Universality and optimality of band-gaps in laminated media

TL;DR

This paper reveals a universal spectral structure in layered composites, enabling the analysis and optimization of band-gaps across various materials, including deformable and multi-physical ones.

Contribution

It introduces a universal spectral representation for layered media, allowing for the analysis and optimization of band-gaps regardless of geometry or material properties.

Findings

Universal spectral structure in layered media.

Rules for tailoring band-gaps based on spectral properties.

Characterization of tunability in soft and multi-physical materials.

Abstract

We find that the frequency spectra of layered phononic and photonic composites admit a universal struc- ture, independent of the geometry of the periodic-cell and the specific physical properties. We show that this representation extends to highly deformable and multi-physical materials of tunable spectra. The structure is employed to establish universal properties of the corresponding band-gaps, and to rigorously determine their sta- tistical and optimal characteristics. Specifically, we investigate the density of the gaps, their maximal width and expected value. As a result, rules for tailoring the laminate according to desired spectra properties follow. Our representation further facilitates characterizing the tunability of the band-structure of soft and multi-physical materials.