Universal estimates for the density of states for aperiodic block subwavelength resonator systems

TL;DR

This paper investigates the spectral properties of aperiodic subwavelength resonator systems, revealing universal density of states behavior, including bandgaps, smooth pass bands, and fractal-like hybridisation regions, with a novel meta-atom prediction method.

Contribution

It provides the first comprehensive analysis of the density of states in aperiodic resonator systems, introducing a meta-atom approach for efficient predictions and extending results to quasiperiodic and hyperuniform arrangements.

Findings

Density of states converges to a non-random function as system size grows.

Density exhibits bandgaps, pass bands, and fractal-like hybridisation regions.

Meta-atom method enables rapid, accurate predictions in hybridisation regions.

Abstract

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 $M\to \infty$, 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.