电子激励微纳结构的衍射辐射及其在太赫兹中的应用
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摘要
近年来,太赫兹科学技术蓬勃发展,而太赫兹辐射源技术作为其中的关键得到极大重视。本论文将从匀速运动电子激励微纳结构的衍射辐射研究出发,探索一种将电子学与光子学相结合的方法来产生太赫兹辐射,并研究其中出现的一些新的物理现象和机制。
在研究匀速运动电子激励微纳结构产生辐射的过程中,本论文主要研究了如下方面的内容并取得如下结果：
1.本论文探讨了匀速运动电子激励亚波长结构的衍射辐射现象。利用运动电子激励亚波长光栅结构,研究了其产生的双边衍射辐射,结果表明亚波长对称光栅上下半空间的衍射辐射场可以由Smith-Purcell辐射公式来解释,即主要由电子运动速度和光栅周期决定,并分别研究了缝隙宽度、光栅厚度对上下半空间衍射辐射的影响。为进一步研究下半空间的衍射辐射场,采用了非对称的光栅结构,研究表明非对称光栅下半空间衍射辐射场不仅取决于电子运动速度和结构下表面的周期,同时也与电子运动激励起的上半空间的辐射频率范围密切相关。对于运动电子激励亚波长孔阵列结构,本节具体分析了孔阵列的厚度、周期等参数对上下空间衍射辐射的影响。
2.本论文研究了匀速运动电子激励亚波长孔阵列加载介质结构(SHAM)的衍射辐射场。电子掠过阵列表面,激励起了上下表面的表面波,在上半空间其表面波相速始终小于光速,因此该场无法辐射；在下半空间,由于介质的出现,表面波的相速在一定条件下可以大于光速,因此其表面波将转化为辐射场,其中-1次空间谐波将转化为衍射辐射场,零次空间谐波将转化为切伦科夫辐射。并且观察到这两种辐射在下半空间形成干涉现象,出现干涉斑点。亚波长周期结构可以支持很强的表面波,而当周期在10-1000微米时,激发的表面波的频率正好位于太赫兹频段,鉴于表面波的局域特性,将其转化为辐射场可有助于新型太赫兹辐射源的探索研究。本论文研究了基于该机理的太赫兹辐射源,采用周期金属圆环加载介质结构将运动电子激励的表面波转化为切伦科夫辐射,理论分析和仿真相结合进行了详细研究。
3.本论文研究了在电子平行金属表面运动激励的条件下,金属与介质界面的表面等离子体波的色散关系等特性,分别讨论了匀速电子在金属块和金属薄膜上方运动激励表面等离子体波两种情况。并用粒子模拟仿真软件,对理论分析进行了验证。结合金属薄膜加载介质结构中电子激励起的表面等离子体波可以转化为切伦科夫辐射的机制,本论文进行了金属薄膜加载介质结构的具体研究。分析平板类型和圆柱类型的表面等离子体切伦科夫辐射源(SPCLS)。这种源可以产生从可见光到紫外频段的可调谐电磁辐射,辐射功率密度可以达到108W/cm2。并且,它结构小,易于加工,可实现集成,对发展新型光源具有重要的实用价值和意义。
4.本论文研究了电子平行于光栅表面运动产生的衍射辐射,分析验证了基于表面等离子体的Smith-Purcell辐射增强效应。运动电子激励起的表面波,因为它的频率始终低于光栅结构可以辐射的最低频率阀值,所以无法在光栅表面被转化为辐射场,而激励起的表面等离子体波,其频率主要由金属的性质和电子能量决定,通过改变光栅的周期,可以使它的频率满足光栅衍射辐射条件,从而可以转化为辐射场。同时,仿真还发现在光栅表面加载银膜,不仅可以增加Smith-Purcell辐射强度外,还可以提高辐射的方向性。研究对于Smith-Purcell辐射的应用具有重要意义,将有助于基于Smith-Purcell机理的辐射源研究。
Terahertz science and technology is developing rapidly, and the developments of the radiation sources are one of the key researches in this area. In this dissertation, the radiation of the micro-nano stucture excited by moving electrons is studied, and it shows that it is a good promising way to combine the electronics and photonics for the generation of terahertz radiation. Also, some new physical phenomena and mechanism are also studied in this work.
The main achievements are as follows:
1. The diffraction radiation of subwavelength structure is explored, and the two cases are discussed:subwavelength grating and subwavelength holes array. The mechanism and characteristics of diffraction radiation of subwavelength metallic grating structure are analyzed. It shows that the diffraction radiation in the upper half-space and lower half-space can also be explained by the formula of Simth-Purcell radiation. Then, the influences of the gap width and the thickness of the grating to the diffracton radiation are also analyzed. Based on the comparison for the asymmetric grating excited by electrons with different beam energies, the physical mechanism of the diffraction radiation in the lower half-space is discussed in further. Then the diffraction radiation of subwavelength holes array is studied, and the influences of the thickness and period of the array are discussed.
2. Under the excitation of a line current of electron beam, a dielectric medium loading in the lower half space of the sub-wavelength holes array brings essential changes to the diffraction radiation. In the lower half space, the surface wave becomes radiation wave. The fundamental space harmonic is transformed into Cherenkov radiation with unique characteristics and the first negative space harmonic is converted into radiation wave with the angle of Smith-Purcell radiation. Consequently, in the lower half-space the interference happens due to these two kinds of diffraction radiation. The results of the numerical calculations based on the analytical theory agree well with the computer simulation. The subwavelength metal array structure could strongly support surface wave, and the frequency of the surface wave can be changed from microwave to THz by varying the period of the array. When the surface wave can be transformed into radiation wave, the THz radiation could be reasonably generated. A THz radiation source based on this mechanism is analyzed in detail. In the structure of a dielectric medium rod covered by subwavelength metal ring, the electron bunch would excite surface wave on the surface of subwavelength metallic array, and then the surface wave could be transformed into Cherenkov radiation in the dielectric medium.
3. The surface polaritons excited by electrons moving along the metal surface are studied, and the surface polaritons of the bulk metal and metal film are analyzed by numerical calculations and computer simulations. Then, based on the mechanism of that the surface polaritons excited by a uniformly moving electron beam bunch can be transformed into Cherenkov radiation in a structure of nano-scale metal film with dielectric medium loading, the planar structure and cylindrical structure of surface polariton Cherenkov light radiation source (SPCLS) are studied. The results show that SPCLS can generate radiation from visible light to ultraviolet frequency regime and the radiation power density can reach or even excess108W/cm2depending on the beam energy and current density. It is a tunable and miniature light radiation source, and promising to be integrated on chip and able to build up a light radiation source array.
