Split-ring resonators and localized modes

Physics

Scientific paper

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Vibrations And Mechanical Waves, Photonic Bandgap Materials, Structural Acoustics And Vibration, Mechanical And Elastic Waves, Vibrations

Scientific paper

The paper presents asymptotic analysis of an eigenvalue problem for the Helmholtz operator in a periodic structure involving split-ring resonators [

originally proposed in J. B. Pendry et al., IEEE Trans. Microwave Theory Tech. 47, 2075 (1999)
]. The eigensolutions are sought in the form of Bloch waves. The main emphasis is given to the study of localized modes within such a structure and to the control of low-frequency bandgaps on the corresponding dispersion diagram. Asymptotic results are explicit and are in good agreement with numerical simulations.

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