Cherenkov radiation based on metamaterials

Lin Yue-Chai; Liu Fang; Huang Yi-Dong

doi:10.7498/aps.69.20200260

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:

Authors and contacts

Department of Electronic Engineering, Beijing National Research Center for Information Science and Technology, Tsinghua University, Beijing 100084, China

Corresponding author: Liu Fang, liu_fang@tsinghua.edu.cn ; Huang Yi-Dong, yidonghuang@tsinghua.edu.cn

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References

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Cited By

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]

Figure 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].

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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k_x轴和k_y轴的方向, 并在(c)图中标出了坐标轴

Figure 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).

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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E_z分量)的仿真结果, 场图对应真空波长为800 nm; (c) 阴阳极电压V_ca为0.25—1.4 kV时, 芯片辐射输出功率; (d) 不同纳米缝隙周期P_slit对应的输出光谱; 引自文献[49]

Figure 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]

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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]

Figure 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].

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图 5 (a) 反向CR的实验示意图以及负折射率材料的照片; (b) 负折射率材料结构单元的顶视和侧视示意图; (c) 在负折射率(实线)和正折射率(虚线)区间, 辐射功率随角度变化的功率谱; (a)图引自文献[69], (b), (c)图引自文献[68]

Figure 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].

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图 6 (a) 反向CR器件构造图, 电子束沿+z方向飞行与器件相互作用; (b) 自由电子和反向CR器件的色散曲线, 负折射率材料的色散曲线通过模型计算和高频结构仿真软件(HFSS)仿真得到; (c) 在端口2和端口1测试反向CR器件的功率谱分布; 引自文献[70], 并在(a)中标记了位于左侧的“Port 2”和右侧的“Port 1”

Figure 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).

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图 7 (a)和(b)是两种非对称结构的Fano共振金属超构材料, 超构材料由亚波长的金属狭缝构成; (c)和(d)是不同入射角度下, 两种非对称结构的透射谱结果, 透射谱中的四个低峰表示p偏振光激励的Fano共振; 引自文献[77]

Figure 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].

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图 8 (a) 自由电子飞过Si周期光栅的示意图; (b) 在给定频率下不同电子速度的辐射强度, BIC附近的SPR得到极大增强; (c) 平面波入射双排Si介质光栅示意图; (d) 归一化频率下介质光栅的反射系数R, 插图为共振频率处| H_y |场图; (e) 共振频率f_R的品质因子Q随光栅间距h的变化关系; (a), (b)图引自文献[79]; (c)−(e)图引自文献[78]

Figure 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].

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图 9 (a) 自由电子和Babinet超表面作用产生SPR的示意图, 均匀带电粒子在超表面上方沿+ x轴方向飞行; (b)和(c)分别是C形孔结构和环结构的超表面, 以及自由电子产生SPR的电场分布模拟结果; 引自文献[93]

Figure 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].

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图 10 (a) 基于石墨烯超表面产生SPR的示意图; (b) SPR辐射强度、相位与石墨烯带状结构宽度w的关系; (c) SPR二阶辐射相位与石墨烯在单位结构中位置Δx的关系; (d) SPR的E_x和E_y分量的强度和相位与石墨烯的旋转角度α之间的关系; 引自文献[95]

Figure 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].

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