Metamaterials, which enable us to realize novel physical effects that cannot be achieved using natural materials, have been extensively studied in recent years and significant progress has been made, especially in the field of optics. This game-changing concept has also initiated a rich variety of research activity in vacuum electronics. Here we review the recent development of metamaterial-based vacuum electronics for terahertz (THz) and microwave science and technology. The reversed Cherenkov radiation (RCR) in double-negative (DNG) metamaterials predicted by Veselago back in the 1960s has been experimentally verified in the microwave frequency range by utilizing specially designed DNG metamaterials. The interaction of an electron beam (e-beam) with DNG metamaterials may lead to the realization of novel applications such as microwave and THz radiation sources, accelerators, and even the visualization of invisibility cloaks. Smith–Purcell radiation (SPR) has recently received renewed interest owing to the development of metamaterials and the concept of spoof surface plasmon polaritons, as discussed in this review, and recent results on e-beam-induced directional and wide-band THz radiation with sharp multiple peaks from a graded grating, as well as directional and monochromatic special SPR and their possible application to THz orotron devices, are also reviewed.

A Brief Review on Metamaterial-Based Vacuum Electronics for Terahertz and Microwave Science and Technology

The reversed Cherenkov radiation is one of the most attractive research topics because of its unique characteristics and promising applications. It was generally believed that reversed Cherenkov radiations exist only in left-handed metamaterials (double negative mediums). In the present paper, we demonstrated that they can also be generated on plasmonic thin-films. Reversed Cherenkov radiations in the terahertz region and in the visible light region were achieved on the metamaterial thin-film and the metal thin-film, respectively. Their radiation frequencies and directions, which are interdependent with each other, are controllable. For the normal Cherenkov radiation, the wavelength on the thin-film increases with the frequency; whereas for the reversed Cherenkov radiation, the opposite is true. Theoretical analyses and simulations revealed that the normal or reversed Cherenkov radiation is generated depending on whether the forward or backward surface modes are excited on the plasmonic thin-film. Requirements of these reversed Cherenkov radiations were found out.

Two-dimensional reversed Cherenkov radiation on plasmonic thin-film.

We present an analysis of a Cherenkov free-electron laser based on a single slab made from negative-index materials. In this system, a flat electron beam with finite thickness travelling close to the surface of the slab interacts with the copropagating electromagnetic surface mode. The dispersion equation for a finitely thick slab is worked out and solved numerically to study the dispersion relation of surface modes supported by negative-index materials, and the calculations are in good agreement with the simulation results from a finite difference time domain code. We find that under suitable conditions there is inherent feedback in such a scheme due to the characteristics of negative-index materials, which means that the system can oscillate without external reflectors when the beam current exceeds a threshold value, i.e., start current. Using the hydrodynamic approach, we setup coupled equations for this system, and solve these equations analytically in the small signal regime to obtain formulas for the spatial growth rate and start current.

Dispersion, spatial growth rate, and start current of a Cherenkov free-electron laser with negative-index material

If the speed of the electron beam excited Surface Plasmon Polaritons (SPPs) exceeds the velocity of light in medium, Cherenkov radiation will be emitted. Here, on this important physical phenomenon, Surface Polariton Cherenkov Light Radiation Source (SPCLS), the quantum theory has been worked out. By this theory, the average field amplitude in SPCLS is obtained. The calculation results show that the quantum theory can explain the classical phenomena precisely and predict nonclassical excitation channels of photons that are based on the quantum nature of the electromagnetic field and the effect of SPPs. These excitation channels can be used to shorten the response time of Cherenkov detectors. The quantum theory also shows that SPCLS has a different fluctuation pattern compared with the ordinary electromagnetic systems where vacuum fluctuation dominates. The fluctuation pattern has two significant characteristics: first, the fluctuation of SPCLS will not vanish in the macroscopic case, which may draw theoretical and experimental interest; second, the fluctuation of SPCLS can be tuned by the velocity of the electron beam. Thus, the fluctuation of SPCLS can be used to enhance the radiation through stochastic resonance. Our investigation shows that important phenomena may be found out with the introduction of quantum theory in macroscopic electromagnetic problems.If the speed of the electron beam excited Surface Plasmon Polaritons (SPPs) exceeds the velocity of light in medium, Cherenkov radiation will be emitted. Here, on this important physical phenomenon, Surface Polariton Cherenkov Light Radiation Source (SPCLS), the quantum theory has been worked out. By this theory, the average field amplitude in SPCLS is obtained. The calculation results show that the quantum theory can explain the classical phenomena precisely and predict nonclassical excitation channels of photons that are based on the quantum nature of the electromagnetic field and the effect of SPPs. These excitation channels can be used to shorten the response time of Cherenkov detectors. The quantum theory also shows that SPCLS has a different fluctuation pattern compared with the ordinary electromagnetic systems where vacuum fluctuation dominates. The fluctuation pattern has two significant characteristics: first, the fluctuation of SPCLS will not vanish in the macroscopic case, which may draw theore...

Quantum theory of surface polariton Cherenkov light radiation source and its fluctuation

In \ifmmode \check{C}\else \v{C}\fi{}erenkov and Smith-Purcell free-electron lasers (FELs), a resonant interaction between the electron beam and the copropagating surface mode can produce a copious amount of coherent terahertz radiation. We perform a three-dimensional (3D) analysis of the surface mode, taking the effect of attenuation into account, and set up 3D Maxwell-Lorentz equations for both these systems. Based on this analysis, we determine the requirements on the electron beam parameters, i.e., beam emittance, beam size and beam current for the successful operation of a \ifmmode \check{C}\else \v{C}\fi{}erenkov FEL.

Three-dimensional analysis of the surface mode supported in Čerenkov and Smith-Purcell free-electron lasers

This Letter presents a Cherenkov radiation oscillator with an electron beam travelling over a finitely thick plate made of negative-index materials. In such a scheme, the external reflectors required in the traditional Cherenkov oscillators are not necessary, since the electromagnetic energy flows backward in the negative-index materials, leading to inherent feedback. We theoretically analyzed the interaction between the electron beam and the electromagnetic wave, and worked out the growth rate and start current through numerical calculations. With the help of particle-in-cell simulation, the theoretical predictions are well demonstrated.

Cherenkov radiation oscillator without reflectors

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Cherenkov radiation oscillator without reflectors