Frequency conversion induced by time-space modulated media

Time-space modulated media are realized by periodically modulating parameters of the media in both time and space. In this paper, we study frequency conversion induced by time-space modulated media. Two types of frequency conversion are theoretically and numerically demonstrated; their underlying mechanisms are explained by considering the unusual properties of Bloch modes. We find that the first type of conversion is induced by energy transmission between different orders of Bloch modes, which can be observed when waves inside time-space modulated media are reflected by boundaries. The second type is caused by the Bragg scattering effect occurring inside time-space modulated media; it can be observed when external waves are reflected by time-space modulated media. The frequency can be up or down converted, and the difference caused by the conversion depends on the modulation frequency, which is tunable. Therefore, these frequency conversion phenomena could be exploited to manipulate waves' frequencies for particular purposes.