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Profile picture Clemens Thalhammer

Uniform Hyperbolicity, Bandgaps and Edge Modes

Authors: Habib Ammari, Clemens Thalhammer, Alexander Uhlmann

Venue: arXiv preprint (2025)

Status: Submitted

Published:

arXiv
aperiodic systems metamaterials subwavelength resonators edge modes bandgap engineering uniform hyperbolicity

Abstract

We aim to characterise the spectral distributions of bi-infinite, semi-infinite, and finite aperiodic one-dimensional arrays of subwavelength resonators, constructed by sampling from a finite library of building blocks. By adopting the modern formalism of uniform hyperbolicity, we are able to strengthen and rigorously prove a Saxon-Hutner-type result, fully characterising the spectral gaps of the composite bi-infinite aperiodic system in terms of its constituent blocks. Crucial to this approach is a change of basis from transfer matrices to propagation matrices, allowing for a block-level characterisation. This approach also enables an explicit characterisation of edge-induced eigenmodes in the semi-infinite setting. Finally, we leverage finite section methods for Jacobi operators to extend our results to finite systems – providing strict bounds for their spectra in terms of their constituent blocks.

Bibtex

@article{ammari2025uniform,
  title={Uniform Hyperbolicity, Bandgaps and Edge Modes in Aperiodic Systems of Subwavelength Resonators},
  author={Ammari, Habib and Thalhammer, Clemens and Uhlmann, Alexander},
  journal={arXiv preprint arXiv:2509.22417},
  year={2025}
}