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

Abstract We consider the spectral properties of aperiodic block subwavelength resonator systems in one dimension, with a primary focus on the density of states (DoS). We prove that for random block configurations, as the number of blocks <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mi>M</mml:mi> <mml:mo accent="false" stretchy="false">→</mml:mo> <mml:mi mathvariant="normal">∞</mml:mi> </mml:mrow> </mml:math> , the integrated DoS converges to a non-random, continuous function. We show both analytically and numerically that the DoS 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 DoS in these hybridisation regions. This approach is shown to extend to systems with quasiperiodic and hyperuniform arrangements of blocks.