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Archive for Rational Mechanics and Analysis

, Volume 229, Issue 3, pp 1197–1221 | Cite as

Effective Maxwell’s Equations for Perfectly Conducting Split Ring Resonators

  • Robert Lipton
  • Ben Schweizer
Article

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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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsLouisiana State UniversityBaton RougeUSA
  2. 2.Fakultät für MathematikTU DortmundDortmundGermany

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