The wire medium is an important example for a complex artificial electromagnetic material, consisting of metallic nanowires embedded in a non-dispersive, dielectric host medium. It has been explored for various applications, but it is also a prototypical metamaterial that supports a nonlocal optical response. With that, it can be considered as a main research theme for studies revolving around the homogenization of metamaterials. In the past, specific analytical models were derived for the effective properties of the wire medium that were equipped with phenomenologically introduced additional interface conditions. However, the phenomenological approach questions the uniqueness of the effective medium description, as other effective medium theories could capture the optical response equally well. To highlight such issues, we apply here a general purpose nonlocal homogenization theory equipped with rigorously derived additional interface conditions to homogenize a wire medium and compare it to a homogenization theory specifically derived for the wire medium. While the bulk properties can be mapped from one effective medium theory to the other, the interface conditions are different, which renders the models different as well. We discuss the implications of both models in situations where the unit cells are (a) much smaller or (b) only smaller than the operational wavelength.
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