@article{antonakakis_asymptotics_2013,
	title = {Asymptotics for metamaterials and photonic crystals {Subject} {Areas} :},
	issn = {1364-5021},
	doi = {Artn 20120533\nDoi 10.1098/Rspa.2012.0533},
	abstract = {Metamaterial and photonic crystal structures are central to modern optics and are typically created from multiple elementary repeating cells.We demon- stratehowone 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 thatwe 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, aswell 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. 1.},
	number = {February},
	journal = {Proceedings of the royal society A},
	author = {Antonakakis, T and Craster, R V and Guenneau, S},
	year = {2013},
	pmid = {23633908},
	note = {ISBN: 1364-5021},
	keywords = {applied mathematics, wave motion},
}

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