Abstract

Characterising the spectra of quasiperiodic operators is a challenging problem that has attracted the attention of mathematicians for several decades. Meanwhile, metamaterial waveguides achieve exceptional wave control feats through carefully designed geometric patterns. These patterns are typically periodic, meaning their spectra can be characterised concisely using Floquet-Bloch analysis. However, modern techniques for describing quasiperiodic patterns are now sufficiently developed that we can use them when designing metamaterial waveguides for specific applications, thereby greatly enlarging the potential design space. This talk will summarise some recent breakthroughs in the characterisation of spectral gaps in quasiperiodic metamaterials and identify opportunities where this theory can be used in applications. In particular, we will look at applications of quasicrystals to graded energy harvesting devices and symmetry-induced waveguides.