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Resonance and Double Negative Behavior in Metamaterials

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Abstract

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.

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Authors and Affiliations

  1. Department of Mathematics, University of Kentucky, Lexington, KY, 40506, USA

    Yue Chen

  2. Department of Mathematics, Louisiana State University, Baton Rouge, LA, 70803, USA

    Robert Lipton

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  1. Yue Chen
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  2. Robert Lipton
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Correspondence to Robert Lipton.

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Communicated by C. Dafermos

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Chen, Y., Lipton, R. Resonance and Double Negative Behavior in Metamaterials. Arch Rational Mech Anal 209, 835–868 (2013). https://doi.org/10.1007/s00205-013-0634-8

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  • DOI: https://doi.org/10.1007/s00205-013-0634-8

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