A generic class of metamaterials is introduced and is shown to exhibit frequency dependent double negative effective properties. We develop a rigorous method for calculating the frequency intervals where either double negative or double positive effective properties appear and show how these intervals imply the existence of propagating Bloch waves inside sub-wavelength structures. The branches of the dispersion relation associated with Bloch modes are shown to be explicitly determined by the Dirichlet spectrum of the high dielectric phase and the generalized electrostatic spectra of the complement. © 2013 Springer-Verlag Berlin Heidelberg.
Publication Source (Journal or Book title)
Archive for Rational Mechanics and Analysis
Chen, Y., & Lipton, R. (2013). Resonance and Double Negative Behavior in Metamaterials. Archive for Rational Mechanics and Analysis, 209 (3), 835-868. https://doi.org/10.1007/s00205-013-0634-8