Robustness of micro-structured devices

Defect-induced localisation

When defects are introduced to materials with otherwise perfectly periodic micro-structures, it can drastically alter wave propagation. While the spectra of the underlying differential operators typically depend continuously on defects [1], the nature of eigenvectors can switch from propagating to localised, meaning energy is no longer transported through the material. When single defects are added, this can be described concisely using asymptotic methods. In recent work, we showed that these methods can be extended to the case of an arbitrary, finite number of defects and the resulting formulas can be used to predict the key features of a completely random system [2].

Topologically protected waveguides

In wave physics, defects are often added to periodic materials to intentionally induce wave localisation. This is the starting point for designing waveguides. For these devices to be practically realisable, it is important that the presence of other defects (e.g. due to manufacuring imperfections) do not disrupt the desired wave guiding function. Perhaps the most promising way to achieve this is to design materials in which waves are guided along topologically non-trivial interfaces. By accounting for the underlying topological properties of the material, it is possible to create waveguides that experience greatly enhaced robustness with respect to imperfections. These ideas are well established in condensed matter theory are were extended to subwavelength resonant PDE models in [3].

An important feature of these waveguides is that they function at a single operating frequency. This can be either a blessing or a curse, depending on the application in hand. Either way, it is desirable to be able to control this operating frequency (ideally, dynamically). A strategy for tuning the localised frequency to any value in the band gap was developed in [4] and this was realised dynamically using photo-responsive materials in [5].

Non-Hermitian skin effects

Systems with non-reciprocal coupling or damping terms can exhibit the so-called "skin-effect" whereby all the eigenmodes are localised at one edge of the system. This strong localisation effect persists in the presence of small imperfections but breaks down when sufficiently large random errors are added to the system. We have characterised the minimal magnitude of defects large enough to cause eigenmodes to be localised within the bulk of the system, rather than at the edge [6] and developed asymptotic models that describe this transition [7].