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

FullText HTML : translate this paragraph

References

[1]	Engheta N, Ziolkowski R W 2006 Metamaterials: Physics and Engineering Explorations (Hoboken: John Wiley & Sons) pp5–9
[2]	Smith D R, Vier D C, Koschny T, Soukoulis C M 2005 Phys. Rev. E 71 036617 Google Scholar
[3]	Zheludev N I, Kivshar Y S 2012 Nat. Mater. 11 917 Google Scholar
[4]	Poddubny A, Iorsh I, Belov P, Kivshar Y 2013 Nat. Photonics 7 948 Google Scholar
[5]	Shekhar P, Atkinson J, Jacob Z 2014 Nano Converg. 1 14 Google Scholar
[6]	Valentine J, Zhang S, Zentgraf T, Ulin-Avila E, Genov D A, Bartal G, Zhang X 2008 Nature 455 376 Google Scholar
[7]	Smith D R, Kroll N 2000 Phys. Rev. Lett. 85 2933 Google Scholar
[8]	Vesseur E J R, Coenen T, Caglayan H, Engheta N, Polman A 2013 Phys. Rev. Lett. 110 013902 Google Scholar
[9]	Moitra P, Yang Y, Anderson Z, Kravchenko I I, Briggs D P, Valentine J 2013 Nat. Photonics 7 791 Google Scholar
[10]	Lin D, Fan P, Hasman E, Brongersma M L 2014 Science 345 298 Google Scholar
[11]	Yu N, Genevet P, Kats M A, Aieta F, Tetienne J-P, Capasso F, Gaburro Z 2011 Science 334 333 Google Scholar
[12]	Elder F R, Gurewitsch A M, Langmuir R V, Pollock H C 1947 Phys. Rev. 71 829
[13]	Hendrickson W A 1991 Science 254 51 Google Scholar
[14]	Asner D M, Bradley R F, de Viveiros L, Doe P J, Fernandes J L, Fertl M, Finn E C, Formaggio J A, Furse D, Jones A M, Kofron J N, LaRoque B H, Leber M, McBride E L, Miller M L, Mohanmurthy P, Monreal B, Oblath N S, Robertson R G H, Rosenberg L J, Rybka G, Rysewyk D, Sternberg M G, Tedeschi J R, Thümmler T, VanDevender B A, Woods N L 2015 Phys. Rev. Lett. 114 162501 Google Scholar
[15]	Bornatici M, Cano R, De Barbieri O, Engelmann F 1983 Nucl. Fusion 23 1153 Google Scholar
[16]	Cherenkov P A 1934 Dokl. Akad. Nauk SSSR 2 451
[17]	Kobzev A P 2010 Phys. Part. Nucl. 41 452 Google Scholar
[18]	Doucas G, Mulvey J H, Omori M, Walsh J, Kimmitt M F 1992 Phys. Rev. Lett. 69 1761 Google Scholar
[19]	Smith S J, Purcell E M 1953 Phys. Rev. 92 1069
[20]	Bolotovskii B M 2009 Phys. Usp. 52 1099 Google Scholar
[21]	Frank I M, Tamm I E 1991 Selected Papers (Berlin, Heidelberg: Springer Berlin Heidelberg) pp29–35
[22]	Eichmeier J A, Thumm M 2008 Vacuum Electronics: Components and Devices (Berlin: Springer Science & Business Media) p315
[23]	Ren H, Deng X, Zheng Y, An N, Chen X 2012 Phys. Rev. Lett. 108 223901 Google Scholar
[24]	Aubert J J, Becker U, Biggs P J, Burger J, Chen M, Everhart G, Goldhagen P, Leong J, McCorriston T, Rhoades T G, Rohde M, Ting S C C, Wu S L, Lee Y Y 1974 Phys. Rev. Lett. 33 1404 Google Scholar
[25]	Chamberlain O, Segrè E, Wiegand C, Ypsilantis T 1955 Phys. Rev. 100 947 Google Scholar
[26]	Fukuda Y, Hayakawa T, Ichihara E, Inoue K, Ishihara K, Ishino H, Itow Y, Kajita T, Kameda J, Kasuga S 1998 Phys. Rev. Lett. 81 1562 Google Scholar
[27]	Bugaev S P, Cherepenin V A, Kanavets V I, Klimov A I, Kopenkin A D, Koshelev V I, Popov V A, Slepkov A I 1990 IEEE Trans. Plasma Sci. 18 525 Google Scholar
[28]	Duan Z, Shapiro M A, Schamiloglu E, Behdad N, Gong Y, Booske J H, Basu B N, Temkin R J 2019 IEEE Trans. Electron Devices 66 207 Google Scholar
[29]	Korovin S D, Eltchaninov A A, Rostov V V, Shpak V G, Yalandin M I, Ginzburg N S, Sergeev A S, Zotova I V 2006 Phys. Rev. E 74 016501
[30]	Saltzberg D, Gorham P, Walz D, Field C, Iverson R, Odian A, Resch G, Schoessow P, Williams D 2001 Phys. Rev. Lett. 86 2802 Google Scholar
[31]	Kotagiri N, Sudlow G P, Akers W J, Achilefu S 2015 Nat. Nanotechnol. 10 370 Google Scholar
[32]	Robertson R, Germanos M S, Li C, Mitchell G S, Cherry S R, Silva M D 2009 Phys. Med. Biol. 54 N355 Google Scholar
[33]	Ruggiero A, Holland J P, Lewis J S, Grimm J 2010 J. Nucl. Med. 51 1123 Google Scholar
[34]	French D M, Shiffler D, Cartwright K 2013 Phys. Plasmas 20 083116 Google Scholar
[35]	Matsui T 2017 J. Infrared Millim. Te. 38 1140 Google Scholar
[36]	Fulton T, Rohrlich F 1960 Ann. Phys. 9 499 Google Scholar
