2025/05/28 by Yan-Long Fang, Jeffrey Galkowski, Fang, Yan-Long +1
Engineering · Materials Science · Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Metamaterials and Metasurfaces Applications #Optics (physics.optics) #Plasmonic and Surface Plasmon Research #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.2505.22253
openalex publication_date 2025/05/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study scattering by metamaterials with negative indices of refraction, which are known to support surface plasmons -- long-lived states that are highly localized at the boundary of the cavity. This type of states has found uses in a variety of modern technologies. In this article, we study surface plasmons in the setting of non-trapping cavities; i.e. when all billiard trajectories outside the cavity escape to infinity. We characterize the indices of refraction which support surface plasmons, show that the corresponding resonances lie super-polynomially close to the real axis, describe the localization properties of the corresponding resonant states, and give an asymptotic formula for their number.