In this paper, we study the behaviour of the coupled subwavelength resonant modes when two high-contrast acoustic resonators are brought close together. We consider the case of spherical resonators and use bispherical coordinates to derive explicit representations for the capacitance coefficients which, we show, capture the system's resonant behaviour at leading order. We prove that the pair of resonators has two subwavelength resonant ...

We survey functional analytic methods for studying subwavelength resonator systems. In particular, rigorous discrete approximations of Helmholtz scattering problems are derived in an asymptotic subwavelength regime. This is achieved by re-framing the Helmholtz equation as a non-linear eigenvalue problem in terms of integral operators. In the subwavelength limit, resonant states are described by the eigenstates of the generalized capacitance ...

This paper shows that the skin effect in systems of non-Hermitian subwavelength resonators is robust with respect to random imperfections in the system. The subwavelength resonators are highly contrasting material inclusions that resonate in a low-frequency regime. The non-Hermiticity is due to the introduction of an imaginary gauge potential, which leads to a skin effect that is manifested by the system's eigenmodes accumulating at one ...

We show that resonant frequencies of a system of coupled resonators in a truncated periodic lattice converge to the essential spectrum of corresponding infinite lattice. We use the capacitance matrix as a model for fully coupled resonators with long-range interactions in three spatial dimensions. For one-, two- or three-dimensional lattices embedded in three-dimensional space, we show that the (discrete) density of states for the finite ...

Robustly manipulating waves on subwavelength scales can be achieved by, firstly, designing a structure with a subwavelength band gap and, secondly, introducing a defect so that localized modes fall within the band gap. We study a one-dimensional array of subwavelength resonators, prove that there is a subwavelength band gap, and show that by introducing a dislocation we can place localized modes at any point within the band gap. We ...