4. With the aid of three-dimensional particle-in-cell code simulation, the enhancement of Smith-Purcell radiation with surface-plasmon excited by electrons is considered. In general, the surface wave excited by electrons lies in the non-radiation region, and the frequency of surface wave is always below the threshold for Smith-Purcell radiation. However, the frequency of the surface-plasmon mode excited by electrons is mainly determined by the beam energy and the metal. It can be larger than the threshold for Smith-Purcell radiation, and then it can be transformed into radiation. In the simulation, the model is a grating covered by an Ag film. The results demonstrate that, when the surface-plasmon mode is excited by electrons, the maximum radiation occurs at an observation angle depending on the surface-plasmon frequency, and the radiation power can be enhanced more than ten times. This work is of significance for developing radiation source based on Smith-Purcell radiation.
在研究匀速运动电子激励微纳结构产生辐射的过程中,本论文主要研究了如下方面的内容并取得如下结果：
1.本论文探讨了匀速运动电子激励亚波长结构的衍射辐射现象。利用运动电子激励亚波长光栅结构,研究了其产生的双边衍射辐射,结果表明亚波长对称光栅上下半空间的衍射辐射场可以由Smith-Purcell辐射公式来解释,即主要由电子运动速度和光栅周期决定,并分别研究了缝隙宽度、光栅厚度对上下半空间衍射辐射的影响。为进一步研究下半空间的衍射辐射场,采用了非对称的光栅结构,研究表明非对称光栅下半空间衍射辐射场不仅取决于电子运动速度和结构下表面的周期,同时也与电子运动激励起的上半空间的辐射频率范围密切相关。对于运动电子激励亚波长孔阵列结构,本节具体分析了孔阵列的厚度、周期等参数对上下空间衍射辐射的影响。
2.本论文研究了匀速运动电子激励亚波长孔阵列加载介质结构(SHAM)的衍射辐射场。电子掠过阵列表面,激励起了上下表面的表面波,在上半空间其表面波相速始终小于光速,因此该场无法辐射；在下半空间,由于介质的出现,表面波的相速在一定条件下可以大于光速,因此其表面波将转化为辐射场,其中-1次空间谐波将转化为衍射辐射场,零次空间谐波将转化为切伦科夫辐射。并且观察到这两种辐射在下半空间形成干涉现象,出现干涉斑点。亚波长周期结构可以支持很强的表面波,而当周期在10-1000微米时,激发的表面波的频率正好位于太赫兹频段,鉴于表面波的局域特性,将其转化为辐射场可有助于新型太赫兹辐射源的探索研究。本论文研究了基于该机理的太赫兹辐射源,采用周期金属圆环加载介质结构将运动电子激励的表面波转化为切伦科夫辐射,理论分析和仿真相结合进行了详细研究。
3.本论文研究了在电子平行金属表面运动激励的条件下,金属与介质界面的表面等离子体波的色散关系等特性,分别讨论了匀速电子在金属块和金属薄膜上方运动激励表面等离子体波两种情况。并用粒子模拟仿真软件,对理论分析进行了验证。结合金属薄膜加载介质结构中电子激励起的表面等离子体波可以转化为切伦科夫辐射的机制,本论文进行了金属薄膜加载介质结构的具体研究。分析平板类型和圆柱类型的表面等离子体切伦科夫辐射源(SPCLS)。这种源可以产生从可见光到紫外频段的可调谐电磁辐射,辐射功率密度可以达到108W/cm2。并且,它结构小,易于加工,可实现集成,对发展新型光源具有重要的实用价值和意义。
4.本论文研究了电子平行于光栅表面运动产生的衍射辐射,分析验证了基于表面等离子体的Smith-Purcell辐射增强效应。运动电子激励起的表面波,因为它的频率始终低于光栅结构可以辐射的最低频率阀值,所以无法在光栅表面被转化为辐射场,而激励起的表面等离子体波,其频率主要由金属的性质和电子能量决定,通过改变光栅的周期,可以使它的频率满足光栅衍射辐射条件,从而可以转化为辐射场。同时,仿真还发现在光栅表面加载银膜,不仅可以增加Smith-Purcell辐射强度外,还可以提高辐射的方向性。研究对于Smith-Purcell辐射的应用具有重要意义,将有助于基于Smith-Purcell机理的辐射源研究。
Terahertz science and technology is developing rapidly, and the developments of the radiation sources are one of the key researches in this area. In this dissertation, the radiation of the micro-nano stucture excited by moving electrons is studied, and it shows that it is a good promising way to combine the electronics and photonics for the generation of terahertz radiation. Also, some new physical phenomena and mechanism are also studied in this work.
The main achievements are as follows:
1. The diffraction radiation of subwavelength structure is explored, and the two cases are discussed:subwavelength grating and subwavelength holes array. The mechanism and characteristics of diffraction radiation of subwavelength metallic grating structure are analyzed. It shows that the diffraction radiation in the upper half-space and lower half-space can also be explained by the formula of Simth-Purcell radiation. Then, the influences of the gap width and the thickness of the grating to the diffracton radiation are also analyzed. Based on the comparison for the asymmetric grating excited by electrons with different beam energies, the physical mechanism of the diffraction radiation in the lower half-space is discussed in further. Then the diffraction radiation of subwavelength holes array is studied, and the influences of the thickness and period of the array are discussed.
2. Under the excitation of a line current of electron beam, a dielectric medium loading in the lower half space of the sub-wavelength holes array brings essential changes to the diffraction radiation. In the lower half space, the surface wave becomes radiation wave. The fundamental space harmonic is transformed into Cherenkov radiation with unique characteristics and the first negative space harmonic is converted into radiation wave with the angle of Smith-Purcell radiation. Consequently, in the lower half-space the interference happens due to these two kinds of diffraction radiation. The results of the numerical calculations based on the analytical theory agree well with the computer simulation. The subwavelength metal array structure could strongly support surface wave, and the frequency of the surface wave can be changed from microwave to THz by varying the period of the array. When the surface wave can be transformed into radiation wave, the THz radiation could be reasonably generated. A THz radiation source based on this mechanism is analyzed in detail. In the structure of a dielectric medium rod covered by subwavelength metal ring, the electron bunch would excite surface wave on the surface of subwavelength metallic array, and then the surface wave could be transformed into Cherenkov radiation in the dielectric medium.
