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Kapitza homogenization of deep gratings for designing dielectric metamaterials

We theoretically investigate the homogenization of the dielectric response to transverse electric waves of a transverse grating characterized by the Kapitza condition, i.e. the permittivity is rapidly modulated with a modulation depth scaling as the large wavelength to modulation period ratio. We show that the resulting effective dielectric permittivity, in addition to the standard average of the underlying dielectric profile, has a further contribution arising from the fast and deep dielectric modulation. Such contribution turns out to be comparable with the other one and hence can provide an additional way for designing dielectric metamaterials. As an example, we discuss an effective metal-to-dielectric transition produced by the Kapitza contribution obtained by changing the grating depth.