Universal estimates for the density of states for aperiodic block subwavelength resonator systems
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| Format: | Preprint |
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2025
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| _version_ | 1866908374935797760 |
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| author | Ammari, Habib Barandun, Silvio Davies, Bryn Hiltunen, Erik Orvehed Uhlmann, Alexander |
| author_facet | Ammari, Habib Barandun, Silvio Davies, Bryn Hiltunen, Erik Orvehed Uhlmann, Alexander |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2505_16677 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Universal estimates for the density of states for aperiodic block subwavelength resonator systems Ammari, Habib Barandun, Silvio Davies, Bryn Hiltunen, Erik Orvehed Uhlmann, Alexander Mathematical Physics Disordered Systems and Neural Networks Materials Science 35J05, 35C20, 35P20, 37A30, 47B36 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. |
| title | Universal estimates for the density of states for aperiodic block subwavelength resonator systems |
| topic | Mathematical Physics Disordered Systems and Neural Networks Materials Science 35J05, 35C20, 35P20, 37A30, 47B36 |
| url | https://arxiv.org/abs/2505.16677 |