3. The surface polaritons excited by electrons moving along the metal surface are studied, and the surface polaritons of the bulk metal and metal film are analyzed by numerical calculations and computer simulations. Then, based on the mechanism of that the surface polaritons excited by a uniformly moving electron beam bunch can be transformed into Cherenkov radiation in a structure of nano-scale metal film with dielectric medium loading, the planar structure and cylindrical structure of surface polariton Cherenkov light radiation source (SPCLS) are studied. The results show that SPCLS can generate radiation from visible light to ultraviolet frequency regime and the radiation power density can reach or even excess108W/cm2depending on the beam energy and current density. It is a tunable and miniature light radiation source, and promising to be integrated on chip and able to build up a light radiation source array.
4. With the aid of three-dimensional particle-in-cell code simulation, the enhancement of Smith-Purcell radiation with surface-plasmon excited by electrons is considered. In general, the surface wave excited by electrons lies in the non-radiation region, and the frequency of surface wave is always below the threshold for Smith-Purcell radiation. However, the frequency of the surface-plasmon mode excited by electrons is mainly determined by the beam energy and the metal. It can be larger than the threshold for Smith-Purcell radiation, and then it can be transformed into radiation. In the simulation, the model is a grating covered by an Ag film. The results demonstrate that, when the surface-plasmon mode is excited by electrons, the maximum radiation occurs at an observation angle depending on the surface-plasmon frequency, and the radiation power can be enhanced more than ten times. This work is of significance for developing radiation source based on Smith-Purcell radiation.
引文
[1]刘盛纲.太赫兹科学技术的新发展[J].中国基础科学,2006,1：7-12
[2]C. A. Schmuttenmaer. Learning new chemistry and physics with THz light[C]. Infrared and Millimeter Waves and 13th International Conference on Terahertz Electronics,2005,2:401-402
[3]N. Kukutsu, A. Hirata, M. Yaita, et al. Toward practical applications over 100 GHz[C]. IMS2010, Anaheim, US., May 2010
[4]P. H. Siegel. Terahertz technology[J]. IEEE Transactions on Microwave Theory and Techniques, 2002,50(3):910-928
[5]G.L. Carr, M. C. Martin, W. R. McKinney, et al. High-Power terahertz radiation from relativistic electron[J]. Nature,2002,420(6912):153-156
[6]傅文杰,鄢扬,黎晓云,等.二次谐波回旋管0.42THz辐射输出[J].科学通报,2011,28：2380-2382
[7]K. Sakamoto, K. Kajiwara, A. Kasugai, et al. A high-power Gyrotron and high-power mm wave technology for Fusion Reactor[J]. Proceedings of ITC,2008,18:62-66
[8]E. W. McCune and J.A. Ruetz. High-power linear-beam tubes. Proc. IEEE,1973,61:299-330
[9]Gruner G.Millimeter and submillimeter wave spectroscopy of solids[J]. Topics in Applied Physics,1998,74(1):51-109
[10]P. H. Siegel, A. Fung, H. Manohara, et al. Nanoklystron:A monolithic tube approach to THz power generation[C]. Int. Space Terahertz Technol. Symp.,2001,1:81-90
[11]P. U. Jepsen, R. H. Jacobsen, S. R. Keiding. Generation and detection of terahertz pulses from biased semiconductor antennas[J]. J. Opt. Soc.,1996,13(11):2424-2436
[12]X. C. Zhang, B. B. Hu, J. T. Darrow, et al. Generation of femtosecond electromagnetic pulses from semiconductor surfaces[J]. Appl. Phys. Lett.,1990,56(11):1011-1013
[13]E. J. Martinez. Next generation of Terahertz sources and detectors[C]. Proc.11th International Symposium on Space Terahertz Technology, Ann Arbor, Michigan, May 2000
[14]B. S. Williams, S. Kumar, H. Callebaut, et al. Terahertz quantum cascade Laser operating up to 137K[J]. Appl.Phys. Lett.,2003,83(25):5142-5144
[15]R. Kohler, A. Tredicucci, F. Beltram, et al. Terahertz semiconductor-heterostructure laser[J]. Nature,2002,417:156-159
[16]W. M. Lee, Q. Qin, S. Kumar, et al. Real-time terahertz imaging over a standoff distance (> 25 meters) [J]. Appl. Phys. Lett.,2006,89:141125
[17]A. Moreti, A. Bertolini, G. Carelli, et al. The vinyl bromide optically pumped far infrared laser: new large offset emissions[J]. IEEE J. of Quantum Electron.,2001,37:489-493
[18]G. Scalari, C. Walther, J. Faist, et al. Electrically switchable, two-color quantum cascade laser emitting at 1.39 and 2.3 THz[J]. Appl. Phys. Lett.,2006,88:141102
[19]S. Ya. Tochitsky, J. E. Ralph, C. Sung, et al. Generation of megawatt-power terahertz pulses by noncollinear difference-frequency mixing in GaAs[J]. J. of Appl. Phys.,2005,98:026101
[20]S. Ya. Tochitsky, J. E. Ralph, C. Sung, et al. High-power terahertz radiation source based on difference frequency mixing of CO2 laser lines[C]. Conference on Date of Conference,2005,2: 1456-1457
[21]姚建铨,徐德纲.光学太赫兹辐射源[C].学科发展咨询报告,2011