[37]	Schwinger J 1949 Phys. Rev. 75 1912 Google Scholar
[38]	Madey J M J 1971 J. Appl. Phys. 42 1906 Google Scholar
[39]	Koch H W, Motz J W 1959 Rev. Mod. Phys. 31 920 Google Scholar
[40]	Tamm I E 1991 Selected Papers (Berlin, Heidelberg: Springer Berlin Heidelberg) pp55–67
[41]	Luo C, Ibanescu M, Johnson S G, Joannopoulos J D 2003 Science 299 368 Google Scholar
[42]	Schächter L 2011 Beam-Wave Interaction in Periodic and Quasi-Periodic Structures (Berlin, Heidelberg : Springer Berlin Heidelberg) pp169–170
[43]	Van den Berg P M 1973 J. Opt. Soc. Am. 63 689 Google Scholar
[44]	Van den Berg P M 1973 J. Opt. Soc. Am. 63 1588 Google Scholar
[45]	Gover A, Dvorkis P, Elisha U 1984 J. Opt. Soc. Am. B 1 723
[46]	García de Abajo F J 2010 Rev. Mod. Phys. 82 209 Google Scholar
[47]	Wahlstrand J K, Merlin R 2003 Phys. Rev. B 68 054301
[48]	Silveirinha M 2017 Nat. Photonics 11 269 Google Scholar
[49]	Liu F, Xiao L, Ye Y, Wang M, Cui K, Feng X, Zhang W, Huang Y 2017 Nat. Photonics 11 289 Google Scholar
[50]	Cortes C, Newman W, Molesky S, Jacob Z 2012 J. Opt. 14 063001 Google Scholar
[51]	Adamo G, MacDonald K F, Fu Y H, Wang C M, Tsai D P, García de Abajo F J, Zheludev N I 2009 Phys. Rev. Lett. 103 113901 Google Scholar
[52]	So J K, García de Abajo F J, MacDonald K F, Zheludev N I 2015 ACS Photonics 2 1236 Google Scholar
[53]	Shekhar P, Pendharker S, Sahasrabudhe H, Vick D, Malac M, Rahman R, Jacob Z 2018 Optica 5 1590 Google Scholar
[54]	Fernandes D E, Maslovski S I, Silveirinha M G 2012 Phys. Rev. B 85 155107 Google Scholar
[55]	Jacob Z, Kim J Y, Naik G V, Boltasseva A, Narimanov E E, Shalaev V M 2010 Appl. Phys. B 100 215 Google Scholar
[56]	Caldwell J D, Kretinin A V, Chen Y, Giannini V, Fogler M M, Francescato Y, Ellis C T, Tischler J G, Woods C R, Giles A J, Hong M, Watanabe K, Taniguchi T, Maier S A, Novoselov K S 2014 Nat. Commun. 5 5221
[57]	Esslinger M, Vogelgesang R, Talebi N, Khunsin W, Gehring P, De Zuani S, Gompf B, Kern K 2014 ACS Photonics 1 1285 Google Scholar
[58]	Narimanov E E, Kildishev A V 2015 Nat. Photonics 9 214 Google Scholar
[59]	Govyadinov A A, Konečná A, Chuvilin A, Vélez S, Dolado I, Nikitin A Y, Lopatin S, Casanova F, Hueso L E, Aizpurua J 2017 Nat. Commun. 8 95 Google Scholar
[60]	屈拓 2019 博士学位论文 (北京: 清华大学) Qu T 2019 Ph. D. Dissertation (Beijing: Tsinghua University) (in Chinese)
[61]	Shekhar P, Pendharker S, Vick D, Malac M, Jacob Z 2019 Opt. Express 27 6970 Google Scholar
[62]	Tao J, Wu L, Zheng G, Yu S 2019 Carbon 150 136 Google Scholar
[63]	Marqués R, Medina F, Rafii-El-Idrissi R 2002 Phys. Rev. B 65 144440 Google Scholar
[64]	Veselago V G 1968 Sov. Phys. Usp. 10 509 Google Scholar
[65]	Zharov A A, Shadrivov I V, Kivshar Y S 2003 Phys. Rev. Lett. 91 037401 Google Scholar
[66]	Lezec H J, Dionne J A, Atwater H A 2007 Science 316 430 Google Scholar
[67]	Shelby R A, Smith D R, Schultz S 2001 Science 292 77 Google Scholar
[68]	Xi S, Chen H, Jiang T, Ran L, Huangfu J, Wu B I, Kong J A, Chen M 2009 Phys. Rev. Lett. 103 194801 Google Scholar
[69]	Zhang S, Zhang X 2009 Physics 2 91 Google Scholar
[70]	Duan Z, Tang X, Wang Z, Zhang Y, Chen X, Chen M, Gong Y 2017 Nat. Commun. 8 14901
[71]	Akopov N, Aschenauer E C, Bailey K, et al. 2002 Nucl. Instrum. Methods Phys. Res., Sect. A 479 511 Google Scholar
[72]	Nishino H, Clark S, Abe K, Hayato Y, Iida T, Ikeda M, Kameda J, Kobayashi K, Koshio Y, Miura M 2009 Phys. Rev. Lett. 102 141801 Google Scholar
[73]	Séguinot J, Ypsilantis T 1977 Nucl. Instrum. Methods 142 377 Google Scholar
[74]	Ginis V, Danckaert J, Veretennicoff I, Tassin P 2014 Phys. Rev. Lett. 113 167402 Google Scholar
[75]	Duan Z, Wu B I, Xi S, Chen H, Chen M 2009 Prog. Electromagn. Res. 90 75 Google Scholar
[76]	Hsu C W, Zhen B, Stone A D, Joannopoulos J D, Soljačić M 2016 Nat. Rev. Mater. 1 16048
[77]	Kim S, Baek I K, Bhattacharya R, Hong D, Sattorov M, Bera A, So J K, Kim D S, Park G S 2018 Adv. Opt. Mater. 6 1800041 Google Scholar
