Department of Electronic Engineering, Beijing National Research Center for Information Science and Technology, Tsinghua University, Beijing 100084, China
Abstract:Cherenkov radiation (CR) is an electromagnetic radiation emitted by charged particles traveling through a dielectric medium at a speed faster than the phase velocity of light. CR plays an important role in the fields of particle detection, biomedicine and electromagnetic-radiation source. Recently, metamaterials demonstrate their novel mechanical, acoustic, and optical properties by delicately designing the structures and materials. In metamaterials, the electromagnetic properties, such as wave propagation, coupling, and radiation, could be flexibly manipulated. Thus, it is expected that the combination of vacuum electronics and micro- & nano-photonics would result in numerous novel phenomena and effects by having free electrons interacting with metamaterials. In this paper, we firstly review the concept and generation mechanism of CR. Then, recent research advances in the CR generation by using different types of metamaterials are reviewed, including threshold-less CR in hyperbolic metamaterials, reverse CR in negative metamaterials, CR lasing based on high Q-factor metamaterials and Smith-Purcell radiation manipulation with metasurfaces. The unique characteristics and interesting mechanisms of CR based on these metamaterials are elaborated. The research and development of interaction between free electrons and various metamaterials open up possibilities for realizing novel integrated free-electron devices. Keywords:metamaterials/ free electrons/ Cherenkov radiation/ Smith-Purcell radiation
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2.Cherenkov辐射的基本概念和原理CR与真空中变速带电粒子辐射的机制有所不同. 变速带电粒子的辐射是粒子本身由于速度的改变而引发的辐射[36,37], 例如电子在磁场中偏转产生的同步辐射[12,13], 或者电子突然减速发出的轫致辐射[38,39]. CR则是由带电粒子与介质相互作用产生, 当带电粒子的速度大于介质中的光速时, 介质中被诱导的极化分子产生的子波叠加形成的辐射[17], 或认为是电子周围消逝场耦合至介质中形成的辐射. CR的产生对电子的加速、减速和运动轨迹并无要求, 辐射的产生取决于带电粒子的速度, 它的发现改变了之前人们对匀速带电粒子能否产生电磁辐射的认识[20,40]. 图1(a)为自由电子产生CR的示意图, 产生的辐射集中在粒子运动轨迹为轴心的圆锥区域内, 辐射方向与粒子运动方向之间的夹角θ满足下式关系[20]: 图 1 (a) CR示意图, 自由电子在介质中飞行, 电子速度v大于介质中的光速c/n[20]; (b) SPR示意图, 电子周围消逝场经光栅散射成为自由空间的辐射[45] Figure1. (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].
3.基于双曲超材料的无阈值Cherenkov辐射在传统的各向同性介质材料中, 产生CR的条件如(2)式所示, 即自由电子的速度超过介质中光的相速. 葡萄牙里斯本大学Silveirinha[48]利用等频率波矢图对CR阈值条件进行解释, 如图2(a)所示, 各向同性介质的等频率波矢图为黄色圆形, 电子速度v必须足够大, 使得电子周围消逝场的波数β (绿色虚线箭头)处于“圆形”区域内, 进而满足与介质中CR的波矢匹配关系, 自由电子周围消逝场可以耦合到介质中产生CR. 若电子能量低于阈值c/n, 电子周围波数由图中红色箭头所示, 此时无法产生辐射. 图 2 (a) 自由电子在各向同性材料中产生CR的波矢匹配图, 速度较快的电子对应较短的波矢(绿色虚线箭头), 与光子态k+和k-满足z方向波矢匹配, 可以激励CR; 而速度较小的电子周围消逝场(红色箭头)不存在与之匹配的光子态, 无法产生CR; (b) 自由电子在双曲超材料中产生CR的波矢匹配图, 慢速的电子(红色箭头)可以产生CR; (c) 由金属和介质多层膜构成的双曲超材料; 引自文献[48], 重新定义了(a), (b)图中的kx轴和ky轴的方向, 并在(c)图中标出了坐标轴 Figure2. (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 kx and ky redefined in (a), (b) and the coordinates marked in (c).
根据(6)式可知, 无论多低能量的自由电子都可以在双曲超材料中产生CR. 与传统介质中产生CR存在电子速度(能量)下限不同, 第II类双曲超材料中产生CR反而存在一定的电子速度(能量)上限. 图3(a)所示为集成CR辐射芯片的示意图和电子显微镜照片. 仿真结果表明, 当电子能量仅为0.1 keV时, 仍可以在多层膜构建的双曲超材料中产生CR, 如图3(b)所示. 实验中, 由钼(Mo)平面电子源发射的自由电子沿超材料表面飞行, 在超材料中产生CR, 再被金属纳米周期狭缝耦合到自由空间中进行探测. 这里产生CR的电子能量仅为0.25—1.4 keV (图3(c)), 比其他方法所需的电子能量降低了2—3个数量级[19,51,52]. 测得的辐射波长覆盖500—900 nm (图3(d)). 图 3 (a) 集成CR芯片示意图和电子显微镜照片, 器件上表面为钼平面电子发射源, 中间为由Au和SiO2多层膜组成的双曲超材料, 下方为周期金属纳米狭缝用于将CR耦合到自由空间; (b)能量为0.1 keV的自由电子在多层膜双曲超材料中产生CR (电场Ez分量)的仿真结果, 场图对应真空波长为800 nm; (c) 阴阳极电压Vca为0.25—1.4 kV时, 芯片辐射输出功率; (d) 不同纳米缝隙周期Pslit对应的输出光谱; 引自文献[49] Figure3. (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 Ez) with electron energy of 0.1 keV when λ0 = 800 nm; (c) optical output power of the chip with cathode-anode voltage Vca varying from 0.25 to 1.4 kV; (d) spectra of output light with different plasmonic nanoslit period of Pslit. Extracted from Ref. [49]
由于Au的表面等离子体(surface plasmon, SP)共振频率处于可见光和近红外波段, Au-SiO2多层膜结构的双曲区间为可见光和近红外波段[53]. 如果要在其他波段获得双曲超材料中的CR, 需要选取不同等离子体频率的材料来实现超构材料. 几种不同材料的SP共振频率如图4(a)所示[53], 加拿大阿尔伯塔大学Shekhar等[53]为了拓展紫外波段的CR, 对Si材料的等离子体特性进行了研究. 通过电子能量损失谱测得Si膜的SP频率约为11.5 eV (对应真空波长107 nm), 处于极紫外波段, 如图4(c)所示. 进而他们提出利用Si和SiO2的多层膜构造双曲超材料, 并仿真了低能量电子激励的极紫外波段CR. 图 4 (a) 从太赫兹到极紫外(extreme ultraviolet, EUV)的范围内, 不同材料的SP共振频率; (b) 电子能量损失谱(electron energy-loss spectroscopy, k-EELS)测量Si膜的光子能带的示意图; (c) 60 nm厚Si膜的光子能带结构测量结果, Si的SP共振频率约为11.5 eV, 处于EUV波段; (d) EUV波段的无阈值CR的示意图, 双曲超材料由Si和SiO2多层膜组成; 引自文献[53] Figure4. (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].