[22]X. L. Wu, S. J. Xiong, Z. Liu, et al. Green light stimulates terahertz emission from mesocrystal microspheres[J]. Nat. nano.,2011,6,103-106
[23]吴培亨,陈健.太赫兹波段的检测[C].第270次香山科学会议,北京,2005
[24]K. L. Wang, D. M. Mittleman. Metal wires for terahertz wave guiding[J]. Nature,2004,432: 376-379
[25]J. B. Pendry, Focus issue:Negative refraction and metamaterials:Introduction[J], Opt. Express, 2003,11:639-639
[26]H. T. Chen, W. J. Padilla, J. M. O. Zide, et al. Active terahertz metamaterial devices [J]. Nature, 2006,444,597-600
[27]H. T. Chen, J. F. O'Hara, A. K. Azad, et al. Experimental demonstration of frequency-agile terahertz metamaterials[J]. Nat. Photon.,2008,2.295-298
[28]刘盛纲.相对论电子学[M].北京：科学出版社,1987,367-403
[29]郭硕鸿.电动力学[M].北京：高等教育出版社,2006,297-337
[30]T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, et al. Extraordinary optical transmission through sub-wavelength hole arrays[J]. Nature,1998,391,667-669
[31]D. E. Grupp, H. J. Lezec, K. M. Pellerin, et al. Fundamental role of metal surface in enhanced transmission through subwavelength apertures[J]. Appl. Phys. Lett.2000,77:1569-1571
[32]Kim, T. Thio. T. W. Ebbesen, D.E. Grupp, et al. Control of optical transmission through metals perforated with subwavelength hole arrays[J]. Opt. Lett.,1999,24:256-258
[33]M. M. J. Treacy, Dynamical diffraction in metallic optical gratings[J], Appl. Phys. Lett. 1999,75:606-608
[34]C. Genet, T. W. Ebbesen. Light in tiny holes[J]. Nature,2007,445(5350):39-46
[35]H. A. Bethe. Theory of diffraction by small holes[J]. Phys. Rev.,1944,66(7&8):163-182
[36]L. Martin-Moreno, F. J. Garica-Vidal, H. J. Lezec, et al. Theory of extraordinary optical transmission through subwavelength hole arrays[J]. Phys. Rev. Lett.,2001,86(6):1114-1117
[37]S. A. Darmanyan, A. V. Zayats. Light tunneling via resonant surface plasmon polariton states and the enhanced transmission of periodically nanostructured metal films:An analytical study[J]. Phys. Rev. B,2003,67(3):035424
[38]Y. Ben-Aryeh. Transmission enhancement by conversion of evanescent waves into propagating waves[J]. Appl. Phys. B:Lasers and Optics,2008,91(1):157-165
[39]B. Hou, J. Mei, M. Ke, et al. Tuning Fabry-Perot resonances via diffraction evanescent waves[J]. Phys. Rev. B,2007,76(5):054303
[40]F. J. Garcia de Abajo, J. J. Saenz, I. Campillo, et al. Site and lattice resonances in metallic hole arrays[J]. Opt. Express,2006,14(1):7-18
[41]D. E. Grupp, H. J. Lezec, T. W. Ebbesen, et al. Crucial role of metal surface in enhanced transmission through subwavelength apertures[J]. Appl. Phys. Lett.,2000,77(11):1569-1571
[42]H.T. Liu & P. Lalanne, Microscopic theory of the extraordinary optical transmission[J]. Nature, 2008,452:728-731.
[43]L. Martin-Moreno and F. J. Garcia-Vidal, Minimal model for optical transmission through holey metal films[J]. J.Phys:Condens. Matter,2008,20:304214
[44]Y. X. Zhang, Y. C. Zhou, L. Dong, et al. Coherent terahertz radiation from high-harmonic component of modulated free-electron beam in a tapered two-asymmetric grating structure[J]. Appl. Phys. Lett.,2012,101:123503
[45]S. G.Liu, M. Hu, Y. X. Zhang, et al. Electromagnetic diffraction radiation of a subwavelength-hole array exited by an electron beam[J]. Phys. Rev. E,2009,80:036602
[46]Y. M. Shin, J. K. So, K. H. Jang, et al. Evanescent tunneling of an effective surface plasmon excited by convection electrons[J]. Phys. Rev. Lett.,2007,99:147402
[47]M. Hu, Y. X. Zhang, Y. Yan, et al. Terahertz radiation from interaction between an electron beam and a planar surface plasmon structure [J]. Chin. Phys. B.,2009,18,3877-3882
[48]Y. X. Zhang, M. Hu, Y. Yan, et al. Terahertz radiation of electron beam-cylindrical mimicking surface plasmon wave interaction[J]. J. Phys. D:Appl. Phys.,2008,42:045211
[49]P. M. Van den Berg, Smith-Purcell radiation from a line charge moving parallel to a reflection grating[J]. J. Opt. Soc. Am.1973,63:689-698
[50]S S.J. mith & E.M. Purcell. Visible light from localized surface charges moving across a grating[J]. Phys. Rev.,1953,92:1069-1069
[51]D. Li & K.. Imasaki, Improvement of grating for Smith-Purcell device[J]. J.TST,2008,1(4): 221-229
[52]曹召良,卢振武,张平,等.红外30μm亚波长抗反射光栅的制作[J].红外与毫米波学报,2004,23(1)：6-10
[53]S. G. Liu, M. Hu, Y. X. Zhang, et al. Electron beam-wave interaction and diffraction radiation in the subwavelength holes array[C]. Invited talk at 2nd SICAST conference, Shenzhen China, 2009
[54]M. Hu, Y. X. Zhang and S. G.Liu. Electromagnetic diffraction of subwavelength holes array[C]. Invited keynote talk at IRMMW-THz, Conference digest of the 33rd International Conference on Infrared and Millimeter Waves and Terahertz. NJ:IEEE, Pusan, Korea,2009,899-900
[55]P. Zhang, Y. X. Zhang, M. Hu, et al. Diffraction radiation of a sub-wavelength hole array with dielectric medium loading[J]. J. Phys. D:Appl. Phys.2012,45:145303.
