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Effective Maxwell’s Equations for Perfectly Conducting Split Ring Resonators

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Abstract

We analyze the time harmonic Maxwell’s equations in a geometry containing perfectly conducting split rings. We derive the homogenization limit in which the typical size η of the rings tends to zero. The split rings act as resonators and the assembly can act, effectively, as a magnetically active material. The frequency dependent effective permeability of the medium can be large and/or negative.

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Authors and Affiliations

  1. Department of Mathematics, Louisiana State University, 384 Lockett Hall, Baton Rouge, USA

    Robert Lipton

  2. Fakultät für Mathematik, TU Dortmund, Vogelpothsweg 87, 44227, Dortmund, Germany

    Ben Schweizer

Authors
  1. Robert Lipton
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  2. Ben Schweizer
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Correspondence to Ben Schweizer.

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Communicated by G. Friesecke

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Lipton, R., Schweizer, B. Effective Maxwell’s Equations for Perfectly Conducting Split Ring Resonators. Arch Rational Mech Anal 229, 1197–1221 (2018). https://doi.org/10.1007/s00205-018-1237-1

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  • DOI: https://doi.org/10.1007/s00205-018-1237-1

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