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Truncated Floquet-Bloch transform for computing the spectral properties of large finite systems of resonators
(2024)SAM Research ReportThis paper aims at providing for the first time the mathematical foundations of the truncated Floquet-Bloch transform, which can be used to characterise the spectral properties of finite periodic and aperiodic large systems of resonators.Report -
Nonlinear subwavelength resonances in three dimensions
(2024)SAM Research ReportIn this paper, we consider the resonance problem for the cubic nonlinear Helmholtz equation in the subwavelength regime. We derive a discrete model for approximating the subwavelength resonances of finite systems of high-contrast resonators with Kerr-type nonlinearities. Our discrete formulation is valid in both weak and strong nonlinear regimes. Compared to the linear formulation, it characterizes the soliton-like extra eigenmodes that ...Report -
Exponentially localised interface eigenmodes in finite chains of resonators
(2024)SAM Research ReportThis paper studies wave localisation in chains of finitely many resonators. There is an extensive theory predicting the existence of localised modes induced by defects in infinitely periodic systems. This work extends these principles to finite-sized systems. We consider finite systems of subwavelength resonators arranged in dimers that have a geometric defect in the structure. This is a classical wave analogue of the Su-Schrieffer-Heeger ...Report