[56]C. K. Birdsall and A. B. Langdon, Plasma physics via computer simulation[M]. New York: McGraw-Hill,1991
[57]J. Zhou, D. Liu, C. Liao, et al. CHIPIC:An efficient code for electromagnetic PIC modeling and simulation[J]. IEEE Transactions on Plasma Science,2009,37(10):2002-2011
[58]C. Genet, M. P. van Exter, J. P. Woerdman. Huygens description of resonance phenomena in subwavelength hole arrays [J]. J. Opt. Soc. Am. A,2005,22(5):998-1002
[59]V. L. Ginzburg. Radiation by uniformly moving sources (Vavilov-Cherenkov effect, transition radiation and other phenomena) [J]. Physics-Uspekhi,1996,39(10):973-982
[60]P. M. van den Berg. Smith-Purcell radiation from a line charge moving parallel to a reflection grating[J]. J.Opt. Soc. Am.,1973,63:689-698
[61]J. B. Pendry, L. Martin-Moreno, F. J. Garcia-Vidal. Mimicking surface plasmons with structured surfaces[J]. Science,2004,305(5685):847-848
[62]A. P. Hibbins, B. R. Evans, J. R. Sambles. Experimental verification of designer surface plasmons[J]. Science,2005,308(5722):670-672
[63]F. J. Garcia-Vidal, L. Martin-Moreno, J. B. Pendry. Surfaces with holes in them:new plasmonic metamaterials[J]. J. Opt. A:Pure Appl. Opt.,2005,7(2):S97-S101
[64]M. Nazarov, J. L. Coutaz, A. Shkurinov, et al. THz surface plasmon jump between two metal edges[J]. Optics Comm.,2007,277(5):33-39
[65]J. B. Pendry, A. J. Holden, W. J. Stewart, et al. Extremely low frequency plasmons in metallic mesostructures[J]. Phys. Rev. Lett.,1996,76(25):4773-4776
[66]H. Raether. Surface plasmons on smooth and rough surfaces and on gratings[M]. New York: Springer,1988,4-27
[67]R. H. Ritchie. Plasma losses by fast electrons in thin films[J]. Phys. Rev.,1957,106:874-881
[68]W. L. Barnes, A. Dereux, T. W. Ebbesen. Surface plasmon subwavelength optics[J]. Nature, 2003,424(6942):824-830
[69]F. J. Garcia de Abajo, Optical excitations in electron microscopy[J], Rev. Mod. Phys.,2010,82: 209-275
[70]J. Zhou, M. Hu, Y. X. Zhang, et al. Numerical analysis of electron-induced surface plasmon excitation using the FDTD method[J]. Journal of Optics,2011,13(3):035003
[71]W. Cai, R. Sainidou, J. Xu, et al. Efficient generation of propagating plasmons by electron beams[J]. Nano Lett.2009,9:1176-1181
[72]M. N. Zervas. Surface plasmon-polariton waves guided by thin metal fIlm[J]. Opt. Lett.,1991, 16(10),720-722
[73]E.N. Economou, Surface plasmons in thin films[J]. Physical review,1969,182(2):539-554
[74]G.Adamo, K. F. MacDonald, Y. H. Fu, et al. Light well:A tunable free-electron light source on a chip[J]. Phys. Rev. Lett.2009,103:113901
[75]G Adamo, K. F. MacDonald, Y. H. Fu, et al. Tuneable electron-beam-driven nanoscale light source[J]. Journal of optics,2010,12:024012
[76]S. G. Liu, H. Min, Y. X. Zhang, et al. Theoretical investigation of a tunable free-electron light source[J]. Phys. Rev. E,2011,83:066609
[77]A. M. Cook, R. Tikholpav, S. Y. Tochitsky, et al. Observation of narrow-band Terahertz coherent Cherenkov radiation from a cylindrical dielectric-lined waveguide[J]. Phys. Rev. Lett., 2009,103:095003
[78]V. M. Agranovich and D. L. Mills. Surface Polaritons:electromagnetic waves at surfaces and interfaces[M]. Amsterdam New York Oxford:North-Holland publishing company,1982
[79]A. D. Boardman. Electromagnetic surface modes[M]. New York:John Wiley & sons Ltd.,1982
[80]M. L. Brongersma and P. G. Kik, Surface plasmon nanophotonics[M]. Velag Berlin: Springer,2009
[81]P. Drude. Zur Elektronentheorie der metalle[J]. Annalen der physik,1900,306(3):566-613
[82]N. W. Ashcroft and N. D. Mermin. Solid State Physics[M]. NewYork:Holt, Rinehart & Winston,1976
[83]E. D. Palik. Handbook of Optical Constants of Solids[M]. Orlando:Academic press, 1985,135-153
[84]C. Luo, M. Ibanescu, S. G.Johnson, et al. Cerenkov radiation in photonic crystals[J]. Science, 2003,299:368-371
[85]Q. Cao and P. Lalanne. Negative role of surface plasmons in the transmission of metallic gratings with very narrow slits[J]. Phys. Rev. Lett.,2002,88:057403
[86]S. G. Liu, Y. X. Zhang, Y. Yan, et al. Cherenkov radiation by an electron bunch moving in Hermitian medium[J]. J. Appl. Phys.,2007,102:044901
[87]P. A. Cerenkov. Visible radiation produced by electrons moving in a medium with velocities exceeding that of light[J]. Phys.Rev.,1937,52:378-379
[88]I. M. Frank, I. E. Tamm. The coherent radiation of a fast electron in a medium[J]. Dokl. Akad. Nauk SSSR,1937,14:107
[89]M. C. Thompson, H. Badakov, A. M. Cook, et al. Breakdown limits on Gigavolt-per-Meter Electron-Beam-Driven wakefields in dielectric structures[J]. Phys. Rev. Lett.,2008,100: 214801
[90]A. M. Cook, R. Tichoplav, S. Y. Tochitsky, et al. Observation of narrow-band terahertz coherent Cherenkov radiation from a cylindrical dielectric-lined waveguide[J]. Phys. Rev. Lett.,2009, 103:095003
[91]I. V. Konoplev, L. Fisher, A. W. Cross, et al. Surface wave Cherenkov maser based on a periodic lattice[J]. Appl. Phys. Lett.,2010,96:261101
[92]J. G Rivas, M. Kuttge, P. H. Bolivar, et al. Propagation of surface plasmon polaritons on semiconductor gratings[J]. Phys. Rev. Lett.,2004,93:256804
[93]Y. M. Shin, J. K. So, K. H. Won, et al. superradiant terahertz Smith-Purcell radiation from surface plasmon excited by countertreaming electron beams[J]. Appl. Phys. Lett.,2007,90: 031502
[94]S. L. Chuang and J. A. Kong. Enhancement of Smith-Purcell radiation from a grating with surface-plasmon excitation[J]. J.Opt. Soc.Am. A,1984, 1(6):672-676
[95]S. Taga, K. Inafune and E. Sano. Analysis of Smith-Purcell radiation in optical region[J]. Opt. Express,2007,15(24):16222-16229
[96]Andrews H L and Brau C A, Gain of a Smith-Purcell free-electron laser[J]. Phys. Rev. Special Topics,2004,7:070701
[97]A. A. Maragos, Z. C. loannidis, I. G.Tigelis. Dispersion characteristics of a rectangular waveguide grating[J]. IEEE Tran. Plas. Scie.,2003,31(5):1075-1082
[98]P. B. Johnson, and R. W. Christy, Optical constants of the noble metals[J]. Phys. Rev. B,1972, 6(12):4370-4379
[99]A. Vial, A. S. Grimault, D. Macias, et al. Application to the modeling of improved analytical fit of gold dispersion:extinction spectra with a finite-difference time-domain method[J], Phys. Rev. B,2005,71:085416
