Asymptotics for metamaterials and photonic crystals.
- Antonakakis T Department of Mathematics , Imperial College London , London SW7 2AZ, UK ; European Organization for Nuclear Research , CERN 1211 , Geneva 23, Switzerland.
- Craster RV
- Guenneau S
- 2013-05-02
Published in:
- Proceedings. Mathematical, physical, and engineering sciences. - 2013
English
Metamaterial and photonic crystal structures are central to modern optics and are typically created from multiple elementary repeating cells. We demonstrate how one replaces such structures asymptotically by a continuum, and therefore by a set of equations, that captures the behaviour of potentially high-frequency waves propagating through a periodic medium. The high-frequency homogenization that we use recovers the classical homogenization coefficients in the low-frequency long-wavelength limit. The theory is specifically developed in electromagnetics for two-dimensional square lattices where every cell contains an arbitrary hole with Neumann boundary conditions at its surface and implemented numerically for cylinders and split-ring resonators. Illustrative numerical examples include lensing via all-angle negative refraction, as well as omni-directive antenna, endoscope and cloaking effects. We also highlight the importance of choosing the correct Brillouin zone and the potential of missing interesting physical effects depending upon the path chosen.
- Language
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- English
- Open access status
- hybrid
- Identifiers
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- DOI 10.1098/rspa.2012.0533
- PMID 23633908
- Persistent URL
- https://sonar.ch/global/documents/260130
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