**1. Introduction**

Terahertz electromagnetic wave is an attractive topic to researchers thanks to its broad application prospects in fields as diverse as biological imaging, materials science, and astrophysics [1]. However, the development of compact, high-power, broadly tunable terahertz sources is challenging [2, 3]. Compared with other kinds of terahertz sources, the free-electron driven sources, such as conventional vacuum electron devices (VEDs) [4] and free electron lasers (FELs) [5], can generate electromagnetic radiation with high power and desirable coherence. However, VEDs can hardly reach the frequency as high as 1 THz and FELs require tremendous costs and cumbersome peripheral equipment. The radiation sources based on the Smith– Purcell radiation (SPR) [6] can avoid the disadvantages of both VEDs and FELs, affording promising ways for developing compact terahertz sources [7–11].

Since its first experimental observation in 1953, Smith–Purcell radiation (SPR), which is generated when a uniformly moving electron beam passes over a periodic surface, has been an attractive research topic for its applications in radiation generation, beam acceleration and nondestructive particle diagnostics etc. [6, 12–15]. It is characterized by the following well-known dispersion relation:

$$
\lambda = -\frac{L}{n} \left( \frac{1}{\beta} - \cos \theta \right),
\tag{1}
$$

where λ is the radiation wavelength, θ the radiation direction, L the structural period, β the ratio of the beam velocity to the speed of light, and n a negative integer indicating the harmonic order.

Unfortunately, the efficiency of conventional SPR in practice is usually not high enough, which restricts the power and efficiency of the terahertz generating sources based on it [16]. Enhancing the efficiency of SPR will substantially improve the performances of the related terahertz sources. Developing new mechanisms or radiation schemes to improve the efficiency and power of SPR terahertz sources is the major goal of the present chapter, which is organized as follows. In Section 2, we will first introduce a unique kind of SPR, so-called Special Smith-Purcell Radiation (S-SPR), which can enhance the efficiency of SPR. And then several variants of S-SPR will be proposed and investigated. In Section 3, a kind of terahertz free-electron laser based on the mechanism of S-SPR will be illustrated, which can generate terahertz radiation with higher power than ordinary SPR devices. Section 4 concludes this chapter.
