Fast Generation of Spectrally-Shaped Disorder

Abstract

Media with correlated disorder display unexpected transport properties, but it is still a challenge to design structures with desired spectral features at scale. In this work, we introduce an optimal formulation of this inverse problem by means of the non-uniform fast Fourier transform, thus arriving at an algorithm capable of generating systems with arbitrary spectral properties, with a computational cost that scales $O(N\log N)$ with system size. The method is extended to accommodate arbitrary real-space interactions, such as short-range repulsion, to simultaneously control short- and long-range correlations. We thus generate the largest-ever stealthy hyperuniform configurations in $2d$ ($N=10^9$) and $3d$ ($N>10^7$). By an Ewald sphere construction we link the spectral and optical properties at the single-scattering level, and show that these structures in $2d$ and $3d$ generically display transmission gaps, providing a concrete example of fine-tuning of a physical property at will. We also show that large $3d$ power-law hyperuniformity in particle packings leads to single-scattering properties near-identical to those of simple hard spheres. Finally, we show that enforcing large spectral power at a small number of peaks with the right symmetry leads to the non-deterministic generation of quasicrystalline structures in both $2d$ and $3d$.

arXiv comment9 pages / 5 figures + 3 pages of appendices / 5 appendix figures + 18 pages and 12 figures in SI

References in corpus (22)

• Hyperuniform States of Matter
• Designer disordered materials with large complete photonic band gaps
• Measurement of areas on a sphere using Fibonacci and latitude-longitude lattices
• CMasher: Scientific colormaps for making accessible, informative and 'cmashing' plots
• Hyperuniformity of critical absorbing states
• Event-chain Monte Carlo algorithms for hard-sphere systems
• Transport Phase Diagram and Anderson Localization in Hyperuniform Disordered Photonic Materials
• Photonic band gap in isotropic hyperuniform disordered solids with low dielectric contrast
• Ensemble Theory for Stealthy Hyperuniform Disordered Ground States
• The Role of Short-Range Order and Hyperuniformity in the Formation of Band Gaps in Disordered Photonic Materials
• Light in correlated disordered media
• The visual appearances of disordered optical metasurfaces
• Random Scalar Fields and Hyperuniformity
• Multifunctional Composites for Elastic and Electromagnetic Wave Propagation
• Collective Coordinate Control of Density Distributions
• Photonic Band Gaps in 3D Network Structures with Short-range Order
• Attraction tames two-dimensional melting: from continuous to discontinuous transitions
• Nonlocal Effective Electromagnetic Wave Characteristics of Composite Media: Beyond the Quasistatic Regime
• Voronoi and Voids Statistics for Super-homogeneous Point Processes
• Generating large disordered stealthy hyperuniform systems with ultra-high accuracy to determine their physical properties
• 3D tomographic analysis of the order-disorder interplay in the Pachyrhynchus congestus mirabilis weevil
• Hyperuniformity and wave localization in pinwheel scattering arrays

Cited by in corpus (6)

• Disordered Optical Metasurfaces: Basics, Properties, and Applications
• Existence of Nonequilibrium Glasses in the Degenerate Stealthy Hyperuniform Ground-State Manifold
• Heterogeneous networks for phase-sensitive engineering of optical disordered materials
• Gyromorphs: a new class of functional disordered materials
• Emergent universal long-range structure in random-organizing systems
• Inferring traits of hyperuniformity from local structures via persistent homology