Boundary conditions for electromagnetic field on the surface of media with weak spatial dispersion

Golubkov, A. A.; Makarov, Vladimir

doi:10.1070/pu1995v038n03abeh000078

Cited by 32 publications

(25 citation statements)

References 27 publications

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“…Different aspects of the quadrupolar response of metamaterials and boundary conditions for media with weak spatial dispersion have been discussed in other works (e.g. [22][23][24][25]), but the topic is clearly in its infancy and is largely virgin territory. This article is organized as follows.…”

Section: Introductionmentioning

confidence: 99%

Boundary conditions for quadrupolar metamaterials

Silveirinha

2014

New J. Phys.

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One of the long-standing problems in effective medium theories is using the knowledge of the bulk material response to predict the behavior of the electromagnetic fields at the material boundaries. Here, using a first principles approach, we derive the boundary conditions satisfied by the macroscopic fields at interfaces between reciprocal metamaterials with a quadrupolar-type response. Our analysis reveals that in addition to the usual Maxwellian-type boundary conditions for the tangential fields, in general-to ensure the conservation of the power flow and Lorentz reciprocity-it is necessary to enforce an additional boundary condition (ABC) at an interface between a quadrupolar material and a standard dielectric. It is shown that the ABC is related to the emergence of an additional wave in the bulk quadrupolar medium.

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Section: Introductionmentioning

confidence: 99%

Boundary conditions for quadrupolar metamaterials

Silveirinha

2014

New J. Phys.

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“…where we have substituted the Landau-Lifshitz permittivity (22). Equating the O(k 2 ) part of (77) and the last term in (80), we obtain…”

Section: Transversal -Longitudinal (Tl) Decompositionmentioning

confidence: 99%

Four definitions of magnetic permeability for periodic metamaterials

2019

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We state and compare four different definitions of magnetic permeability for periodic, artificial media, or metamaterials. The connection between them, and properties in general, are discussed in detail, including causality, passivity, symmetry, asymptotic behavior, and origin dependence. The analysis is limited to metamaterials made from linear and nonmagnetic constituents. arXiv:1810.07996v2 [physics.class-ph]

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“…Let us now develop the equations for the electromagnetic fields on the macroscopic scale in a WSM. We employ the Landau-Lifshitz [30,31] definition of the macroscopic fields…”

Section: Optics/plasmonics Within Wsmmentioning

confidence: 99%

Nonlocal electrodynamics in Weyl semimetals

2017

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Recently synthesized 3D materials with Dirac spectrum exhibit peculiar electric transport qualitatively different from its 2D analogue, graphene. Neglecting impuritiy scattering, the real part of the conductivity is strongly frequency dependent (linear), while the imaginary part is non-zero (unlike in undoped, clean graphene). The Coulomb interaction between electrons is unscreened as in a dielectric and hence is long range. We demonstrate that the interaction correction renders the electrodynamics nonlocal on a mesoscopic scale. The longitudinal conductivity σL (related by charge conservation to the electric susceptibility) and the transverse conductivity σT are different in the long wave length limit and consequently the standard local Ohm's law description does not apply. This leads to several remarkable effects in transport and optical response. We predict a charging effect in DC transport that is a direct signature of the nonlocality. The optical response of the WSM is also sensitive to the nonlocality. In these materials p-polarized light generates bulk plasmons as well as the transversal waves. The propagation inside the WSM is only slightly attenuated. At a specific (material parameter dependent) frequency the two modes coincide, a phenomenon impossible in a local medium. Remarkably, for any frequency there is an incident angle where total absorption occurs, turning the WSM opaque. PACS numbers:One of the common assumptions of electrodynamics in electrically active media is that the effect of external electric fields can be described locally by constitutive relations connecting the "induced" currents to the electric field even when spatial dispersion is present. Generally, due to space -time translational symmetry of the material, the relation between Fourier components (ω is the frequency, k the wavevector) of the electric field and these of the induced current density within linear response reads:Here σ is the AC conductivity tensor with indices i, j = x, y, z. The locality of the electrodynamic response in Fourier space means that the long wavelength limit exists: σ ij (ω, k = 0) ≡ σ ij (ω). The conductivity tensor for a homogeneous, isotropic, space and time-reversal invariant (nongyrotropic) material at k = 0 simplifies into the simple form of Ohm's law:or J (ω) =σ (ω) E (ω). On the microscopic level the locality is not guaranteed [1]. It hinges on the nature of the charges in the condensed matter system and presence of long-range interaction between them. These in turn determine the long-wave excitations of the material. In an insulator (or semiconductor at low temperatures) locality is simply a result of absence of gapless charged excitations. This does not apply to metals.In the free electron gas model of an ideal metal, i.e. neglecting both disorder and electron-electron interactions, there is no energy gap, so there are gapless charged excitations. The conductivity tensor in a metal can be uniquely decomposed into a transversal and a longitudinal part (assuming rotational and reflection symmetry...

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Boundary conditions for electromagnetic field on the surface of media with weak spatial dispersion

Cited by 32 publications

References 27 publications

Boundary conditions for quadrupolar metamaterials

Boundary conditions for quadrupolar metamaterials

Four definitions of magnetic permeability for periodic metamaterials

Nonlocal electrodynamics in Weyl semimetals

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