Studies in Applied Mathematics

Journal: Studies in Applied Mathematics

Stud. appl. math. (Cambr.)

Wiley-Blackwell

0022-2526
1467-9590

Publications 1 - 2 of 2

Optical soliton bullets in (2+1)D nonlinear Bragg resonant periodic geometries
Dohnal, Tomáš; Aceves, Alejandro B. (2005)
Studies in Applied Mathematics
Exponentially localized interface eigenmodes in finite chains of resonators
Ammari, Habib; Barandun, Silvio Alberto; Davies, Bryn; et al. (2024)
Studies in Applied Mathematics
This paper studies wave localization in chains of finitely many resonators. There is an extensive theory predicting the existence of localized modes induced by defects in infinitely periodic systems. This work extends these principles to finite-sized systems. We consider one-dimensional, finite systems of subwavelength resonators arranged in dimers that have a geometric defect in the structure. This is a classical wave analog 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 localization of their associated eigenmode. Then, for sufficiently large-size systems, we show the existence and uniqueness of an eigenvalue in the gap in the defect structure, proving the existence of a unique localized interface mode. To the best of our knowledge, our method, based on Chebyshev polynomials, is the first to characterize quantitatively the localized interface modes in systems of finitely many resonators.

Publications 1 - 2 of 2