Resonant metasurfaces at oblique incidence: interplay of order and disorder

Albooyeh, Mohammad; Kruk, Sergey; Menzel, Christoph; Helgert, Christian; Kröll, Matthias; Krysinski, Adam; Decker, Manuel; Neshev, Dragomir N.; Pertsch, Thomas; Etrich, C.; Rockstuhl, Carsten; Tretyakov, Sergei; Simovski, Constantin; Kivshar, Yuri S.

doi:10.1038/srep04484

Cited by 62 publications

(52 citation statements)

References 36 publications

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“…A common way to introduce disorder into an otherwise ordered system, such as a perfect crystal or quasicrystal, is to randomly perturb the particle positions of that system [1][2][3][4]. A perturbed lattice is a point pattern (process) in d-dimensional Euclidean space R d obtained by displacing each point in a Bravais lattice [5] according to some stochastic rule [1,[6][7][8].…”

Section: Introductionmentioning

confidence: 99%

Cloaking the underlying long-range order of randomly perturbed lattices

2020

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Random, uncorrelated displacements of particles on a lattice preserve the hyperuniformity of the original lattice, that is, normalized density fluctuations vanish in the limit of infinite wavelengths. In addition to a diffuse contribution, the scattering intensity from the the resulting point pattern typically inherits the Bragg peaks (long-range order) of the original lattice. Here we demonstrate how these Bragg peaks can be hidden in the effective diffraction pattern of independent and identically distributed perturbations. All Bragg peaks vanish if and only if the sum of all probability densities of the positions of the shifted lattice points is a constant at all positions. The underlying longrange order is then 'cloaked' in the sense that it cannot be reconstructed from the pair correlation function alone. On the one hand, density fluctuations increase monotonically with the strength of perturbations a, as measured by the hyperuniformity order metric Λ. On the other hand, the disappearance and reemergence of long-range order, depending on whether the system is cloaked or not as the perturbation strength increases, is manifestly captured by the τ order metric. Therefore, while the perturbation strength a may seem to be a natural choice for an order metric of perturbed lattices, the τ order metric is a superior choice. It is noteworthy that cloaked perturbed lattices allow one to easily simulate very large samples (with at least 10 6 particles) of disordered hyperuniform point patterns without Bragg peaks.

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Section: Introductionmentioning

confidence: 99%

Cloaking the underlying long-range order of randomly perturbed lattices

2020

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“…We note that this can also be achieved using dielectric nanoparticles, such as disk or ring resonators [28]. Moreover, we also note that recent works have extended investigations of randomness to the field of metasurfaces [29,30]. Insets show the real part of at the corresponding resonance frequencies using a rainbow colormap (min in blue, zero in green, and max in red).…”

Section: From 1-srr To 4-srrmentioning

confidence: 99%

Multipoles of Even/Odd Split-Ring Resonators

et al. 2015

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Abstract:The ultimate goal of metamaterial engineering is to have complete control over the electromagnetic constitutive parameters in three-dimensional space. This engineering can be done by considering either single meta-atoms or full meta-arrays. We follow the first route and perform numerical simulations of split-ring resonators, with different gap numbers and under varying illumination scenarios, to investigate their individual multipolar scattering response. For the fundamental resonance, we observe that odd-gap rings always exhibit overlapping electric and magnetic dipole responses while even-gap rings only exhibit that behavior accidentally. We expect our results to foster progress in the engineering of three-dimensional disordered metamaterials.

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“…However, relatively few works have focused on disordered metamaterials. These limited studies have shown that size [10][11][12][13] and positional [14][15][16][17][18][19][20][21][22][23] disorder of a metamaterial's resonator elements lead to resonance broadening and effective scattering loss. While these works provide important insights, they overlook one of the most important aspects of disorder: percolation.…”

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Negative refractive index induced by percolation in disordered metamaterials

Slovick

2017

Phys. Rev. B

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An effective medium model is developed for disordered metamaterials containing a spatially random distribution of dielectric spheres. Similar to effective medium models for ordered metamaterials, this model predicts resonances in the effective permeability and permittivity arising from electricand magnetic-dipole Mie resonances in the spheres. In addition, the model predicts a redshift of the electric resonance with increasing particle loading. Interestingly, when the particle loading exceeds the percolation threshold of 33%, the model predicts that the electric resonance overlaps with the magnetic resonance, resulting in a negative refractive index.Metamaterials, inhomogeneous composite materials that behave macroscopically as homogeneous materials, are of great fundamental and technological interest. The ability to tailor the macroscopic electromagnetic parameters, namely the permittivity and permeability, by changing the geometry and arrangement of the included elements has led to a number of important material designs and applications [1]. Most notable among these are materials with negative refractive index [2,3], which have both negative permittivity and permeability. Negative index materials exhibit unusual properties such as negative refraction and exponential growth of evanescent near fields, which have been utilized for applications such as cloaking [4] and superresolution imaging [5].To date, the metamaterial literature has focused primarily on designs where the included elements are arranged in a periodic lattice [6]. This is largely due to the ease of computation and suppression of scattering, as disorder of the lattice leads to spatial inhomogeneities. However, fabrication of periodic metamaterials on a large scale can be cost prohibitive, particularly for metamaterials operating in the optical band, where the lattice dimensions are submicron and require the use of electronbeam lithography [7,8]. Self-assembly based nanosphere lithography has been used to fabricate centimeter-scale optical metasurfaces [9], but this approach is not scalable to much larger areas.Disordered metamaterials provide a scalable alternative to periodic structures, provided that the scattering can be managed and their performance can be predicted. However, relatively few works have focused on disordered metamaterials. These limited studies have shown that size [10-13] and positional [14-23] disorder of a metamaterial's resonator elements lead to resonance broadening and effective scattering loss. While these works provide important insights, they overlook one of the most important aspects of disorder: percolation. Percolation occurs in random composites at high loading when the particles form a continuous path through the composite, and it can have dramatic consequences on the effective electromagnetic parameters [24,25] In this Letter, it is shown that percolation induces a negative refractive index in disordered metamaterials containing Mie-resonant particles. To this end, the classic Bruggeman percolation theory [24,26] ...

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Resonant metasurfaces at oblique incidence: interplay of order and disorder

Cited by 62 publications

References 36 publications

Cloaking the underlying long-range order of randomly perturbed lattices

Cloaking the underlying long-range order of randomly perturbed lattices

Multipoles of Even/Odd Split-Ring Resonators

Negative refractive index induced by percolation in disordered metamaterials

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