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In this paper we develop homogenization theory for spatiotemporally modulatedwire medium. We first solve for the modal waves that are supported by thiscomposite medium, we show peculiar properties such as extraordinary waves thatpropagate at frequencies below the cut-off frequency of the correspondingstationary medium. We explain how these unique solutions give rise to anextreme Fresnel drag that exists already with weak and slow spatiotemporalmodulation. Next, we turn to derive the effective material permittivity thatcorresponds to each of the first few supported modes, and write the averagefields and Poynting's vector. Nonlocality, nonreciprocity, and anisotropy dueto the spatiotemporal modulation direction, are three inherent properties ofthis medium, and are clearly seen in the effective material parameters. As afigure of merit, we also derive the effective permittivity of a plasma mediumwith spatiotemporally modulated plasma frequency. This comparison isinteresting since the plasma medium can be considered as the effective mediumthat is obtained by a stationary wire medium. We validate that homogenizationand spatiotemporal variation are not necessarily interchangeable operations.And indeed, in certain parameter regimes the homogenization should be performeddirectly on spatiotemporally modulated composite medium, rather than firsthomogenize the stationary medium and then phenomenologically introduce theeffect of the space-time modulation.

Wave Analysis and Homogenization of Spatiotemporally Modulated Wire Medium