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Roadmap on metamaterial theory, modelling and design

As part of the UK Metamaterials Network's recent work to map out the future of the field, we have published a roadmap article in Journal of Physics D. Featuring 39 contributions from authors across the UK and some international partners, we have surveyed the state of metamaterial theory, modelling and design strategies, and proposed some open challenges, opportunities and possible directions for the future.

PhD vacancy now open

I am looking to recruit a PhD student through Warwick's HetSys CDT. The project, co-supervised with Radu Cimpeanu, concerns multi-stable meta-fluids and will involve a mixture of asymptotic and numerical techniques. More details on the project are [here] and practical details on how to apply are [here]. Feel free to get in touch with questions [email].

Super band gaps: a route to periodic approximation of quasicrystals.

Quasicrystals have spectral properties that are notoriously difficult to predict or characterise, so it's often tempting to approximate them with periodic materials (known as supercells). The expectation is that by making the unit cell of the periodic approximant larger, the exotic spectral properties of the quasicrystal can be predicted. Recent research shows that sequences of periodic approximants share spectral gaps that persist for all sufficiently large unit cells. These "super band gaps" can be proved to correspond to spectral gaps in the quasicrystal. 

Graded quasicrystals: a new direction for metamaterial energy harvesting.

Recent research published in Physical Review Letters shows how quasicrystals can be spatially graded to produce a metamaterial that performs the well-known "rainbow trapping" effect based on fractal spectra that contain many large spectral gaps. This leads to broadband energy harvesting through a fractal rainbow effect.

Crossing the gap from finite to infinite.

Most metamaterials and photonic crystals feature periodic geometries and are designed based on infinite-sized periodic models (using Bloch boundary conditions). However, any physical device will be finite-sized and its spectral properties will be influenced by the boundaries. Recent work has shown how both the Bloch spectra and localised defect modes of high-contrast finite-sized metamaterials converge to the spectra of their infinitely periodic counterparts in the limit of large size.

Why you need maths to dance. 

Sophisticated and challenging maths underpins even simple, everyday tasks. A recent column in Plus magazine explains how the mathematical theory of multiple wave scattering describes how sounds are scattered around our environment, allowing us to talk to one another and dance to our favourite songs.

Laser-excitation for dynamically tunable waveguides. 

A new approach for building dynamically tunable topological waveguides has been published in Applied Physics Letters. In collaboration with colleagues from Imperial, Exeter and Turin, a photo-responsive device was developed which performs topological wave localisation and whose operating frequency can be tuned dynamically through external excitation by a laser. This was chosen as an Editor's Pick and is the culmination of a longstanding series of projects, spanning spectral theory and asymptotic analysis.

Using functional analysis to design the materials of the future.

Even the most complicated materials can be described concisely with the right mathematical tools. A new generation of materials known as metamaterials is based on exploiting locally resonant materials to achieve novel wave control effects. To achieve the most precise wave control, these resonances should be due to deeply subwavelength structures which often need to have highly contrasting material coefficients. This regime is challenging to model, however recent research has revealed how matrix formulations can accurately model the subwavelength resonance of highly contrasting heterogeneous systems. This approach was summarised in the LMS Newsletter and surveyed in a recent review article.

Designing machines that hear like humans.

The fundamental principles of human hearing can be replicated in both physical and electronic devices. Recent work has developed a mathematical framework for creating bio-inspired graded metamaterials that mimic the function of the cochlea. Further, the insight gained from this approach allows additional processing steps to be developed, beginning to replicate the sophistication of human auditory processing.

Exotic resonances at subwavelength scales.

Recent work on the occurrence of bound states in the continuum and Fano resonances in subwavelength resonator arrays has been published in the Journal of Mathematical Physics and was selected as an Editor's Pick.