A general relation is derived between the band structure of an arbitrary low-loss unit cell and its effective index of refraction. In addition, we determine the maximum unit cell size that defines the "metamaterial regime" [D. R. Smith et al., Phys. Rev. E 71, 036617 (2005)]. Furthermore, these general rules allow for the design of a subwavelength near-infrared negative-index material, where the negative refractive index is verified by band calculations to be a bulk property. Full-wavelength simulations of prisms consisting of these unit cells suggest behavior consistent with Snell's law in the negative-index regime.
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Zhang et al. (2008) studied this question.
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