[78]	Song Y, Jiang N, Liu L, Hu X, Zi J 2018 Phys. Rev. Appl. 10 064026 Google Scholar
[79]	Yang Y, Massuda A, Roques-Carmes C, Kooi S E, Christensen T, Johnson S G, Joannopoulos J D, Miller O D, Kaminer I, Soljačić M 2018 Nat. Phys. 14 894 Google Scholar
[80]	Kodigala A, Lepetit T, Gu Q, Bahari B, Fainman Y, Kanté B 2017 Nature 541 196 Google Scholar
[81]	Marinica D C, Borisov A G, Shabanov S V 2008 Phys. Rev. Lett. 100 183902 Google Scholar
[82]	Kimura W D, Kim G H, Romea R D, Steinhauer L C, Pogorelsky I V, Kusche K P, Fernow R C, Wang X, Liu Y 1995 Phys. Rev. Lett. 74 546 Google Scholar
[83]	Kumar V, Kim K-J 2006 Phys. Rev. E 73 026501 Google Scholar
[84]	Ye Y, Liu F, Cui K, Feng X, Zhang W, Huang Y 2018 Opt. Express 26 31402 Google Scholar
[85]	Denis T, van Dijk M W, Lee J H H, van der Meer R, Strooisma A, van der Slot P J M, Vos W L, Boller K J 2016 Phys. Rev. A 94 053852 Google Scholar
[86]	Von Laven S, Branscum J, Golub J, Layman R, Walsh J 1982 Appl. Phys. Lett. 41 408 Google Scholar
[87]	Wiggins S M, Jaroszynski D A, McNeil B W J, Robb G R M, Aitken P, Phelps A D R, Cross A W, Ronald K, Ginzburg N S, Shpak V G, Yalandin M I, Shunailov S A, Ulmaskulov M R 2000 Phys. Rev. Lett. 84 2393 Google Scholar
[88]	Kim K J, Song S B 2001 Nucl. Instrum. Methods Phys. Res., Sect. A 475 158 Google Scholar
[89]	Chen H-T, Taylor A J, Yu N 2016 Rep. Prog. Phys. 79 076401 Google Scholar
[90]	Kildishev A V, Boltasseva A, Shalaev V M 2013 Science 339 1232009 Google Scholar
[91]	Yu N, Capasso F 2014 Nat. Mater. 13 139 Google Scholar
[92]	Brownell J H, Doucas G 2005 Phys. Rev. Spec. Top. Accel Beams 8 091301
[93]	Wang Z, Yao K, Chen M, Chen H, Liu Y 2016 Phys. Rev. Lett. 117 157401 Google Scholar
[94]	Yang Y, Roques-Carmes C, Kaminer I, Zaidi A, Massuda A, Yang Y, Kooi S E, Berggren K K, Soljačić M Conference on Lasers and Electro-Optics San Jose, California, May 13, 2018 pFW4 H.1
[95]	Su Z, Cheng F, Li L, Liu Y 2019 ACS Photonics 6 1947 Google Scholar
[96]	Gamzina D, Li H, Himes L, Barchfeld R, Popovic B, Pan P, Letizia R, Mineo M, Feng J, Paoloni C, Luhmann N C 2016 IEEE Trans. Nanotechnol. 15 85 Google Scholar
[97]	Hu P, Lei W, Jiang Y, Huang Y, Song R, Chen H, Dong Y 2019 IEEE Electron Device Lett. 40 973 Google Scholar
[98]	Liu S, Zhang C, Hu M, Chen X, Zhang P, Gong S, Zhao T, Zhong R 2014 Appl. Phys. Lett. 104 201104 Google Scholar
[99]	Shin Y M, So J K, Jang K H, Won J H, Srivastava A, Park G S 2007 Appl. Phys. Lett. 90 031502 Google Scholar
[100]	Breuer J, Hommelhoff P 2013 Phys. Rev. Lett. 111 134803 Google Scholar
[101]	Esarey E, Schroeder C B, Leemans W P 2009 Rev. Mod. Phys. 81 1229 Google Scholar
[102]	Peralta E A, Soong K, England R J, Colby E R, Wu Z, Montazeri B, McGuinness C, McNeur J, Leedle K J, Walz D, Sozer E B, Cowan B, Schwartz B, Travish G, Byer R L 2013 Nature 503 91 Google Scholar
[103]	Rosolen G, Wong L J, Rivera N, Maes B, Soljačić M, Kaminer I 2018 Light-Sci. Appl. 7 1 Google Scholar
[104]	Friedman A, Gover A, Kurizki G, Ruschin S, Yariv A 1988 Rev. Mod. Phys. 60 471 Google Scholar
[105]	Gover A, Yariv A 1974 J. Appl. Phys. 45 2596 Google Scholar
[106]	Mikhailov S A 2013 Phys. Rev. B 87 115405 Google Scholar
[107]	Tsui D C, Gornik E, Logan R A 1980 Solid State Commun. 35 875 Google Scholar
[108]	Chen C D, Hu X P, Xu Y L, Xu P, Zhao G, Zhu S N 2012 Appl. Phys. Lett. 101 071113 Google Scholar
[109]	Tien P K, Ulrich R, Martin R J 1970 Appl. Phys. Lett. 17 447 Google Scholar
[110]	Saltiel S M, Sheng Y, Voloch-Bloch N, Neshev D N, Krolikowski W, Arie A, Koynov K, Kivshar Y S 2009 IEEE J. Quantum Electron. 45 1465 Google Scholar
[111]	Zhang Y, Gao Z D, Qi Z, Zhu S N, Ming N B 2008 Phys. Rev. Lett. 100 163904 Google Scholar
[112]	Wai P K A, Menyuk C R, Lee Y C, Chen H H 1986 Opt. Lett. 11 464 Google Scholar
[113]	Coen S, Randle H G, Sylvestre T, Erkintalo M 2013 Opt. Lett. 38 37 Google Scholar
[114]	Brasch V, Geiselmann M, Herr T, Lihachev G, Pfeiffer M H, Gorodetsky M L, Kippenberg T J 2016 Science 351 357 Google Scholar

