Abstract

Artificial periodic structures (metamaterials and photonic crystals) with feature sizes smaller than the wavelength can be capable of supporting backward waves and producing negative refraction. However, backward waves may only exist if the lattice cell size is a sufficiently large fraction of the vacuum wavelength and/or the Bloch wavelength. Explicit lower bounds for the cell size are established and imply, in particular, a limit on the optical resolution of negative-index lenses. A key tool in the analysis is Fourier decomposition of Bloch waves and related eigenfrequency estimates. Numerical examples and a detailed exposition of the mechanism of backward waves are included.

© 2008 Optical Society of America

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