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 $3d$.

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

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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