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].

DownLoad: Full-Size Img PowerPoint

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).

DownLoad: Full-Size Img PowerPoint

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]

DownLoad: Full-Size Img PowerPoint

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].

DownLoad: Full-Size Img PowerPoint

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].

DownLoad: Full-Size Img PowerPoint

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).

DownLoad: Full-Size Img PowerPoint

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].

DownLoad: Full-Size Img PowerPoint

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].

DownLoad: Full-Size Img PowerPoint

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].

DownLoad: Full-Size Img PowerPoint

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].

DownLoad: Full-Size Img PowerPoint

map

[1]	Engheta N, Ziolkowski R W 2006 Metamaterials: Physics and Engineering Explorations (Hoboken: John Wiley & Sons) pp5–9
[2]	Smith D R, Vier D C, Koschny T, Soukoulis C M 2005 Phys. Rev. E 71 036617 Google Scholar
[3]	Zheludev N I, Kivshar Y S 2012 Nat. Mater. 11 917 Google Scholar
[4]	Poddubny A, Iorsh I, Belov P, Kivshar Y 2013 Nat. Photonics 7 948 Google Scholar
[5]	Shekhar P, Atkinson J, Jacob Z 2014 Nano Converg. 1 14 Google Scholar
[6]	Valentine J, Zhang S, Zentgraf T, Ulin-Avila E, Genov D A, Bartal G, Zhang X 2008 Nature 455 376 Google Scholar
[7]	Smith D R, Kroll N 2000 Phys. Rev. Lett. 85 2933 Google Scholar
[8]	Vesseur E J R, Coenen T, Caglayan H, Engheta N, Polman A 2013 Phys. Rev. Lett. 110 013902 Google Scholar
[9]	Moitra P, Yang Y, Anderson Z, Kravchenko I I, Briggs D P, Valentine J 2013 Nat. Photonics 7 791 Google Scholar
[10]	Lin D, Fan P, Hasman E, Brongersma M L 2014 Science 345 298 Google Scholar
[11]	Yu N, Genevet P, Kats M A, Aieta F, Tetienne J-P, Capasso F, Gaburro Z 2011 Science 334 333 Google Scholar
[12]	Elder F R, Gurewitsch A M, Langmuir R V, Pollock H C 1947 Phys. Rev. 71 829
[13]	Hendrickson W A 1991 Science 254 51 Google Scholar
[14]	Asner D M, Bradley R F, de Viveiros L, Doe P J, Fernandes J L, Fertl M, Finn E C, Formaggio J A, Furse D, Jones A M, Kofron J N, LaRoque B H, Leber M, McBride E L, Miller M L, Mohanmurthy P, Monreal B, Oblath N S, Robertson R G H, Rosenberg L J, Rybka G, Rysewyk D, Sternberg M G, Tedeschi J R, Thümmler T, VanDevender B A, Woods N L 2015 Phys. Rev. Lett. 114 162501 Google Scholar
[15]	Bornatici M, Cano R, De Barbieri O, Engelmann F 1983 Nucl. Fusion 23 1153 Google Scholar
[16]	Cherenkov P A 1934 Dokl. Akad. Nauk SSSR 2 451
[17]	Kobzev A P 2010 Phys. Part. Nucl. 41 452 Google Scholar
[18]	Doucas G, Mulvey J H, Omori M, Walsh J, Kimmitt M F 1992 Phys. Rev. Lett. 69 1761 Google Scholar
[19]	Smith S J, Purcell E M 1953 Phys. Rev. 92 1069
[20]	Bolotovskii B M 2009 Phys. Usp. 52 1099 Google Scholar
[21]	Frank I M, Tamm I E 1991 Selected Papers (Berlin, Heidelberg: Springer Berlin Heidelberg) pp29–35
[22]	Eichmeier J A, Thumm M 2008 Vacuum Electronics: Components and Devices (Berlin: Springer Science & Business Media) p315
