Fig. 1. (a) Schematic of CR. An electron passes through a dielectric medium at a speed (v) greater than the phase velocity of light (c/n)^[20]; (b) schematic of SPR. The evanescent field surrounding the electron is scattered into free space by a periodic grating^[45].

Fig. 2. (a) Diagram of wave-vector matching for CR generation in the isotropic material. Fast electrons (e^–) (dashed green arrow) can satisfy the wave-vector matching condition with two photonic states k₊ and k_– in the considered plane, and thereby emit CR. In contrast, slow electrons (solid red arrow) can not excite photonic states to satisfy the matching condition; (b) diagram of wave-vector matching for CR generation in the hyperbolic metamaterial. Slow electrons (solid red arrow) can emit CR; (c) hyperbolic metamaterial formed by a stack of metal and dielectric slabs. Reproduced from Ref. [48] with k_x and k_y redefined in (a), (b) and the coordinates marked in (c).

Fig. 3. (a) Schematic of the integrated CR emitter and scanning electron microscopy images. The planar Mo electrodes is on the top surface of the emitter. The hyperbolic metamaterial in the middle is formed by alternating Au and SiO₂ films. The plasmonic nanoslits under the emitter are used to couple the CR in the hyperbolic metamaterial to free space; (b) numerical simulation of CR (electric field E_z) with electron energy of 0.1 keV when λ₀ = 800 nm; (c) optical output power of the chip with cathode-anode voltage V_ca varying from 0.25 to 1.4 kV; (d) spectra of output light with different plasmonic nanoslit period of P_slit. Extracted from Ref. [49]

Fig. 4. (a) Measured surface plasmon resonance for various materials across the electromagnetic spectrum from terahertz to EUV; (b) schematic showing the k-EELS technique for measuring the photonic band structure of silicon; (c) the photonic band structure of 60 nm thick silicon films. It shows evidence of the SP of silicon in the EUV; (d) schematic of thresholdless CR in the EUV excited in a hyperbolic metamaterial composed of Si and SiO₂ multilayer stack. Extracted from Ref. [53].

Fig. 5. (a) Schematic of the experimental configuration used to demonstrate backward CR and the photographic image of the negative index metamaterials; (b) the top and side view of the negative index metamaterials; (c) spectra of the radiation power in each angle in the negative band (solid line) and positive band (dashed line). (a) is extracted from Ref. [69]. (b), (c) are extracted from Ref. [68].

Fig. 6. (a) Schematic diagram of the constructed structure interacting with a single sheet electron beam bunch travelling along the +z direction; (b) dispersion curves characterized by frequency versus phase advance. The dispersion curve of the negative metamaterial is obtained by model calculation and high frequency structure simulator (HFSS) simulation; (c) measured power spectral densities of the reversed Cherenkov radiation and its reflection signals at ports 2 and 1. Extracted from Ref. [70] with “Ports 2” and “Port 1” marked in (a).

Fig. 7. (a), (b) Fano-enhanced metallic metamaterials consisting of subwavelength slits with two different structural asymmetries; (c), (d) transmission results with different angles of incidence and structural asymmetries. The four sharp dips represent the excitation of the Fano resonance by capturing the p-polarized incident wave. Extracted from Ref. [77].

Fig. 8. (a) Schematic of free electrons flying over a silicon-on-insulator grating; (b) emission probability at a given frequency for different electron velocities, and strongly enhanced SPR near the BIC; (c) schematic of the normal impinging of a propagating plane wave upon a double silicon grating; (d) specular reflection coefficient R as a function of normalized frequency. Inset: the profile of |H_y| at resonant frequency. (e) Q factor at f_R as a function of the distance h. (a), (b) are extracted from Ref. [79]. (c)−(e) are extracted from Ref. [78].

Fig. 9. (a) Schematic of the SPR produced by the interaction of free electrons and a Babinet metasurface. The uniform sheet of free electrons moves closely parallel to the metasurface along the +x axis; (b), (c) the structures of C-aperture and C-ring metasurfaces, and the electric field distributions of SPR generated via the interaction with free electrons. Extracted from Ref. [93].

Fig. 10. (a) Schematic of SPR mediated by graphene metasurfaces; (b) dependence of the SPR amplitude and phase on the width of the graphene ribbons; (c) dependence of the SPR phase on the displacement of a graphene ribbon in its unit cell for the second-order SPR; (d) dependence of the amplitude and phase of electric field E_x and E_y on the rotating angle of rectangular graphene patches. Extracted from Ref. [95].