[100]A. D. Rakic, Algorithm for the determination of intrinsic optical constants of metal films: application to aluminum[J]. Appl. Opt..1995,34(22):4755-4767
[101]A. D.Rakic, A. B. Djurisic, J. M. Elazar, et al. Optical properties of metallic films for Vertical-Cavity optoelectronic devices[J]. Appl. Opt.,1998,37(22):5271-5283
[102]J. Urata, M. Goldstein, M. F. Kimmitt, et al. Superradiant Smith-Purcell emission[J]. Phys. Rev. Lett.,1998,80:516-519
[103]A. Hessel. Resonances in the Smith-Purcell effect[J]. Canadian Journal of Physics,1964,42(6): 1195-1211
[2]C. A. Schmuttenmaer. Learning new chemistry and physics with THz light[C]. Infrared and Millimeter Waves and 13th International Conference on Terahertz Electronics,2005,2:401-402
[3]N. Kukutsu, A. Hirata, M. Yaita, et al. Toward practical applications over 100 GHz[C]. IMS2010, Anaheim, US., May 2010
[4]P. H. Siegel. Terahertz technology[J]. IEEE Transactions on Microwave Theory and Techniques, 2002,50(3):910-928
[5]G.L. Carr, M. C. Martin, W. R. McKinney, et al. High-Power terahertz radiation from relativistic electron[J]. Nature,2002,420(6912):153-156
[6]傅文杰,鄢扬,黎晓云,等.二次谐波回旋管0.42THz辐射输出[J].科学通报,2011,28：2380-2382
[7]K. Sakamoto, K. Kajiwara, A. Kasugai, et al. A high-power Gyrotron and high-power mm wave technology for Fusion Reactor[J]. Proceedings of ITC,2008,18:62-66
[8]E. W. McCune and J.A. Ruetz. High-power linear-beam tubes. Proc. IEEE,1973,61:299-330
[9]Gruner G.Millimeter and submillimeter wave spectroscopy of solids[J]. Topics in Applied Physics,1998,74(1):51-109
[10]P. H. Siegel, A. Fung, H. Manohara, et al. Nanoklystron:A monolithic tube approach to THz power generation[C]. Int. Space Terahertz Technol. Symp.,2001,1:81-90
[11]P. U. Jepsen, R. H. Jacobsen, S. R. Keiding. Generation and detection of terahertz pulses from biased semiconductor antennas[J]. J. Opt. Soc.,1996,13(11):2424-2436
[12]X. C. Zhang, B. B. Hu, J. T. Darrow, et al. Generation of femtosecond electromagnetic pulses from semiconductor surfaces[J]. Appl. Phys. Lett.,1990,56(11):1011-1013
[13]E. J. Martinez. Next generation of Terahertz sources and detectors[C]. Proc.11th International Symposium on Space Terahertz Technology, Ann Arbor, Michigan, May 2000
[14]B. S. Williams, S. Kumar, H. Callebaut, et al. Terahertz quantum cascade Laser operating up to 137K[J]. Appl.Phys. Lett.,2003,83(25):5142-5144
[15]R. Kohler, A. Tredicucci, F. Beltram, et al. Terahertz semiconductor-heterostructure laser[J]. Nature,2002,417:156-159
[16]W. M. Lee, Q. Qin, S. Kumar, et al. Real-time terahertz imaging over a standoff distance (> 25 meters) [J]. Appl. Phys. Lett.,2006,89:141125
[17]A. Moreti, A. Bertolini, G. Carelli, et al. The vinyl bromide optically pumped far infrared laser: new large offset emissions[J]. IEEE J. of Quantum Electron.,2001,37:489-493
[18]G. Scalari, C. Walther, J. Faist, et al. Electrically switchable, two-color quantum cascade laser emitting at 1.39 and 2.3 THz[J]. Appl. Phys. Lett.,2006,88:141102
[19]S. Ya. Tochitsky, J. E. Ralph, C. Sung, et al. Generation of megawatt-power terahertz pulses by noncollinear difference-frequency mixing in GaAs[J]. J. of Appl. Phys.,2005,98:026101
[20]S. Ya. Tochitsky, J. E. Ralph, C. Sung, et al. High-power terahertz radiation source based on difference frequency mixing of CO2 laser lines[C]. Conference on Date of Conference,2005,2: 1456-1457
[21]姚建铨,徐德纲.光学太赫兹辐射源[C].学科发展咨询报告,2011
[22]X. L. Wu, S. J. Xiong, Z. Liu, et al. Green light stimulates terahertz emission from mesocrystal microspheres[J]. Nat. nano.,2011,6,103-106
[23]吴培亨,陈健.太赫兹波段的检测[C].第270次香山科学会议,北京,2005
[24]K. L. Wang, D. M. Mittleman. Metal wires for terahertz wave guiding[J]. Nature,2004,432: 376-379
[25]J. B. Pendry, Focus issue:Negative refraction and metamaterials:Introduction[J], Opt. Express, 2003,11:639-639
[26]H. T. Chen, W. J. Padilla, J. M. O. Zide, et al. Active terahertz metamaterial devices [J]. Nature, 2006,444,597-600
[27]H. T. Chen, J. F. O'Hara, A. K. Azad, et al. Experimental demonstration of frequency-agile terahertz metamaterials[J]. Nat. Photon.,2008,2.295-298
[28]刘盛纲.相对论电子学[M].北京：科学出版社,1987,367-403
[29]郭硕鸿.电动力学[M].北京：高等教育出版社,2006,297-337
[30]T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, et al. Extraordinary optical transmission through sub-wavelength hole arrays[J]. Nature,1998,391,667-669
[31]D. E. Grupp, H. J. Lezec, K. M. Pellerin, et al. Fundamental role of metal surface in enhanced transmission through subwavelength apertures[J]. Appl. Phys. Lett.2000,77:1569-1571
[32]Kim, T. Thio. T. W. Ebbesen, D.E. Grupp, et al. Control of optical transmission through metals perforated with subwavelength hole arrays[J]. Opt. Lett.,1999,24:256-258
[33]M. M. J. Treacy, Dynamical diffraction in metallic optical gratings[J], Appl. Phys. Lett. 1999,75:606-608
[34]C. Genet, T. W. Ebbesen. Light in tiny holes[J]. Nature,2007,445(5350):39-46
[35]H. A. Bethe. Theory of diffraction by small holes[J]. Phys. Rev.,1944,66(7&8):163-182
[36]L. Martin-Moreno, F. J. Garica-Vidal, H. J. Lezec, et al. Theory of extraordinary optical transmission through subwavelength hole arrays[J]. Phys. Rev. Lett.,2001,86(6):1114-1117
[37]S. A. Darmanyan, A. V. Zayats. Light tunneling via resonant surface plasmon polariton states and the enhanced transmission of periodically nanostructured metal films:An analytical study[J]. Phys. Rev. B,2003,67(3):035424
[38]Y. Ben-Aryeh. Transmission enhancement by conversion of evanescent waves into propagating waves[J]. Appl. Phys. B:Lasers and Optics,2008,91(1):157-165
[39]B. Hou, J. Mei, M. Ke, et al. Tuning Fabry-Perot resonances via diffraction evanescent waves[J]. Phys. Rev. B,2007,76(5):054303
[40]F. J. Garcia de Abajo, J. J. Saenz, I. Campillo, et al. Site and lattice resonances in metallic hole arrays[J]. Opt. Express,2006,14(1):7-18
[41]D. E. Grupp, H. J. Lezec, T. W. Ebbesen, et al. Crucial role of metal surface in enhanced transmission through subwavelength apertures[J]. Appl. Phys. Lett.,2000,77(11):1569-1571
[42]H.T. Liu & P. Lalanne, Microscopic theory of the extraordinary optical transmission[J]. Nature, 2008,452:728-731.