[23]	Ren H, Deng X, Zheng Y, An N, Chen X 2012 Phys. Rev. Lett. 108 223901 Google Scholar
[24]	Aubert J J, Becker U, Biggs P J, Burger J, Chen M, Everhart G, Goldhagen P, Leong J, McCorriston T, Rhoades T G, Rohde M, Ting S C C, Wu S L, Lee Y Y 1974 Phys. Rev. Lett. 33 1404 Google Scholar
[25]	Chamberlain O, Segrè E, Wiegand C, Ypsilantis T 1955 Phys. Rev. 100 947 Google Scholar
[26]	Fukuda Y, Hayakawa T, Ichihara E, Inoue K, Ishihara K, Ishino H, Itow Y, Kajita T, Kameda J, Kasuga S 1998 Phys. Rev. Lett. 81 1562 Google Scholar
[27]	Bugaev S P, Cherepenin V A, Kanavets V I, Klimov A I, Kopenkin A D, Koshelev V I, Popov V A, Slepkov A I 1990 IEEE Trans. Plasma Sci. 18 525 Google Scholar
[28]	Duan Z, Shapiro M A, Schamiloglu E, Behdad N, Gong Y, Booske J H, Basu B N, Temkin R J 2019 IEEE Trans. Electron Devices 66 207 Google Scholar
[29]	Korovin S D, Eltchaninov A A, Rostov V V, Shpak V G, Yalandin M I, Ginzburg N S, Sergeev A S, Zotova I V 2006 Phys. Rev. E 74 016501
[30]	Saltzberg D, Gorham P, Walz D, Field C, Iverson R, Odian A, Resch G, Schoessow P, Williams D 2001 Phys. Rev. Lett. 86 2802 Google Scholar
[31]	Kotagiri N, Sudlow G P, Akers W J, Achilefu S 2015 Nat. Nanotechnol. 10 370 Google Scholar
[32]	Robertson R, Germanos M S, Li C, Mitchell G S, Cherry S R, Silva M D 2009 Phys. Med. Biol. 54 N355 Google Scholar
[33]	Ruggiero A, Holland J P, Lewis J S, Grimm J 2010 J. Nucl. Med. 51 1123 Google Scholar
[34]	French D M, Shiffler D, Cartwright K 2013 Phys. Plasmas 20 083116 Google Scholar
[35]	Matsui T 2017 J. Infrared Millim. Te. 38 1140 Google Scholar
[36]	Fulton T, Rohrlich F 1960 Ann. Phys. 9 499 Google Scholar
[37]	Schwinger J 1949 Phys. Rev. 75 1912 Google Scholar
[38]	Madey J M J 1971 J. Appl. Phys. 42 1906 Google Scholar
[39]	Koch H W, Motz J W 1959 Rev. Mod. Phys. 31 920 Google Scholar
[40]	Tamm I E 1991 Selected Papers (Berlin, Heidelberg: Springer Berlin Heidelberg) pp55–67
[41]	Luo C, Ibanescu M, Johnson S G, Joannopoulos J D 2003 Science 299 368 Google Scholar
[42]	Schächter L 2011 Beam-Wave Interaction in Periodic and Quasi-Periodic Structures (Berlin, Heidelberg : Springer Berlin Heidelberg) pp169–170
[43]	Van den Berg P M 1973 J. Opt. Soc. Am. 63 689 Google Scholar
[44]	Van den Berg P M 1973 J. Opt. Soc. Am. 63 1588 Google Scholar
[45]	Gover A, Dvorkis P, Elisha U 1984 J. Opt. Soc. Am. B 1 723
[46]	García de Abajo F J 2010 Rev. Mod. Phys. 82 209 Google Scholar
[47]	Wahlstrand J K, Merlin R 2003 Phys. Rev. B 68 054301
[48]	Silveirinha M 2017 Nat. Photonics 11 269 Google Scholar
[49]	Liu F, Xiao L, Ye Y, Wang M, Cui K, Feng X, Zhang W, Huang Y 2017 Nat. Photonics 11 289 Google Scholar
[50]	Cortes C, Newman W, Molesky S, Jacob Z 2012 J. Opt. 14 063001 Google Scholar
[51]	Adamo G, MacDonald K F, Fu Y H, Wang C M, Tsai D P, García de Abajo F J, Zheludev N I 2009 Phys. Rev. Lett. 103 113901 Google Scholar
[52]	So J K, García de Abajo F J, MacDonald K F, Zheludev N I 2015 ACS Photonics 2 1236 Google Scholar
[53]	Shekhar P, Pendharker S, Sahasrabudhe H, Vick D, Malac M, Rahman R, Jacob Z 2018 Optica 5 1590 Google Scholar
[54]	Fernandes D E, Maslovski S I, Silveirinha M G 2012 Phys. Rev. B 85 155107 Google Scholar
