2023/11/10 by Konstantinos Alexopoulos, Alexopoulos, Konstantinos, Bryn Davies +1
Engineering · Physics and Astronomy · #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Geophysics and Sensor Technology #Mathematical Physics (math-ph) #Mechanical and Optical Resonators #Optics (physics.optics) #Photorefractive and Nonlinear Optics
paper · pdf · doi:10.48550/arxiv.2311.05998
openalex publication_date 2023/11/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
This work extends the theory of topological protection to dispersive systems. This theory has emerged from the field of topological insulators and has been established for continuum models in both classical and quantum settings. It predicts the existence of localised interface modes based on associated topological indices and shows that, when such modes exist, they benefit from enhanced robustness with respect to imperfections. This makes topologically protected modes an ideal starting point for building wave guiding devices. However, in many practical applications such as optics or locally resonant meta-structures, materials are dispersive in the operating frequency range. In this case, the associated spectral theory is less straightforward. This work shows that the existing theory of topological protection can be extended to dispersive settings. We consider time-harmonic waves in one-dimensional systems with no damping.