Resonance and Double Negative Behavior in Metamaterials

Chen, Yue; Lipton, Robert

doi:10.1007/s00205-013-0634-8

Cited by 28 publications

(31 citation statements)

References 56 publications

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“…However, this approach also has two drawbacks from the perspective of numerical implementation: the higher-order expansions are only expected to be accurate if ε is sufficiently small, and may lead nonelliptic differential equations, as shown in [8]. In recent years, the use of the asymptotic approach in quantifying the effective properties of composites has been extended to materials with frequencydependent electric permittivity in [12], [7], where the influence of higher-order terms on the convergence estimates for truncations of the corresponding power series is also investigated.…”

mentioning

confidence: 99%

Full Two-Scale Asymptotic Expansion and Higher-Order Constitutive Laws in the Homogenization of the System of Quasi-static Maxwell Equations

Cherednichenko¹,

Evans²

2016

Multiscale Model. Simul.

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Abstract. For the system of Maxwell equations of electromagnetism in an l-periodic composite medium of overall size L (0 < l < L < ∞), in the low-frequency quasi-static approximation, we develop an electromagnetic version of strain-gradient theories, where the magnetic field is not a function of the magnetic induction alone but also of its spatial gradients, and the electric field depends not only on the displacement but also on displacement gradients. Following the work [V. P. Smyshlyaev and K. D. Cherednichenko, J. Mech. Phys. Solids, 48 (2000), pp. 1325-1357], we propose a combination of variational and asymptotic approaches to the multiscale analysis of the Maxwell system. We provide rigorous convergence estimates of higher order of smallness with respect to the inverse of the "scale separation parameter" L/l. Using a special "ensemble averaging" procedure for a family of periodic problems, we derive an infinite-order version of the standard homogenized operator of second order.

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mentioning

confidence: 99%

Full Two-Scale Asymptotic Expansion and Higher-Order Constitutive Laws in the Homogenization of the System of Quasi-static Maxwell Equations

Cherednichenko¹,

Evans²

2016

Multiscale Model. Simul.

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“…It is worth noting that there is no connection between the blow up of the power and the localized resonance in general [32]. Finally, we want to mention that the design of metamaterials poses new and interesting problems that are being extensively investigated in the litterature, see [8,10,14,18] and the refences therein.…”

Section: Other Topics and Future Directionsmentioning

confidence: 99%

Negative Index Materials: Some Mathematical Perspectives

Nguyên

2018

Acta Math Vietnam

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Negative index materials are artificial structures whose refractive index has a negative value over some frequency range. These materials were postulated and investigated theoretically by Veselago in 1964 and were confirmed experimentally by Shelby, Smith, and Schultz in 2001. New fabrication techniques now allow for the construction of negative index materials at scales that are interesting for applications, which has made them a very active topic of investigation. In this paper, we report various mathematical results on the properties of negative index materials and their applications. The topics discussed herein include superlensing using complementary media, cloaking using complementary media, cloaking an object via anomalous localized resonance, and the well-posedness and the finite speed propagation in media consisting of dispersive metamaterials. Some of the results have been refined and have simpler proofs than the original ones.

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“…In what follows R represents the rod core cross section containing high dielectric material, P the coating containing the plasmonic material and H denotes the connected host material. Following [8] we introduce the expansions for the Bloch wave u d eigenvalue ξ pair…”

Section: (23)mentioning

confidence: 99%

“…The coated cylinders are parallel to the x 3 axis and made from a frequency independent high dielectric core and a frequency dependent dielectric plasmonic coating ( Figure 1). We apply the mathematical analysis developed by the authors in [8] to express the effective dielectric constant and magnetic permeability in terms of spectral representation formulas. These formulas are determined by the Dirichlet spectra of the core and the generalized electrostatic resonances associated with the region exterior to the core.…”

Section: Introductionmentioning

confidence: 99%

Double Negative Dispersion Relations from Coated Plasmonic Rods

Chen¹,

Lipton²

2013

Multiscale Model. Simul.

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A metamaterial with frequency dependent double negative effective properties is constructed from a sub-wavelength periodic array of coated rods. Explicit power series are developed for the dispersion relation and associated Bloch wave solutions. The expansion parameter is the ratio of the length scale of the periodic lattice to the wavelength. Direct numerical simulations for finite size period cells show that the leading order term in the power series for the dispersion relation is a good predictor of the dispersive behavior of the metamaterial.

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Resonance and Double Negative Behavior in Metamaterials

Cited by 28 publications

References 56 publications

Full Two-Scale Asymptotic Expansion and Higher-Order Constitutive Laws in the Homogenization of the System of Quasi-static Maxwell Equations

Full Two-Scale Asymptotic Expansion and Higher-Order Constitutive Laws in the Homogenization of the System of Quasi-static Maxwell Equations

Negative Index Materials: Some Mathematical Perspectives

Double Negative Dispersion Relations from Coated Plasmonic Rods

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