[55]	Jacob Z, Kim J Y, Naik G V, Boltasseva A, Narimanov E E, Shalaev V M 2010 Appl. Phys. B 100 215 Google Scholar
[56]	Caldwell J D, Kretinin A V, Chen Y, Giannini V, Fogler M M, Francescato Y, Ellis C T, Tischler J G, Woods C R, Giles A J, Hong M, Watanabe K, Taniguchi T, Maier S A, Novoselov K S 2014 Nat. Commun. 5 5221
[57]	Esslinger M, Vogelgesang R, Talebi N, Khunsin W, Gehring P, De Zuani S, Gompf B, Kern K 2014 ACS Photonics 1 1285 Google Scholar
[58]	Narimanov E E, Kildishev A V 2015 Nat. Photonics 9 214 Google Scholar
[59]	Govyadinov A A, Konečná A, Chuvilin A, Vélez S, Dolado I, Nikitin A Y, Lopatin S, Casanova F, Hueso L E, Aizpurua J 2017 Nat. Commun. 8 95 Google Scholar
[60]	屈拓 2019 博士学位论文 (北京: 清华大学) Qu T 2019 Ph. D. Dissertation (Beijing: Tsinghua University) (in Chinese)
[61]	Shekhar P, Pendharker S, Vick D, Malac M, Jacob Z 2019 Opt. Express 27 6970 Google Scholar
[62]	Tao J, Wu L, Zheng G, Yu S 2019 Carbon 150 136 Google Scholar
[63]	Marqués R, Medina F, Rafii-El-Idrissi R 2002 Phys. Rev. B 65 144440 Google Scholar
[64]	Veselago V G 1968 Sov. Phys. Usp. 10 509 Google Scholar
[65]	Zharov A A, Shadrivov I V, Kivshar Y S 2003 Phys. Rev. Lett. 91 037401 Google Scholar
[66]	Lezec H J, Dionne J A, Atwater H A 2007 Science 316 430 Google Scholar
[67]	Shelby R A, Smith D R, Schultz S 2001 Science 292 77 Google Scholar
[68]	Xi S, Chen H, Jiang T, Ran L, Huangfu J, Wu B I, Kong J A, Chen M 2009 Phys. Rev. Lett. 103 194801 Google Scholar
[69]	Zhang S, Zhang X 2009 Physics 2 91 Google Scholar
[70]	Duan Z, Tang X, Wang Z, Zhang Y, Chen X, Chen M, Gong Y 2017 Nat. Commun. 8 14901
[71]	Akopov N, Aschenauer E C, Bailey K, et al. 2002 Nucl. Instrum. Methods Phys. Res., Sect. A 479 511 Google Scholar
[72]	Nishino H, Clark S, Abe K, Hayato Y, Iida T, Ikeda M, Kameda J, Kobayashi K, Koshio Y, Miura M 2009 Phys. Rev. Lett. 102 141801 Google Scholar
[73]	Séguinot J, Ypsilantis T 1977 Nucl. Instrum. Methods 142 377 Google Scholar
[74]	Ginis V, Danckaert J, Veretennicoff I, Tassin P 2014 Phys. Rev. Lett. 113 167402 Google Scholar
[75]	Duan Z, Wu B I, Xi S, Chen H, Chen M 2009 Prog. Electromagn. Res. 90 75 Google Scholar
[76]	Hsu C W, Zhen B, Stone A D, Joannopoulos J D, Soljačić M 2016 Nat. Rev. Mater. 1 16048
[77]	Kim S, Baek I K, Bhattacharya R, Hong D, Sattorov M, Bera A, So J K, Kim D S, Park G S 2018 Adv. Opt. Mater. 6 1800041 Google Scholar
[78]	Song Y, Jiang N, Liu L, Hu X, Zi J 2018 Phys. Rev. Appl. 10 064026 Google Scholar
[79]	Yang Y, Massuda A, Roques-Carmes C, Kooi S E, Christensen T, Johnson S G, Joannopoulos J D, Miller O D, Kaminer I, Soljačić M 2018 Nat. Phys. 14 894 Google Scholar
[80]	Kodigala A, Lepetit T, Gu Q, Bahari B, Fainman Y, Kanté B 2017 Nature 541 196 Google Scholar
[81]	Marinica D C, Borisov A G, Shabanov S V 2008 Phys. Rev. Lett. 100 183902 Google Scholar
[82]	Kimura W D, Kim G H, Romea R D, Steinhauer L C, Pogorelsky I V, Kusche K P, Fernow R C, Wang X, Liu Y 1995 Phys. Rev. Lett. 74 546 Google Scholar
[83]	Kumar V, Kim K-J 2006 Phys. Rev. E 73 026501 Google Scholar
[84]	Ye Y, Liu F, Cui K, Feng X, Zhang W, Huang Y 2018 Opt. Express 26 31402 Google Scholar
