Homogenization Theory of Space-Time Metamaterials

The theory of homogenization of material parameters has been a cornerstone in the development of metamaterials. The conventional framework, however, is not applicable to the $s{{0}{0ex}}p{{0}{0ex}}a{{0}{0ex}}t{{0}{0ex}}i{{0}{0ex}}o{{0}{0ex}}t{{0}{0ex}}e{{0}{0ex}}m{{0}{0ex}}p{{0}{0ex}}o{{0}{0ex}}r{{0}{0ex}}a{{0}{0ex}}l$ metamaterials that give access to additional wave phenomena, thanks to properties tailored not only in space but also in time. This study presents an analytic framework for the homogenization theory of space-time metamaterials, and yields physical insight into their behavior, including regimes of nonreciprocity and conditions for huge effective bianisotropy. This approach also deepens our understanding of the connections between space-time modulations and moving matter.