# Generalized Space-Time Periodic Diffraction Gratings: Theory and Applications

## TL;DR

This paper develops a comprehensive theory for space-time periodic diffraction gratings, revealing their unique properties and potential applications in advanced communication systems and nonreciprocal devices.

## Contribution

It introduces a novel theoretical framework for STP diffraction gratings, including rigorous analysis and numerical validation, and proposes a practical full-duplex communication system utilizing these gratings.

## Key findings

- STP gratings produce infinite sets of temporal diffraction orders for each spatial order.
- Theoretical analysis aligns with FDTD simulations for transmissive and reflective gratings.
- Conditions for Bragg and Raman-Nath diffraction regimes in STP gratings are established.

## Abstract

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.