[85]	Denis T, van Dijk M W, Lee J H H, van der Meer R, Strooisma A, van der Slot P J M, Vos W L, Boller K J 2016 Phys. Rev. A 94 053852 Google Scholar
[86]	Von Laven S, Branscum J, Golub J, Layman R, Walsh J 1982 Appl. Phys. Lett. 41 408 Google Scholar
[87]	Wiggins S M, Jaroszynski D A, McNeil B W J, Robb G R M, Aitken P, Phelps A D R, Cross A W, Ronald K, Ginzburg N S, Shpak V G, Yalandin M I, Shunailov S A, Ulmaskulov M R 2000 Phys. Rev. Lett. 84 2393 Google Scholar
[88]	Kim K J, Song S B 2001 Nucl. Instrum. Methods Phys. Res., Sect. A 475 158 Google Scholar
[89]	Chen H-T, Taylor A J, Yu N 2016 Rep. Prog. Phys. 79 076401 Google Scholar
[90]	Kildishev A V, Boltasseva A, Shalaev V M 2013 Science 339 1232009 Google Scholar
[91]	Yu N, Capasso F 2014 Nat. Mater. 13 139 Google Scholar
[92]	Brownell J H, Doucas G 2005 Phys. Rev. Spec. Top. Accel Beams 8 091301
[93]	Wang Z, Yao K, Chen M, Chen H, Liu Y 2016 Phys. Rev. Lett. 117 157401 Google Scholar
[94]	Yang Y, Roques-Carmes C, Kaminer I, Zaidi A, Massuda A, Yang Y, Kooi S E, Berggren K K, Soljačić M Conference on Lasers and Electro-Optics San Jose, California, May 13, 2018 pFW4 H.1
[95]	Su Z, Cheng F, Li L, Liu Y 2019 ACS Photonics 6 1947 Google Scholar
[96]	Gamzina D, Li H, Himes L, Barchfeld R, Popovic B, Pan P, Letizia R, Mineo M, Feng J, Paoloni C, Luhmann N C 2016 IEEE Trans. Nanotechnol. 15 85 Google Scholar
[97]	Hu P, Lei W, Jiang Y, Huang Y, Song R, Chen H, Dong Y 2019 IEEE Electron Device Lett. 40 973 Google Scholar
[98]	Liu S, Zhang C, Hu M, Chen X, Zhang P, Gong S, Zhao T, Zhong R 2014 Appl. Phys. Lett. 104 201104 Google Scholar
[99]	Shin Y M, So J K, Jang K H, Won J H, Srivastava A, Park G S 2007 Appl. Phys. Lett. 90 031502 Google Scholar
[100]	Breuer J, Hommelhoff P 2013 Phys. Rev. Lett. 111 134803 Google Scholar
[101]	Esarey E, Schroeder C B, Leemans W P 2009 Rev. Mod. Phys. 81 1229 Google Scholar
[102]	Peralta E A, Soong K, England R J, Colby E R, Wu Z, Montazeri B, McGuinness C, McNeur J, Leedle K J, Walz D, Sozer E B, Cowan B, Schwartz B, Travish G, Byer R L 2013 Nature 503 91 Google Scholar
[103]	Rosolen G, Wong L J, Rivera N, Maes B, Soljačić M, Kaminer I 2018 Light-Sci. Appl. 7 1 Google Scholar
[104]	Friedman A, Gover A, Kurizki G, Ruschin S, Yariv A 1988 Rev. Mod. Phys. 60 471 Google Scholar
[105]	Gover A, Yariv A 1974 J. Appl. Phys. 45 2596 Google Scholar
[106]	Mikhailov S A 2013 Phys. Rev. B 87 115405 Google Scholar
[107]	Tsui D C, Gornik E, Logan R A 1980 Solid State Commun. 35 875 Google Scholar
[108]	Chen C D, Hu X P, Xu Y L, Xu P, Zhao G, Zhu S N 2012 Appl. Phys. Lett. 101 071113 Google Scholar
[109]	Tien P K, Ulrich R, Martin R J 1970 Appl. Phys. Lett. 17 447 Google Scholar
[110]	Saltiel S M, Sheng Y, Voloch-Bloch N, Neshev D N, Krolikowski W, Arie A, Koynov K, Kivshar Y S 2009 IEEE J. Quantum Electron. 45 1465 Google Scholar
[111]	Zhang Y, Gao Z D, Qi Z, Zhu S N, Ming N B 2008 Phys. Rev. Lett. 100 163904 Google Scholar
[112]	Wai P K A, Menyuk C R, Lee Y C, Chen H H 1986 Opt. Lett. 11 464 Google Scholar
[113]	Coen S, Randle H G, Sylvestre T, Erkintalo M 2013 Opt. Lett. 38 37 Google Scholar
[114]	Brasch V, Geiselmann M, Herr T, Lihachev G, Pfeiffer M H, Gorodetsky M L, Kippenberg T J 2016 Science 351 357 Google Scholar

