Dynamical modeling of terahertz Smith–Purcell radiation via the current-transient approach in hexagonal metasurfaces

While terahertz (THz) technologies have shown great promise in applications such as radar, remote sensing, homeland security, medical imaging, and high-speed communications, their practical use has been hindered by the lack of high-performance THz sources. THz sources based on Smith–Purcell radiation have gained significant attention due to their tunable frequencies and wide-angle radiation characteristics within the electron-skimming plane. The ability to modulate terahertz beam width is crucial for radar stealth applications. However, THz sources utilizing one-dimensional gratings from Smith–Purcell radiation are unable to adjust the beam width in the plane perpendicular to the electron-skimming plane. To address this limitation, we introduce a two-dimensional hexagonally patterned grating designed to generate THz radiation through Smith–Purcell mechanisms, which exhibits a dynamically adjustable beam width in the elevation plane, facilitating optimized grazing-incidence electron-beam excitation at a velocity of 0.6c. Compared to ordinary gratings, square structures, and circular structures, the hexagonal structure produces a narrower beam width. In addition, we propose a current transient model to elucidate the Smith–Purcell radiation mechanism in two-dimensional periodic structures, providing a theoretical framework for understanding the radiation properties of these sources and offering accurate predictions for designing advanced device structures.