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We consider multilayered metal-dielectric metamaterials composed of alternating nanolayers of two types and calculate the components of their effective dielectric permittivity tensors as functions of both frequency and wave vector. We demonstrate that such structures can be described as strongly nonlocal uniaxial effective media, and we analyze how the nonlocal permittivity tensor components are related to other manifestations of strong spatial dispersion in such structures, and how the resonance of permittivity depends on the propagation direction.
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