Effective Maxwell’s Equations for Perfectly Conducting Split Ring Resonators | Zendy

Robert Lipton | Zendy; Ben Schweizer | Zendy

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Effective Maxwell’s Equations for Perfectly Conducting Split Ring Resonators

Author(s) -

Robert Lipton,

Ben Schweizer

Publication year - 2018

Publication title -

archive for rational mechanics and analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 2.933

H-Index - 106

eISSN - 1432-0673

pISSN - 0003-9527

DOI - 10.1007/s00205-018-1237-1

Subject(s) - maxwell's equations , homogenization (climate) , resonator , electromagnetism , mathematical analysis , physics , limit (mathematics) , nonlinear system , metamaterial , mathematics , classical mechanics , quantum mechanics , optics , biodiversity , ecology , biology

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 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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