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.

中文翻译：

---

时空调制媒体引起的频率转换

时空调制媒体是通过在时间和空间上周期性地调制媒体的参数来实现的。在本文中，我们研究了时空调制媒体引起的频率转换。从理论上和数值上论证了两种类型的频率转换。通过考虑Bloch模式的异常特性来解释其基本机制。我们发现第一类转换是由不同阶的Bloch模之间的能量传输引起的，当时空调制介质内的波被边界反射时，可以观察到这种转换。第二类是由于发生在时空调制介质内部的布拉格散射效应引起的。当外部波被时空调制介质反射时，可以观察到。频率可以上下转换，转换引起的差异取决于调制频率，该频率是可调的。因此，可以利用这些频率转换现象来为特定目的操纵波的频率。