@article{d00c7453d33a422284c6fe9c513dbca1, title = "PLASMON RESONANCE WITH FINITE FREQUENCIES: A VALIDATION OF THE QUASI-STATIC APPROXIMATION FOR DIAMETRICALLY SMALL INCLUSIONS", abstract = "We study resonance for the Helmholtz equation with a finite frequency in a plasmonic material of negative dielectric constant in two and three dimensions. We show that the quasi-static approximation is valid for diametrically small inclusions. In fact, we quantitatively prove that if the diameter of an inclusion is small compared to the loss parameter, then resonance occurs exactly at eigenvalues of the Neumann{Poincare operator associated with the inclusion. {\textcopyright} 2016 Society for Industrial and Applied Mathematics", keywords = "eigenvalues, finite frequency, Helmholtz equation, Neumann-Poincar{\'e} operator, plasmon resonance, quasi-static limit", author = "KAZUNORI ANDO and HYEONBAE KANG and HONGYU LIU", year = "2016", doi = "10.1137/15M1025943", language = "English", volume = "76", pages = "731--749", journal = "SIAM Journal on Applied Mathematics", issn = "0036-1399", publisher = "Society for Industrial and Applied Mathematics", number = "2", }