2025/05/22 by Habib Ammari, Ammari, Habib, S Barandun +7 · 3 citations
Materials Science · Physics and Astronomy · #35C20 #35J05 #35P20 #37A30 #47B36 #Disordered Systems and Neural Networks (cond-mat.dis-nn) #FOS: Physical sciences #Materials Science (cond-mat.mtrl-sci) #Mathematical Physics (math-ph) #Metamaterials and Metasurfaces Applications #Photonic Crystals and Applications #Quasicrystal Structures and Properties
paper · pdf · doi:10.48550/arxiv.2505.16677
openalex publication_date 2025/05/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider the spectral properties of aperiodic block subwavelength resonator systems in one dimension, with a primary focus on the density of states. We prove that for random block configurations, as the number of blocks M→ ∞, the integrated density of states converges to a non-random, continuous function. We show both analytically and numerically that the density of states exhibits a tripartite decomposition: it vanishes identically within bandgaps; it forms smooth, band-like distributions in shared pass bands (a consequence of constructive eigenmode interactions); and, most notably, it exhibits a distinct fractal-like character in hybridisation regions. We demonstrate that this fractal-like behaviour stems from the limited interaction between eigenmodes within these hybridisation regions. Capitalising on this insight, we introduce an efficient meta-atom approach that enables rapid and accurate prediction of the density of states in these hybridisation regions. This approach is shown to extend to systems with quasiperiodic and hyperuniform arrangements of blocks.