Abstract
We consider a simplified model of a nonlinear magnetic metamaterial, consisting of a weakly-coupled, periodic split-ring resonator (SRR) array capable of nonlinear capacitive response. We analyze three related problems: (a) The calculation of localized modes around simple magnetoinductive impurities located at the surface or at the bulk of the array, in closed form for both, linear and nonlinear cases. (b) The scattering of magnetoinductive waves across internal (external) capacitive (inductive) defects coupled to the SRR array and the occurrence of Fano resonances, and how to tune them by changing the external parameters of the system. (c) Description of a method for building a stable localized magnetoinductive mode embedded in the linear band of extended states.
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Notes
- 1.
In the presence of dissipation, a term of the form \(i \gamma \Omega\) enters Eq. (3). For a complex wavevector \(k=k_{r}-i k_{i}\), with \(|k_{i}|\ll |k_{r}|\), one obtains \(\Omega^{2}\approx (1+\sum\nolimits_{n m} \lambda_{n m} \cos(m k_{r}))^{-1}\) and \(k_{i}\approx \gamma ( 1+\sum\nolimits_{n m} \lambda_{n m} \cos(m k_{r}))^{1/2}/\sum\nolimits_{m} \lambda_{n m} \sin(m k_{r})\). Neglect of dissipation effects is valid provided \(|k_{i}| L\ll 1\).
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Acknowledgments
This work was supported by Fondecyt (Grant 1080374), Programa ICM P10-030-F, and Programa de Financiamiento Basal de Conicyt (Grant FB0824/2008).
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Molina, M.I. (2012). Defect Modes, Fano Resonances and Embedded States in Magnetic Metamaterials. In: Malomed, B. (eds) Spontaneous Symmetry Breaking, Self-Trapping, and Josephson Oscillations. Progress in Optical Science and Photonics, vol 1. Springer, Berlin, Heidelberg. https://doi.org/10.1007/10091_2012_15
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DOI: https://doi.org/10.1007/10091_2012_15
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