[43]L. Martin-Moreno and F. J. Garcia-Vidal, Minimal model for optical transmission through holey metal films[J]. J.Phys:Condens. Matter,2008,20:304214
[44]Y. X. Zhang, Y. C. Zhou, L. Dong, et al. Coherent terahertz radiation from high-harmonic component of modulated free-electron beam in a tapered two-asymmetric grating structure[J]. Appl. Phys. Lett.,2012,101:123503
[45]S. G.Liu, M. Hu, Y. X. Zhang, et al. Electromagnetic diffraction radiation of a subwavelength-hole array exited by an electron beam[J]. Phys. Rev. E,2009,80:036602
[46]Y. M. Shin, J. K. So, K. H. Jang, et al. Evanescent tunneling of an effective surface plasmon excited by convection electrons[J]. Phys. Rev. Lett.,2007,99:147402
[47]M. Hu, Y. X. Zhang, Y. Yan, et al. Terahertz radiation from interaction between an electron beam and a planar surface plasmon structure [J]. Chin. Phys. B.,2009,18,3877-3882
[48]Y. X. Zhang, M. Hu, Y. Yan, et al. Terahertz radiation of electron beam-cylindrical mimicking surface plasmon wave interaction[J]. J. Phys. D:Appl. Phys.,2008,42:045211
[49]P. M. Van den Berg, Smith-Purcell radiation from a line charge moving parallel to a reflection grating[J]. J. Opt. Soc. Am.1973,63:689-698
[50]S S.J. mith & E.M. Purcell. Visible light from localized surface charges moving across a grating[J]. Phys. Rev.,1953,92:1069-1069
[51]D. Li & K.. Imasaki, Improvement of grating for Smith-Purcell device[J]. J.TST,2008,1(4): 221-229
[52]曹召良,卢振武,张平,等.红外30μm亚波长抗反射光栅的制作[J].红外与毫米波学报,2004,23(1)：6-10
[53]S. G. Liu, M. Hu, Y. X. Zhang, et al. Electron beam-wave interaction and diffraction radiation in the subwavelength holes array[C]. Invited talk at 2nd SICAST conference, Shenzhen China, 2009
[54]M. Hu, Y. X. Zhang and S. G.Liu. Electromagnetic diffraction of subwavelength holes array[C]. Invited keynote talk at IRMMW-THz, Conference digest of the 33rd International Conference on Infrared and Millimeter Waves and Terahertz. NJ:IEEE, Pusan, Korea,2009,899-900
[55]P. Zhang, Y. X. Zhang, M. Hu, et al. Diffraction radiation of a sub-wavelength hole array with dielectric medium loading[J]. J. Phys. D:Appl. Phys.2012,45:145303.
[56]C. K. Birdsall and A. B. Langdon, Plasma physics via computer simulation[M]. New York: McGraw-Hill,1991
[57]J. Zhou, D. Liu, C. Liao, et al. CHIPIC:An efficient code for electromagnetic PIC modeling and simulation[J]. IEEE Transactions on Plasma Science,2009,37(10):2002-2011
[58]C. Genet, M. P. van Exter, J. P. Woerdman. Huygens description of resonance phenomena in subwavelength hole arrays [J]. J. Opt. Soc. Am. A,2005,22(5):998-1002
[59]V. L. Ginzburg. Radiation by uniformly moving sources (Vavilov-Cherenkov effect, transition radiation and other phenomena) [J]. Physics-Uspekhi,1996,39(10):973-982
[60]P. M. van den Berg. Smith-Purcell radiation from a line charge moving parallel to a reflection grating[J]. J.Opt. Soc. Am.,1973,63:689-698
[61]J. B. Pendry, L. Martin-Moreno, F. J. Garcia-Vidal. Mimicking surface plasmons with structured surfaces[J]. Science,2004,305(5685):847-848
[62]A. P. Hibbins, B. R. Evans, J. R. Sambles. Experimental verification of designer surface plasmons[J]. Science,2005,308(5722):670-672
[63]F. J. Garcia-Vidal, L. Martin-Moreno, J. B. Pendry. Surfaces with holes in them:new plasmonic metamaterials[J]. J. Opt. A:Pure Appl. Opt.,2005,7(2):S97-S101
[64]M. Nazarov, J. L. Coutaz, A. Shkurinov, et al. THz surface plasmon jump between two metal edges[J]. Optics Comm.,2007,277(5):33-39
[65]J. B. Pendry, A. J. Holden, W. J. Stewart, et al. Extremely low frequency plasmons in metallic mesostructures[J]. Phys. Rev. Lett.,1996,76(25):4773-4776
[66]H. Raether. Surface plasmons on smooth and rough surfaces and on gratings[M]. New York: Springer,1988,4-27
[67]R. H. Ritchie. Plasma losses by fast electrons in thin films[J]. Phys. Rev.,1957,106:874-881
[68]W. L. Barnes, A. Dereux, T. W. Ebbesen. Surface plasmon subwavelength optics[J]. Nature, 2003,424(6942):824-830
[69]F. J. Garcia de Abajo, Optical excitations in electron microscopy[J], Rev. Mod. Phys.,2010,82: 209-275
[70]J. Zhou, M. Hu, Y. X. Zhang, et al. Numerical analysis of electron-induced surface plasmon excitation using the FDTD method[J]. Journal of Optics,2011,13(3):035003
[71]W. Cai, R. Sainidou, J. Xu, et al. Efficient generation of propagating plasmons by electron beams[J]. Nano Lett.2009,9:1176-1181
[72]M. N. Zervas. Surface plasmon-polariton waves guided by thin metal fIlm[J]. Opt. Lett.,1991, 16(10),720-722