[1]	Chen Le-Di, Fan Ren-Hao, Liu Yu, Tang Gong-Hui, Ma Zhong-Li, Peng Ru-Wen, Wang Mu. Broadband modulation of terahertz wave polarization states with flexible metamaterial. Acta Physica Sinica, 2022, 71(18): 187802. doi: 10.7498/aps.71.20220801
[2]	Li Jing, Liu Yun-Quan. Relativistic free electrons based quantum physics. Acta Physica Sinica, 2022, 71(23): 233302. doi: 10.7498/aps.71.20221289
[3]	Zhou Yi, Chen Rui, Chen Wen-Jie, Ma Yun-Gui. Advances in spatial analog optical computing devices. Acta Physica Sinica, 2020, 69(15): 157803. doi: 10.7498/aps.69.20200283
[4]	Quan Jia-Qi, Sheng Zong-Qiang, Wu Hong-Wei. Omnidirectional cloaking based on spoof surface plasmonic structure. Acta Physica Sinica, 2019, 68(15): 154101. doi: 10.7498/aps.68.20190283
[5]	Yao Yao, Shen Yue, Hao Jia-Ming, Dai Ning. Antireflection coatings based on subwavelength artificial engineering microstructures. Acta Physica Sinica, 2019, 68(14): 147802. doi: 10.7498/aps.68.20190702
[6]	Xu Jin, Li Rong-Qiang, Jiang Xiao-Ping, Wang Shen-Yun, Han Tian-Cheng. Ultra-wideband linear polarization converter based on square split ring. Acta Physica Sinica, 2019, 68(11): 117801. doi: 10.7498/aps.68.20190267
[7]	Yang Peng, Han Tian-Cheng. Polarization-controlled dual-band broadband infrared absorber. Acta Physica Sinica, 2018, 67(10): 107801. doi: 10.7498/aps.67.20172716
[8]	Pu Ming-Bo, Wang Chang-Tao, Wang Yan-Qin, Luo Xian-Gang. Subwavelength electromagnetics below the diffraction limit. Acta Physica Sinica, 2017, 66(14): 144101. doi: 10.7498/aps.66.144101
[9]	Ran Mao-Yi, Hu Yao-Gai, Zhao Zheng-Yu, Zhang Yuan-Nong. Effect of high power microwave injection on tropospheric freon. Acta Physica Sinica, 2017, 66(4): 045101. doi: 10.7498/aps.66.045101
[10]	Ma Xiao-Liang, Li Xiong, Guo Ying-Hui, Zhao Ze-Yu, Luo Xian-Gang. Meta-antenna: principle, device and application. Acta Physica Sinica, 2017, 66(14): 147802. doi: 10.7498/aps.66.147802
[11]	Deng Jun-Hong, Li Gui-Xin. Nonlinear photonic metasurfaces. Acta Physica Sinica, 2017, 66(14): 147803. doi: 10.7498/aps.66.147803
[12]	Long Yang, Ren Jie, Jiang Hai-Tao, Sun Yong, Chen Hong. Quantum spin Hall effect in metamaterials. Acta Physica Sinica, 2017, 66(22): 227803. doi: 10.7498/aps.66.227803
[13]	Cao Miao-Miao, Liu Wen-Xin, Wang Yong, Zhu Jue-Yuan, Li Ke. High frequency characteristics of dielectric-loaded grating for terahertz Smith-Purcell radiation. Acta Physica Sinica, 2016, 65(1): 014101. doi: 10.7498/aps.65.014101
[14]	Fu Tao, Ouyang Zheng-Biao. Simulation of cherenkov radiation oscillation in a plasma-filled metallic photonic crystal. Acta Physica Sinica, 2016, 65(7): 074208. doi: 10.7498/aps.65.074208
[15]	Chen Da-Xin, Chen Zhi-Feng, Xu Chu-Dong, Lai Tian-Shu. Physical origin of transient Kerr peak induced by circularly polarized laser in ferromagnetic films. Acta Physica Sinica, 2010, 59(10): 7362-7367. doi: 10.7498/aps.59.7362
[16]	Gao Xi, Yang Zi-Qiang, Hou Jun, Qi Li-Mei, Lan Feng, Shi Zong-Jun, Li Da-Zhi, Liang Zheng. Relativistic Cherenkov source with modified photonic band-gap cells. Acta Physica Sinica, 2009, 58(2): 1105-1109. doi: 10.7498/aps.58.1105
[17]	ZHAO DONG-HUAN. ANALYSIS OF EFFECTIVE TIME OF INTERACTION BETWEEN ELECTRON AND RADIATIVE WAVE IN THE FEL. Acta Physica Sinica, 1996, 45(4): 573-579. doi: 10.7498/aps.45.573
[18]	ZHAO DONG-HUAN, LEI SHI-ZHAN. CLASSICAL THEORETICAL ANALYSIS OF RADIATIONS FIELDS IN THE FREE ELECTRON LASER. Acta Physica Sinica, 1996, 45(2): 192-200. doi: 10.7498/aps.45.192
[19]	LIU SHENG-GANG, SUN YAN. A STUDY ON THE RELATIONSHIP BETWEEN THE SPONTANEOUS RADIATION AND THE STIMULATED RADIATION IN TRANSITION RADIATION FREE ELECTRON LASERS. Acta Physica Sinica, 1988, 37(9): 1505-1509. doi: 10.7498/aps.37.1505
[20]	ZHANG YI-BO. STUDY OF RELATIONSHIP BETWEEN SPONTANEOUS RADIATION AND STIMULATED RADIATION IN CERENKOV FREE ELECTRON LASERS. Acta Physica Sinica, 1987, 36(10): 1344-1348. doi: 10.7498/aps.36.1344

Catalog

Vol. 69, Issue 15 - 2020-08-05

Metrics

Abstract views: 10752
PDF Downloads: 422
Cited By: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

Search

Article

留言板