We study photonic band gap formation in two-dimensional high refractive index disordered materials where the dielectric structure is derived from packing disks in real and reciprocal space. Numerical calculations of the photonic density of states demonstrate the presence of a band gap for all polarizations in both cases. We find that the band gap width is controlled by the increase in positional correlation inducing short-range order and hyperuniformity concurrently. Our findings suggest that the optimization of short-range order, in particular the tailoring of Bragg scattering at the isotropic Brillouin zone, are of key importance for designing disordered PBG materials.
We develop a multiple scattering theory for the absorption of waves in disordered media. Based on a general expression of the average absorbed power, we discuss the possibility to maximize absorption by using structural correlations of disorder as a degree of freedom. In a model system made of absorbing scatterers in a transparent background, we show that a stealth hyperuniform distribution of the scatterers allows the average absorbed power to reach its maximum value. This study provides a theoretical framework for the design of efficient non-resonant absorbers made of dilute disordered mater…
Structural and physical properties of gyromorphs and disordered stealthy hyperuniform media
Princeton Materials Institute, Princeton University（普林斯顿材料研究所，普林斯顿大学）；Department of Electrical & Computer Engineering, Boston University（波士顿大学电气与计算机工程系）；Department of Physics, Boston University（波士顿大学物理系）；Division of Materials Science & Engineering, Boston University（波士顿大学材料与工程分院）；Department of Chemistry, Princeton University（普林斯顿大学化学系）；Program in Applied and Computational Mathematics, Princeton University（普林斯顿大学应用与计算数学项目）
We present designs of 2D isotropic, disordered photonic materials of arbitrary size with complete band gaps blocking all directions and polarizations. The designs with the largest gaps are obtained by a constrained optimization method that starts from a hyperuniform disordered point pattern, an array of points whose number variance within a spherical sampling window grows more slowly than the volume. We argue that hyperuniformity, combined with uniform local topology and short-range geometric order, can explain how complete photonic band gaps are possible without long-range translational order…
We study the density of states (DOS) in band gaps of ideal and disordered three-dimensional photonic crystals of finite size. The ideal crystal is a diamond lattice of resonant point scatterers (atoms) whereas the disordered one is obtained from it by displacing the scatterers by random distances in random directions. We find that DOS inside a band gap of the ideal crystal decreases as the inverse of the crystal size. Disorder narrows the band gap and DOS exhibits enhanced fluctuations near the new band edges. However, the average DOS still exhibits the same scaling with the crystal size withi…
Recently, disordered photonic media and random textured surfaces have attracted increasing attention as strong light diffusers with broadband and wide-angle properties. We report the first experimental realization of an isotropic complete photonic band gap (PBG) in a two-dimensional (2D) disordered dielectric structure. This structure is designed by a constrained-optimization method, which combines advantages of both isotropy due to disorder and controlled scattering properties due to low density fluctuations (hyperuniformity) and uniform local topology. Our experiments use a modular design co…
Novel hollow-core THz waveguides featuring hyperuniform disordered reflectors are proposed, fabricated, and characterized. The reflector comprise aperiodically positioned dielectric cylinders connected with dielectric bridges. The proposed waveguides are fabricated using a 3D stereolithography printer. Optical properties of the fabricated waveguide are investigated numerically using finite element method, as well as experimentally using THz-TDS spectroscopy. The results confirm that proposed waveguides exhibit sizable photonic band gaps (20%) even when relatively low refractive index contrast …
Hyperuniform disordered photonic materials (HDPM) are spatially correlated dielectric structures with unconventional optical properties. They can be transparent to long-wavelength radiation while at the same time have isotropic band gaps in another frequency range. This phenomenon raises fundamental questions concerning photon transport through disordered media. While optical transparency is robust against recurrent multiple scattering, little is known about other transport regimes like diffusive multiple scattering or Anderson localization. Here we investigate band gaps, and we report Anderso…
Using finite difference time domain and band structure computer simulations, we show that it is possible to construct optical cavities and waveguide architectures in hyperuniform disordered photonic solids that are unattainable in photonic crystals. The cavity modes can be classified according to the symmetry (monopole, dipole, quadrupole,etc.) of the confined electromagnetic wave pattern. Owing to the isotropy of the band gaps characteristic of hyperuniform disordered solids, high-quality waveguides with freeform geometries (e.g., arbitrary bending angles) can be constructed that have no anal…
