Beyond local effective material properties for metamaterials

Mnasri, Karim; Khrabustovskyi, Andrii; Stohrer, Christian; Plum, Michael; Rockstuhl, Carsten

doi:10.1103/physrevb.97.075439

Cited by 30 publications

(47 citation statements)

References 33 publications

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“…With the objective to homogenization, a displacement field D, in the presence of light with an electric field E, has been lately introduced in Ref. 28 in the frequency domain that reads…”

Section: Setting Up the Fresnel Equationsmentioning

confidence: 99%

“…In region Ω, the solutions to the wave equation, i.e., the dispersion relations (k z,σ (k 0 , k t )) 2 are multiple, with σ = ±1, are derived and discussed in depth in Ref. 28. The polarizations in this case differ remarkably such that the TE and TM polarizations show different functional dependency of k z,σ (k 0 , k t ).…”

Section: Setting Up the Fresnel Equationsmentioning

confidence: 99%

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Retrieving effective material parameters of metamaterials characterized by nonlocal constitutive relations

et al. 2019

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The parameter retrieval is a procedure in which effective material properties are assigned to a given metamaterial. A widely used technique bases on the inversion of reflection and transmission from a metamaterial slab. Thus far, local constitutive relations have been frequently considered in this retrieval procedure to describe the metamaterial at the effective level. This, however, is insufficient. The retrieved local material properties frequently fail to predict reliably the optical response from the slab in situations that deviate from those that have been considered in the retrieval, e.g. when illuminating the slab at a different incidence angle. To significantly improve the situation, we describe here a parameter retrieval, also based on the inversion of reflection and transmission from a slab, that describes the metamaterial at the effective level with nonlocal constitutive relations. We retrieve the effective material parameters at the example of a basic metamaterial, namely dielectric spheres on a cubic lattice but also on a more advanced, anisotropic metamaterial of current interest, i.e., the fishnet metamaterial. We demonstrate that the nonlocal constitutive relation can describe the optical response much better than local constitutive relation would do. Our approach is widely applicable to a large class of metamaterials. PACS numbers: 41.20. Jb,78.20.Bh,78.20.Ci,78.67.Pt c is the free space wavenumber and ω and c are the frequency of the considered time-harmonic field and the speed of light in vacuum, respectively. We refer to the description of a metamaterial with these two parameters only, as the Weak Spatial Dispersion (WSD) or local approximation. It is a local constitutive relation since the electric displacement D(r, k 0 ) and the magnetic induction B(r, k 0 ) depend only locally on the electric field E(r, k 0 ) and the magnetic field H(r, k 0 ), respectively.However, metamaterials are usually made from building blocks, also called meta-atoms, that have a size in the order of several tens or even hundreds of nanometers, while being designed to operate at optical or nearinfrared wavelengths. This is in stark contrast to natural materials that have critical dimensions of merely a fraction of one nanometer. The disparate length scales between critical feature size and operational wavelength for natural materials justifies their treatment with local constitutive relations. Indeed, it is quite a challenge to trace signatures of a nonlocal character with natural materials 12,13 . The assumption of a local medium, however, ceases to be applicable for optical metamaterials when their critical length scale is no longer much smaller than the wavelength but only smaller. Then, nonlocal effects can no longer be neglected.But how can we judge, which effective description is appropriate? Well, first of all and with the purpose to treat the material as effectively homogeneous, we require it to be sub-wavelength under all circumstances. A fre-arXiv:1808.00748v3 [physics.optics]

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“…With the objective to homogenization, a displacement field D, in the presence of light with an electric field E, has been lately introduced in Ref. 28 in the frequency domain that reads…”

Section: Setting Up the Fresnel Equationsmentioning

confidence: 99%

Section: Setting Up the Fresnel Equationsmentioning

confidence: 99%

Retrieving effective material parameters of metamaterials characterized by nonlocal constitutive relations

et al. 2019

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“…with q = ǫ/η and p = (2k 2 0 ηµ) −1 [19]. This relation has four mathematical solutions in total, two of which are physical.…”

Section: Materials Models and Dispersion Relationsmentioning

confidence: 99%

“…In contrast, η is associated to a strong spatial dispersion, it is a nonlocal material parameter. These constitutive relations allow for a rigorous mathematical derivation of interface conditions that extend the known conditions from basic electrodynamics [19]. Therefore, not just light propagation in bulk material can be described but also functional elements thereof.…”

Section: Introductionmentioning

confidence: 96%

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Surface plasmon polaritons sustained at the interface of a nonlocal metamaterial

et al. 2018

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Studying basic physical effects sustained in metamaterials characterized by specific constitutive relation is a research topic with a long standing tradition. Besides intellectual curiosity, it derives its importance from the ability to predict observable phenomena that are, if found with an actual metamaterial, a clear indication on its properties. Here, we consider a nonlocal (strong spatial dispersion), lossy, and isotropic metamaterial and study the impact of the nonlocality on the dispersion relation of surface plasmon polaritons sustained at an interface between vacuum and such metamaterial. For that, Fresnel coefficients are calculated and appropriate surface plasmon polaritons existence conditions are being proposed. Predictions regarding the experimentally observable reflection from a frustrated internal reflection geometry are being made. A different behavior for TE and TM polarization is observed. Our work unlocks novel opportunities to seek for traces of the nonlocality in experiments made with nowadays metamaterials.

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Nonlocal Approaches to the Dynamics of Metamaterials

Failla

Ghavanloo

2021

Springer Tracts in Mechanical Engineering

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Beyond local effective material properties for metamaterials

Cited by 30 publications

References 33 publications

Retrieving effective material parameters of metamaterials characterized by nonlocal constitutive relations

Retrieving effective material parameters of metamaterials characterized by nonlocal constitutive relations

Surface plasmon polaritons sustained at the interface of a nonlocal metamaterial

Nonlocal Approaches to the Dynamics of Metamaterials

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