[73]E.N. Economou, Surface plasmons in thin films[J]. Physical review,1969,182(2):539-554
[74]G.Adamo, K. F. MacDonald, Y. H. Fu, et al. Light well:A tunable free-electron light source on a chip[J]. Phys. Rev. Lett.2009,103:113901
[75]G Adamo, K. F. MacDonald, Y. H. Fu, et al. Tuneable electron-beam-driven nanoscale light source[J]. Journal of optics,2010,12:024012
[76]S. G. Liu, H. Min, Y. X. Zhang, et al. Theoretical investigation of a tunable free-electron light source[J]. Phys. Rev. E,2011,83:066609
[77]A. M. Cook, R. Tikholpav, S. Y. Tochitsky, et al. Observation of narrow-band Terahertz coherent Cherenkov radiation from a cylindrical dielectric-lined waveguide[J]. Phys. Rev. Lett., 2009,103:095003
[78]V. M. Agranovich and D. L. Mills. Surface Polaritons:electromagnetic waves at surfaces and interfaces[M]. Amsterdam New York Oxford:North-Holland publishing company,1982
[79]A. D. Boardman. Electromagnetic surface modes[M]. New York:John Wiley & sons Ltd.,1982
[80]M. L. Brongersma and P. G. Kik, Surface plasmon nanophotonics[M]. Velag Berlin: Springer,2009
[81]P. Drude. Zur Elektronentheorie der metalle[J]. Annalen der physik,1900,306(3):566-613
[82]N. W. Ashcroft and N. D. Mermin. Solid State Physics[M]. NewYork:Holt, Rinehart & Winston,1976
[83]E. D. Palik. Handbook of Optical Constants of Solids[M]. Orlando:Academic press, 1985,135-153
[84]C. Luo, M. Ibanescu, S. G.Johnson, et al. Cerenkov radiation in photonic crystals[J]. Science, 2003,299:368-371
[85]Q. Cao and P. Lalanne. Negative role of surface plasmons in the transmission of metallic gratings with very narrow slits[J]. Phys. Rev. Lett.,2002,88:057403
[86]S. G. Liu, Y. X. Zhang, Y. Yan, et al. Cherenkov radiation by an electron bunch moving in Hermitian medium[J]. J. Appl. Phys.,2007,102:044901
[87]P. A. Cerenkov. Visible radiation produced by electrons moving in a medium with velocities exceeding that of light[J]. Phys.Rev.,1937,52:378-379
[88]I. M. Frank, I. E. Tamm. The coherent radiation of a fast electron in a medium[J]. Dokl. Akad. Nauk SSSR,1937,14:107
[89]M. C. Thompson, H. Badakov, A. M. Cook, et al. Breakdown limits on Gigavolt-per-Meter Electron-Beam-Driven wakefields in dielectric structures[J]. Phys. Rev. Lett.,2008,100: 214801
[90]A. M. Cook, R. Tichoplav, S. Y. Tochitsky, et al. Observation of narrow-band terahertz coherent Cherenkov radiation from a cylindrical dielectric-lined waveguide[J]. Phys. Rev. Lett.,2009, 103:095003
[91]I. V. Konoplev, L. Fisher, A. W. Cross, et al. Surface wave Cherenkov maser based on a periodic lattice[J]. Appl. Phys. Lett.,2010,96:261101
[92]J. G Rivas, M. Kuttge, P. H. Bolivar, et al. Propagation of surface plasmon polaritons on semiconductor gratings[J]. Phys. Rev. Lett.,2004,93:256804
[93]Y. M. Shin, J. K. So, K. H. Won, et al. superradiant terahertz Smith-Purcell radiation from surface plasmon excited by countertreaming electron beams[J]. Appl. Phys. Lett.,2007,90: 031502
[94]S. L. Chuang and J. A. Kong. Enhancement of Smith-Purcell radiation from a grating with surface-plasmon excitation[J]. J.Opt. Soc.Am. A,1984, 1(6):672-676
[95]S. Taga, K. Inafune and E. Sano. Analysis of Smith-Purcell radiation in optical region[J]. Opt. Express,2007,15(24):16222-16229
[96]Andrews H L and Brau C A, Gain of a Smith-Purcell free-electron laser[J]. Phys. Rev. Special Topics,2004,7:070701
[97]A. A. Maragos, Z. C. loannidis, I. G.Tigelis. Dispersion characteristics of a rectangular waveguide grating[J]. IEEE Tran. Plas. Scie.,2003,31(5):1075-1082
[98]P. B. Johnson, and R. W. Christy, Optical constants of the noble metals[J]. Phys. Rev. B,1972, 6(12):4370-4379
[99]A. Vial, A. S. Grimault, D. Macias, et al. Application to the modeling of improved analytical fit of gold dispersion:extinction spectra with a finite-difference time-domain method[J], Phys. Rev. B,2005,71:085416
[100]A. D. Rakic, Algorithm for the determination of intrinsic optical constants of metal films: application to aluminum[J]. Appl. Opt..1995,34(22):4755-4767
[101]A. D.Rakic, A. B. Djurisic, J. M. Elazar, et al. Optical properties of metallic films for Vertical-Cavity optoelectronic devices[J]. Appl. Opt.,1998,37(22):5271-5283
[102]J. Urata, M. Goldstein, M. F. Kimmitt, et al. Superradiant Smith-Purcell emission[J]. Phys. Rev. Lett.,1998,80:516-519
[103]A. Hessel. Resonances in the Smith-Purcell effect[J]. Canadian Journal of Physics,1964,42(6): 1195-1211