Fast Generation of Spectrally-Shaped Disorder

TL;DR

This paper introduces an efficient algorithm using non-uniform fast Fourier transform to generate large-scale media with customizable spectral properties, enabling control over optical and structural features in 2D and 3D systems.

Contribution

It presents a novel inverse design method for correlated disorder structures with arbitrary spectral features, scalable to billion-particle configurations, and extends to real-space interactions.

Findings

Generated largest stealthy hyperuniform configurations in 2D and 3D.

Structures exhibit transmission gaps linked to spectral properties.

Large 3D hyperuniform packings mimic hard sphere scattering.

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 $3d$.