point frequencies is important for the theory of homogenization.

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“…Simple theories, for example, the ones employing quasi-static approximation [4,5], do not deal with electromagnetic coupling and spatial dispersion, and as such may not be sufficient to describe the complex behavior of metamaterials, artificial materials with nonconventional or exotic electromagnetic response. Recently, more refined homogenization theories [6][7][8][9][10][11][12][13][14] have been developed to take into account complex effects, such as chirality, spatial dispersion, and/or magnetoelectric coupling.…”

Section: Introductionmentioning

confidence: 99%

Artificial magnetism at terahertz frequencies from three-dimensional lattices of TiO_2 microspheres accounting for spatial dispersion and magnetoelectric coupling

et al. 2014

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We employ the generalized Lorentz-Lorenz method to investigate how both magnetoelectric coupling and spatial dispersion influence the artificial magnetic capabilities at terahertz frequencies of the representative case of a metamaterial consisting of a three-dimensional (3D) lattice of TiO 2 microspheres. The complex wavenumber dispersion relations pertaining to modes supported by the array, traveling along one of the principal axes of the array with electric or magnetic field polarized transversely and longitudinally (with respect to the mode traveling direction), are studied and thoroughly characterized. One mode with transverse polarization is dominant at any given frequency for the analyzed dimensions, proving that the 3D lattice can be treated as a homogeneous medium with defined electromagnetic material parameters. We show, however, that bianisotropy is a direct consequence of magnetoelectric coupling, and the dyadic expressions of both effective and equivalent material parameters are derived. In particular, we analyze the effect of spatial dispersion on the effective parameters relative to a composite material made by a 3D lattice of TiO 2 microspheres with filling fraction around 30% and near the first Mie magnetic dipolar resonance. Finally, we homogenize the metamaterial in terms of equivalent index and impedance, and by comparison with full-wave simulations, we explain the presence of the unphysical antiresonance permittivity behavior observed in previous work.

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Current-driven metamaterial homogenization

Cited by 73 publications

References 11 publications

Effective constitutive relations for waves in composites and metamaterials

Effective constitutive relations for waves in composites and metamaterials

Applicability of effective medium description to photonic crystals in higher bands: Theory and numerical analysis

Artificial magnetism at terahertz frequencies from three-dimensional lattices of TiO_2 microspheres accounting for spatial dispersion and magnetoelectric coupling

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