We have derived simple analytical expressions for the frequency-dependent effective permittivity tensor of a one-dimensional metal-dielectric photonic crystal in the long wavelength limit. Our results describe the transition between the regime described by Rytov's formulas and that predicted by Xu et al [5], where the effective plasma frequency is independent of the metallic-layer parameters. The derived expressions can be useful for determining the frequency intervals where such an anisotropic system can exhibit metamaterial behavior.
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10., "An explicit expression for T=-1 (G) has been derived in Ref. [9] (see Eqs. (33){(37) therein),".
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doi:10.1134/S0021364009210073
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