We introduce the first designs for high-Q photonic cavities in slab architectures in hyperuniform disordered solids displaying isotropic band gaps. Despite their disordered character, hyperuniform disordered structures have the ability to tightly confine the TE-polarised radiation in slab configurations that are readily fabricable. The architectures are based on carefully designed local modifications of otherwise unperturbed hyperuniform dielectric structures. We identify a wide range of confined cavity modes, which can be classified according to their approximate symmetry (monopole, dipole, q…
The formation of gaps -- forbidden ranges in the values of a physical parameter -- is a ubiquitous feature of a variety of physical systems: from energy bandgaps of electrons in periodic lattices and their analogs in photonic, phononic, and plasmonic systems to pseudo energy gaps in aperiodic quasicrystals. Here, we report on a `thermalization' gap for light propagating in finite disordered structures characterized by disorder-immune chiral symmetry -- the appearance of the eigenvalues and eigenvectors in skew-symmetric pairs. In this class of systems, the span of sub- thermal photon statistic…
We present wave transport experiments in hyperuniform disordered arrays of cylinders with high dielectric permittivity. Using microwaves, we show that the same material can display transparency, photon diffusion, Anderson localization, or a full band gap, depending on the frequency $ν$ of the electromagnetic wave. Interestingly, we find a second weaker band gap, which appears to be related to the second peak of the structure factor. Our results emphasize the importance of spatial correlations on different length scales for the formation of photonic band gaps.
The optical properties of photonic structures made with more than two materials are very interesting for optical filtering and lighting applications. Herein, we compared the transmission properties of one-dimensional photonic crystals made with three, four and five materials, showing that, with a photonic crystal made of t different materials, the band gap splits in t-1 bands. The same optical thickness for the different materials layers results in split photonic band gaps with the same intensity. Photonic crystals with more than two materials result in a simple structure that could be used fo…
Strong suppression of the photonic density of states in three-dimensional disordered silicon networks
University of Fribourg（弗里堡大学）；Université Côte d’Azur（蔚蓝海岸大学）；CNRS, Institut de Physique de Nice – INPHYNI（法国国家科学研究中心，尼斯物理研究所-INPHYNI）；Optoelectronics Research Centre, University of Southampton（南安普顿大学光电研究中心）
Hyperuniform disordered photonic materials have recently been shown to display large, complete photonic band gaps and isotropic optical properties, and are emerging as strong candidates for a plethora of optoelectronic applications, making them competitive with many of their periodic and quasiperiodic counterparts. In this work, high quality factor optical cavities in hyperuniform disordered architectures are fabricated through semiconductor slabs and experimentally addressed by scanning near-field optical microscopy. The wide range of confined cavity modes that we detect arise from carefully …
Periodicity is usually assumed to be the necessary and sufficient condition for the formation of band gaps, i.e., energy bands with a suppressed density of states. Here, we check this premise by analyzing the band gap properties of three structures that differ in the degree of periodicity and ordering. We consider a photonic crystal, disordered lattice, and ordered but nonperiodic quasicrystalline structure. A real-space metric allows us to compare the degree of periodicity of these different structures. Using this metric, we reveal that the disordered lattice and the ordered quasicrystal can …
The gaps separating two different states widely exist in various physical systems: from the electrons in periodic lattices to the analogs in photonic, phononic, plasmonic systems, and even quasicrystals. Recently, a thermalization gap, an inaccessible range of photon statistics, was proposed for light in disordered structures [Nat. Phys. 11, 930 (2015)], which is intrinsically induced by the disorder-immune chiral symmetry and can be reflected by the photon statistics. The lattice topology was further identified as a decisive role in determining the photon statistics when the chiral symmetry i…
Among the remarkable scattering properties of correlated disordered materials, the origin of pseudo-gaps and the formation of localized states are some of the most puzzling features. Fundamental differences between scalar and vector waves in both these aspects make their comprehension even more problematic. Here we present an in-depth and comprehensive analysis of the order-to-disorder transition in 2D resonant systems. We show with exact ab initio numerical simulations in hyperuniform media that localization of 2D vector waves can occur in the presence of correlated disorder, in a regime of m…
