Photonic Time Crystals and Time-Varying Electromagnetic Metamatter: A New Direction for Ultrafast Tunable Photonic and Microwave Materials and Devices.

Spatial control of materials properties through nanostructuring and hierarchical design is an important on-going area of materials research. Controlling physical properties in time represents a new direction to further advance the frontiers of functional materials and devices with particular attention to matter-radiation interactions. Such time-varying crystals and dynamic heterogeneous media can interact with radiation in an unexpected manner, resulting in emergent properties that have no static counterpart. Here, we briefly discuss theoretical and analytical techniques used to understand time-varying electromagnetic materials and highlight novel phenomena in these systems. Further, we examine the state-of-the-art numerical modeling tools and design techniques for photonic time crystals and time-varying metamaterials and highlight the need for continued efforts to develop these tools. Representative examples from experimental studies on thin films, 2D materials, and mesoscale composites that are essential building blocks for time metamatter are then reviewed toward high-speed modulation of optical constants. Finally, we discuss outstanding materials challenges in this emerging field and point out that collaborative cross-disciplinary research is needed to better understand photon interactions with electrons, spin order, and the lattice.