On the current-driven model in the classical electrodynamics of continuous media

Markel, Vadim A.

doi:10.1088/0953-8984/22/48/485401

Cited by 4 publications

(7 citation statements)

References 14 publications

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“…Moreover, in can be seen from the data of Figs. 8,9 that renormalization of effective parameters according to (37) does not worsen or, indeed, noticeably modify the predictions of current-driven homogenization.…”

Section: A Example Amentioning

confidence: 90%

“…But the only physically-realizable case is k = q. Therefore, it is not clear why the pair of effective parameters predicted by current-driven homogenization is "better" than any other pair obtained by the transformation (37). This point will be illustrated numerically in Sec.…”

Section: B Step Two: Calculation Of Local Parametersmentioning

confidence: 97%

“…with the renormalization factor ξ = µ xx . In (37), ǫ nd µ are tensors while ξ is a scalar. Renormalization (37) does not affect the equivalence of the induced currents (10) and ( 12) when each formula is evaluated on-shell, that is, for k = q.…”

Section: A Example Amentioning

confidence: 99%

“…In (37), ǫ nd µ are tensors while ξ is a scalar. Renormalization (37) does not affect the equivalence of the induced currents (10) and ( 12) when each formula is evaluated on-shell, that is, for k = q. The renormalized parameters are also given in Table I.…”

Section: A Example Amentioning

confidence: 99%

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Current-driven homogenization and effective medium parameters for finite samples

Markel

Tsukerman

2013

Phys. Rev. B

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Reflection and refraction of electromagnetic waves by artificial periodic composites (metamaterials) can be accurately modeled by an effective medium theory only if the boundary of the medium is explicitly taken into account and the two effective parameters of the medium -the index of refraction and the impedance -are correctly determined. Theories that consider infinite periodic composites do not satisfy the above condition. As a result, they cannot model reflection and transmission by finite samples with the desired accuracy and are not useful for design of metamaterial-based devices. As an instructive case in point, we consider the "current-driven" homogenization theory, which has recently gained popularity. We apply this theory to the case of one-dimensional periodic medium wherein both exact and homogenization results can be obtained analytically in closed form. We show that, beyond the well-understood zero-cell limit, the current-driven homogenization result is inconsistent with the exact reflection and transmission characteristics of the slab.

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Section: A Example Amentioning

confidence: 90%

Section: B Step Two: Calculation Of Local Parametersmentioning

confidence: 97%

Section: A Example Amentioning

confidence: 99%

Section: A Example Amentioning

confidence: 99%

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Current-driven homogenization and effective medium parameters for finite samples

Markel

Tsukerman

2013

Phys. Rev. B

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“…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 . Previously, we have derived (1) and defined Σ(ω, q) for general threedimensional PCs without appealing to the concept of "impressed" currents 20,26 .…”

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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External versus induced and free versus bound electric currents and related fundamental questions of the classical electrodynamics of continuous media: discussion

Markel

2018

J. Opt. Soc. Am. A

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On the current-driven model in the classical electrodynamics of continuous media

Abstract: The current-driven model in which a continuous medium is excited by a pre-determined current which overlaps with the medium in all points in space but is not subject to constitutive relations is critically analyzed.

Cited by 4 publications

References 14 publications

Current-driven homogenization and effective medium parameters for finite samples

Current-driven homogenization and effective medium parameters for finite samples

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

External versus induced and free versus bound electric currents and related fundamental questions of the classical electrodynamics of continuous media: discussion

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