  This 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 model. We prove
the existence of a spectral gap for defectless finite dimer structures and find
a direct relationship between eigenvalues being within the spectral gap and the
localisation of their associated eigenmode. Then we show the existence and
uniqueness of an eigenvalue in the gap in the defect structure, proving the
existence of a unique localised interface mode. To the best of our knowledge,
our method, based on Chebyshev polynomials, is the first to characterise
quantitatively the localised interface modes in systems of finitely many
resonators.
