Angle-resolved multimode engineering in spacetime crystals

Spatiotemporally varying media, which simultaneously modulating both in space and time, offer a versatile platform for dynamic control of electromagnetic waves. The multimode properties of such media are crucial for applications in quantum simulation, large-scale optical computing, and high-capacity communication systems. Here, we present a reconfigurable approach for applying spatiotemporal electromagnetic modulation in a substrate-integrated waveguide (SIW), enabling the resolution and engineering of multiple modes in spacetime crystals (STCs). We begin by demonstrating the diffraction of Floquet modes in a time crystal, analogous to a time grating. By superimposing spatial modulation, we impart additional momentum to these modes, allowing the Floquet modes to radiate into free space at distinct, angle-resolved directions. Furthermore, by incorporating multicolor spatiotemporal modulation, we achieve precise control over the Floquet-Bloch modes, facilitating multi-user video distribution. Our approach paves the way for the engineering of multiple Floquet-Bloch modes in STCs, offering promising prospects for quantum simulation, optical computing, and next-generation wireless communications.