Truncated Floquet–Bloch transform for computing the spectral properties of large finite systems of resonators

In subwavelength physics, a challenging problem is to characterise the spectral properties of finite systems of subwavelength resonators. In particular, it is important to identify localised modes as well as bandgaps and associated mobility edges. It was shown numerically that the truncated Floquet–Bloch transform can be used to characterise the spectral properties of finite periodic and some aperiodic large systems of resonators. In this paper, for the first time, the mathematical foundations of this transform are provided. In particular, it is proved that the truncated Floquet–Bloch transform enables an accurate recovery of the structure's bandgap and defect localised eigenmodes.