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...

We investigate the possibility of using the independence of the transmitted speckle pattern on the illumination condition as a signature of Anderson localization in a single configuration of a two-dimensional and open disordered medium. The analysis is based on exact numerical simulations of multiple light scattering. We introduce a similarity function that we propose as a reliable observable to probe Anderson localization without requiring any statistical averaging over an ensemble.Initially proposed as an explanation for the metal-insulator transition in disordered solids [1], Anderson localization has become a concept at the center of wave physics, with impact far beyond solid-state physics [2,3]. Although the existence of localization in electronic transport has been clearly established [4], the search for convincing evidences of Anderson localization of other kinds of classical or quantum waves has remained an active area of research. The observation of localization has been reported in acoustics [5,6], for electromagnetic waves [7], matter waves [8], and in optics [9,10]. In optics, the observation of localization in three dimensions (3D) is still under debate due to the inherent presence of absorption [11], of nonlinearities [12], or the influence of polarization degrees of freedom [13].Anderson localization cannot be described using classical transport theory, a wave theory being necessary to handle the interferences between multiply scattered amplitudes that induce localization. The scaling theory uses β(g) = ∂ log g/∂ log L as a central concept, with g the dimensionless conductance and L the size of the system [14]. It predicts different behaviors for different space dimensions [one-dimensional (1D) and two-dimensional (2D) systems are always localized while a phase transition is expected in 3D]. The so-called self-consistent theory provides a transport model for the averaged energy density, taking into account interferences between coherently multiply scattered waves [15]. Random matrix theory is another approach that in quasi-1D geometries (disordered waveguides) also predicts wave localization, based on computations of the statistical distribution of the transmission eigenvalues [16][17][18][19]. It is interesting to note that all quantities in these approaches are averaged over a set of realizations of a stochastic process that generates different configurations of the disorder medium (e.g., the spatial distribution of the potential or the position of the scattering centers). This is probably a consequence of the original observation of Anderson localization for electronic conduction, for which the only observable is the (self) averaged conductance. Since, at least for classical waves, it is possible to observe the wavefield in a given realization of the disordered * remi.carminati@espci.fr medium [20][21][22], one can question whether a signature of Anderson localization in a single realization of disorder can be found that does not require any statistical measurement. The purpose of this paper is ...