High-density hyperuniform materials can be transparent

Abstract

We show that materials made of scatterers distributed on a stealth hyperuniform point pattern can be transparent at densities for which an uncorrelated disordered material would be opaque due to multiple scattering. The conditions for transparency are analyzed using numerical simulations, and an explicit criterion is found based on a perturbative theory. The broad applicability of the concept offers perspectives for various applications in photonics, and more generally in wave physics.PACS numbers: 42.25.Dd, 61.43.Dq INTRODUCTIONThe study of light propagation in scattering media has been a very active field in the past decades, stimulated by fundamental questions in mesoscopic physics [1, 2] and by the development of innovative imaging techniques [3]. Recently, a new trend has emerged, with the possibility to control electromagnetic wave propagation in disordered media up to the optical frequency range. On the one hand, wavefront shaping techniques offer the possibility to overcome the distorsions induced by a scattering material, even in the multiple scattering regime [4][5][6]. On the other hand, the possibility to engineer the disorder itself, by controlling the degree of structural correlation, opens new perspectives for the design of materials with specific properties (e.g., absorbers or filters for photonics) [7][8][9][10][11]. These materials combine the advantages of disordered materials, in terms of process scalability and robustness to fabrication errors, with the possibility to develop a real engineering of their scattering and transport properties through the control of the degree of correlation in the disorder. For example, it has been shown that correlations can substantially change basic transport properties, such as the mean-free path [12], the density of states [13,14] including the appearance of bandgaps [15][16][17], or the Anderson localization length [18].A specific class of correlated materials has appeared recently, initially referred to as "superhomogeneous materials" [19], and now called "hyperuniform materials" [20]. These materials are made of discrete scatterers distributed on a hyperuniform point pattern, a correlated pattern with a structure factor S(q) vanishing in the neighborhood of |q| = 0. The geometrical properties of hyperuniform point patterns have been extensively studied, in particular in terms of packing properties [21][22][23][24][25]. Regarding wave propagation, it has been shown that bandgaps could be observed for electromagnetic waves in two-dimensional (2D) disordered hyperuniform materials [26][27][28][29][30]. Although understanding the origin of the bandgaps is still a matter of study [31,32], these results have stimulated the design and fabrication of threedimensional (3D) hyperuniform structures for wave control at optical frequencies [33,34].In this Letter, we demonstrate that stealth hyperuniform point patterns, a special class of hyperuniform structures for which S(q) = 0 in a finite domain around |q| = 0, offer the possibility to design disordered materials...

Role of packing density and spatial correlations in strongly scattering 3D systems

“…To this purpose, we adopt a numerical approach allowing us to define, quantify, and independently vary all physical parameters of the scattering medium one at a time, encompassing for the first time, to the best of our knowledge, the whole parameter space in terms of both volume concentrations and spatial correlations. Here, we focus on the specific type of correlations induced by the packing of hard spheres, but our approach can be applied to any kind of spatial correlation in discrete systems, including deterministic aperiodic [41], potentialbased [42], hyperuniform [8], or random fractal [43] structures. Owing to this richer characterization, novel insight is gained by analyzing the interplay between particle density and spatial correlations in terms of two key functionals of the 3D point statistics, namely the first moments of the nearest-neighbor distance and pore-size distributions.…”

Can exotic disordered “stealthy” particle configurations tolerate arbitrarily large holes?

“…13,14 A major focus of this paper is the study of a particular property of the void space between point particles in disordered "stealthy" systems, [15][16][17][18][19] which are disordered many-particle configurations that anomalously suppress large-scale density fluctuations, endowing them with unique physical properties. [20][21][22][23][24][25] The specific question that we investigate is whether disordered stealthy systems can contain arbitrarily large holes. Here we define a "hole" as a spherical region of a certain radius that is empty of particle centers.…”

“…Such systems have received considerable attention because they anomalously suppress density fluctuations. [20][21][22][23][24][25] Specifically, if one places a spherical window of radius R into a d-dimensional many-particle system and counts the number of particles in the window, then the number variance, σ 2 (R), scales as R d for large R in typical disordered systems. Any system in which σ 2 (R) grows slower than R d is said to be hyperuniform.…”

“…Nevertheless, different hyperuniform systems have different levels of suppression for large-scale density fluctuations. While any system in which lim |k|→0 S(k) = 0 is considered hyperuniform, the "stealthy" variants of hyperuniform systems have S(k) = 0 in the entire interval |k| ∈ (0, K] for a certain value of K. Stealthy hyperuniform systems are known to possess many unique physical properties, including negative thermal expansion behavior, 20 complete isotropic photonic band gaps comparable in size to those of a photonic crystal, [21][22][23] transparency even at high densities, 24 and nearly optimal transport properties. 25 The behavior of S(k) near k = 0 in stealthy systems is identical to that in perfect crystals.…”

Transport, geometrical, and topological properties of stealthy disordered hyperuniform two-phase systems

“…22 It has also been shown that dielectric networks derived from stealthy disordered hyperuniform point configurations possess complete photonic band gaps comparable in size to those of a photonic crystal, while at the same time maintain statistical isotropy, enabling waveguide geometries not possible with photonic crystals as well as high-density disordered transparent materials. 17,[27][28][29] However, the determination of physical/chemical properties of stealthy disordered hyperuniform materials is generally an unexplored area of research.…”