  This paper studies the theory and applications of the diffraction of
electromagnetic waves by space-time periodic (STP) diffraction gratings. We
show that, in contrast with conventional spatially periodic grating, a STP
diffraction grating produces spatial diffraction orders, each of which is
formed by an infinite set of temporal diffraction orders. Such spatiotemporally
periodic gratings are endowed with enhanced functionalities and exotic
characteristics, such as asymmetric diffraction pattern, nonreciprocal and
asymmetric transmission and reflection, and an enhanced diffraction efficiency.
The theory of the wave diffraction by STP gratings is formulated through
satisfying the conservation of both momentum and energy, and rigorous Floquet
mode analysis. Furthermore, the theoretical analysis of the structure is
supported by time and frequency domain FDTD numerical simulations for both
transmissive and reflective STP diffraction gratings. Additionally, we provide
the conditions for Bragg and Raman-Nath diffraction regimes for STP gratings.
Finally, as a particular example of a practical application of the STP
diffraction gratings to communication systems, we propose an original multiple
access communication system featuring full-duplex operation. STP diffraction
gratings are expected to find exotic practical applications in communication
systems, especially for the realization of enhanced-efficiency or full-duplex
beam coders, nonreciprocal beam splitters, nonreciprocal and
enhanced-resolution holograms, and illusion cloaks.
