Kapitza homogenization of deep gratings for designing dielectric metamaterials

TL;DR

This paper explores how rapid, deep dielectric modulations in gratings can be used to engineer the effective dielectric response of metamaterials, enabling novel design strategies such as metal-to-dielectric transitions.

Contribution

It introduces a Kapitza homogenization approach that accounts for fast dielectric modulations, providing a new method for designing dielectric metamaterials with tailored properties.

Findings

Effective dielectric permittivity includes a new contribution from rapid modulation.

Kapitza effect enables control over dielectric properties, including metal-to-dielectric transitions.

Deep gratings can be used to engineer metamaterials with desired electromagnetic responses.

Abstract

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.