Theory of Mesoscopic Magnetism in Photonic Crystals

Felbacq, Didier; Bouchitté, Guy

doi:10.1103/physrevlett.94.183902

Cited by 91 publications

(75 citation statements)

References 21 publications

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“…It follows that the induced magnetic activity cannot result simply from the superposition of independent Helmholtz micro-resonators as depicted in [12]. Interactions between the inclusions and the substrate have to be well understood.…”

Section: Introduction and Description Of The Modelmentioning

confidence: 99%

Homogenization Near Resonances and Artificial Magnetism in Three Dimensional Dielectric Metamaterials

Bouchitté

Bourel

Felbacq

2017

Arch Rational Mech Anal

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ABSTRACT. It is now well established that the homogenization of a periodic array of parallel dielectric fibers with suitably scaled high permittivity can lead to a (possibly) negative frequency-dependent effective permeability. However this result based on a two-dimensional approach holds merely in the case of linearly polarized magnetic fields, reducing thus its applications to infinite cylindrical obstacles. In this paper we consider a dielectric structure placed in a bounded domain of 3 and perform a full 3D asymptotic analysis. The main ingredient is a new averaging method for characterizing the bulk effective magnetic field in the vanishing-period limit. We evidence a vectorial spectral problem on the periodic cell which determines micro-resonances and encodes the oscillating behavior of the magnetic field from which artificial magnetism arises. At a macroscopic level we deduce an effective permeability tensor that we can be make explicit as a function of the frequency. As far as sign-changing permeability are sought after, we may foresee that periodic bulk dielectric inclusions could be an efficient alternative to the very popular metallic split-ring structure proposed by Pendry. Part of these results have been announced in [8].

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Section: Introduction and Description Of The Modelmentioning

confidence: 99%

Homogenization Near Resonances and Artificial Magnetism in Three Dimensional Dielectric Metamaterials

Bouchitté

Bourel

Felbacq

2017

Arch Rational Mech Anal

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“…The cloaking device is usually given by coefficients with extreme values, large or small, or by negative coefficients in some part of the domain. In this sense, many ideas for cloaking can be considered as realizable only since the invention of negative index metamaterials [22], for which mathematical justifications can be found for instance in [7,3,13,4].…”

Section: Introductionmentioning

confidence: 99%

Cloaking of Small Objects by Anomalous Localized Resonance

Bouchitté

Schweizer

2010

The Quarterly Journal of Mechanics and Applied Mathematics

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We investigate operators L η u = ∇ · (a η ∇u) and solutions u η of L η u η = 0 to various boundary conditions. The coefficients a η are assumed to have a real part with changing sign and a small, non-negative imaginary part. We investigate a ring geometry with radii 1 and R in two space dimensions and use Fourier expansions in polar coordinates to analyze the qualitative behavior of solutions when boundary conditions on a small inclusion B ε (x 0 ) are imposed. Our result is that u η depends qualitatively on the position of the inclusion. If |x 0 | is larger than the cloaking radius R * := R 3/2 , then u η behaves as if no ring were present. If, instead, |x 0 | is smaller than R * , then the small inclusion is invisible in the limit η → 0.

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“…Previous studies have for example noticed a correlation between the resonances of single dielectric objects and the opening of photonic band gaps (PBGs) in arrays of them [15,16]. In the context of MMs, arrays of dielectric rods in p-polarized light (magnetic field parallel to the axis of the rods) have been shown to possess an effective, dispersive, magnetic permeability [17,18]. Interestingly, it has further been suggested that dielectric rods in s-polarized light (electric field parallel to the axis of the rods) could exhibit both electric and magnetic dipole resonances, and thus, possibly constitute a so-called left-handed (LH) medium with simultaneously negative permittivity and permeability [11,12].…”

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confidence: 99%

All-Dielectric Rod-Type Metamaterials at Optical Frequencies

et al. 2009

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Light propagation in all-dielectric rod-type metamaterials is studied theoretically. The electric and magnetic dipole moments of the rods are derived analytically in the long-wavelength limit. The effective permittivity and permeability of a square lattice of rods are calculated by homogenizing the corresponding array of dipoles. The role of dipole resonances in the optical properties of the rod array is interpreted. This structure is found to exhibit a true left-handed behavior, confirming previous experiments [L. Peng et al., Phys. Rev. Lett. 98, 157403 (2007)]. A scaling analysis shows that this effect holds at optical frequencies and can be obtained by using rods made, for example, of silicon.

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Theory of Mesoscopic Magnetism in Photonic Crystals

Cited by 91 publications

References 21 publications

Homogenization Near Resonances and Artificial Magnetism in Three Dimensional Dielectric Metamaterials

Homogenization Near Resonances and Artificial Magnetism in Three Dimensional Dielectric Metamaterials

Cloaking of Small Objects by Anomalous Localized Resonance

All-Dielectric Rod-Type Metamaterials at Optical Frequencies

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