Subwavelength Localisation in Disordered Systems

Abstract

We elucidate the different mechanisms of wave localisation in disordered finite systems of subwavelength resonators, where the disorder is in the spatial arrangement of the resonators. To do so, we employ the capacitance matrix formalism and develop a variety of tools to understand localisation in this setting. Namely, we adapt the Thouless criterion of localisation to quantify the various mechanisms of localisation. We also employ a propagation matrix approach to prove a Saxon-Hutner type theorem ensuring the existence of band gaps for disordered systems and to predict the corresponding Lyapunov exponents. We further investigate the stabilities of bandgaps and localised eigenmodes with respect to fluctuations in the system by introducing a method of defect mode prediction based on the discrete Green function and illuminating the phenomena of Anderson localisation and level repulsion under global disorder.