Space-time modulated loaded-wire metagratings for magnetless nonreciprocity and near-complete frequency conversion

In recent years, significant progress has been made in the development of magnet-less nonreciprocity using space-time modulation, both in electromagnetics and acoustics. This approach has so far resulted in a plethora of non-reciprocal devices, such as isolators and circulators, over different parts of the spectrum, for guided waves. On the other hand, very little work has been performed on non-reciprocal devices for waves propagating in free space, which can also have many practical applications. For example, it was shown theoretically that non-reciprocal scattering by a metasurface can be obtained if the surface-impedance operator is continuously modulated in space and time. However, the main challenge in the realization of such a metasurface is due to the high complexity required to modulate in space and time many sub-wavelength unit-cells of which the metasurface consists. In this paper, we show that spatiotemporally modulated metagratings can lead to strong nonreciprocal responses, even though they are based on electrically-large unit cells and use only three modulation domains. We specifically focus on wire metagratings loaded with time-modulated capacitances. We use the discrete-dipole approximation and an ad-hoc generalization of the theory of polarizability for time-modulated particles and demonstrate an effective non-reciprocal anomalous reflection (diffraction) with an efficient frequency conversion. Thus, our work opens a venue for a practical design and implementation of highly non-reciprocal magnet-less metasurfaces in electromagnetics and acoustics.