## Spatial dispersion and effective constitutive parameters of electromagnetic metamaterials

#### Gennady ShvetsUniversity of Texas at Austin

A current-driven extraction (CDE) approach to calculating all $36$ linear constitutive parameters of a metamaterial crystal is presented. Spatial dispersion is accounted for by evaluating the constitutive parameters as a function of frequency and wavenumber. For two-dimensional centrosymmetric crystals spatial dispersion is shown to result in bianisotropy. The accuracy of the CDE constitutive parameters is verified by comparing the radiation efficiencies of a simple directional antenna embedded inside the homogenized and un-homogenized metamaterial slabs.

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