Fig. 1. High-energy photon radiation source based on microwave dielectric undulator. (a) Interaction between a dielectric nanopillar array and a resonant cavity (purple square box) with a microwave standing wave (green wavefront) polarized along the $y$-axis with an amplitude of $80\mathrm{MV}/\mathrm{m}$ is depicted in panel (b), which produces a periodic transverse near-field as shown in panel (b). Panel (c) is the detailed view of panel (b), which shows that the nanopillar array generates a polarization field, with the effect of microwaves, and the white arrows show the electric field lines around the periodic near-field channel. (d) Schematic showing the electrons oscillating and generating radiation in this structure.

Fig. 2. (a) Dependence of electron radiation on azimuthal angle $\theta$ for electron energies of 1 and 10 MeV. (b)–(c) Dependence of electron kinetic energy on radiation photon energy with a undulator period of 50 nm. The orange dash line in panel (c) is the energy of photons with a wavelength of 50 nm, which means only the high kinetic energy electrons with a speed higher than 0.5c have the frequency upconversion effect. The purple dash-dot lines of panels (b) and (c) show the energy thresholds of ultraviolet (UV), extreme ultraviolet radiation (EUV), hard X-ray, and $\gamma$-ray.

Fig. 3. (a) Radiation spectra of single 1, 3, and 6 MeV electrons in the device at $\theta =0$. (b) Amplification of the 1 MeV electron radiation spectrum in panel (a).

Fig. 4. (a) Radiation spectra of single 10, 15, and 20 MeV electrons in the device at $\theta =0$. (b) Amplification of the 10 MeV electron radiation spectrum in panel (a).

Fig. 5. Relationship between the electron radiation intensity and the radius of the dielectric nanopillar. The green line is the analytical solution, and the blue dot is the simulation result. The radius of the dielectric nanopillar mainly affects the intensity and range of the near-field effect on the electron. When the radius of the nanopillar is too small, the near-field effect on the electron will be very weak, which greatly reduces the radiation intensity and makes it more susceptible to the noise field. For practical operation, the best scheme is to make the radius of the dielectric nanopillar account for more than 40% of the array period.

Fig. 6. Schematic diagram of using wavefront tilted laser to generate the quasi-static periodic near-field. The red thin arrows are the wavefronts of laser beams. The tilted wavefront is used to match the laser phase velocity with the longitudinal velocity of the electrons, thereby maintaining a local quasi-static electric field around the electron beam.

Fig. 7. Parameter comparison between this model (red dot with a green square frame) and structures in several typical references. The red dots represent the parameters of the dielectric-based undulators,^13,28 and the black squares represent the parameters of the plasma-based undulators.