Abstract

High-contrast particulate media are an attractive platform for microscopic wave control, thanks to their ability to support resonance at subwavelength scales. We have developed an asymptotic method for characterising these high-contrast scattering problems, which uses boundary integral representations to derive a characterisation of subwavelength resonance in terms of eigenstates of the generalised capacitance matrix (GCM). The GCM provides a concise framework to explore some of the important applications and exotic phenomena related to these materials. We will use this framework to show that introducing perturbations to periodic structures creates localised eigenmodes. We will see that these localised modes in large but finite-sized structures converge to those in infinite structures. Further, we will characterise the coupling between multiple localised modes and observe a possible mechanism for the onset of Anderson localisation in random media. These results are collaborations with Habib Ammari and Erik Orvehed Hiltunen.