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The unique optical and physical properties of surface plasmon polaritons (SPP) has brought about a series of novel phenomena such as SPP-enhanced transmission, local resonance, etc., and SPP has become a research hotspot around the world. In this paper, the dispersion characteristics and modes of rectangular metal grating based on spoof surface plasmons (SSP) are studied theoretically and numerically. The electromagnetic fields of SSP which are below and above the grating surface are presented using eigenmode expansion method and under periodic boundary conditions, besides the fact that the SSP dispersion relations are obtained by matching the boundary conditions of electromagnetic fields both for rectangular metal grating with roofed metal plate and that without roofed metal plate. Results for these two different cases are given according to numerical calculation and it is found that the roofed metal plate can introduce an additional fast wave mode which is beyond the light line in the dispersion diagram. And the results of analytical SSP dispersion are verified by electromagnetic simulations based on the finite difference method and finite integration method. The dependence of the dispersion characteristics and mode distributions on various parameters of metal grating is studied theoretically. It is shown that the dispersion relations obtained by eigenmode expansion method agree well with the results of electromagnetic simulations. The phase velocity of SSP on the grating surface can be decreased by increasing metal grating depth or decreasing grating period. The bandwidth of electron beam-SSP interaction can be extended by increasing grating period ratio. The influence of the distance between the roofed metal plate and the grating surface on the SSP dispersion is studied and is found that the role of roofed metal plate is insensitive to the slow wave SSP mode. The SSP dispersion and modes for the 3-D metal grating which are extended from the above 2-D SSP dispersion are also given. The SSP symmetric modes and anti-symmetric modes manifest themself alternately in the dispersion diagram on the 3-D grating surface. Compared with the 2-D SSP bound mode without roofed metal plate, it is found that in the 3-D grating structure the slow wave SSP modes and fast wave SSP modes coexist. The 3-D SSP mode with various grating lateral width is studied, and the competition and degeneracy of modes are analyzed particularly. The SSP mode intervals can be enlarged by decreasing the lateral width of the grating, which is optimum for avoiding mode competitions. Studies on dispersion and modes of the 2-D and 3-D metal grating structures based on SSP will lay the foundations for further studies of electron beam-SSP interaction, and development of the novel terahertz vacuum electronic source with high-efficiency and wide-bandwidth.
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Keywords:
- spoof surface plasmons /
- rectangular grating /
- dispersion characteristic /
- mode competition
[1] Barnes W L, Dereux A, Ebbesen T W 2003 Nature 424 824
[2] Pendry J B, Martín-Moreno L, Garcia-Vidal F J 2004 Science 305 847
[3] Wang Z L 2009 Progress in Physics 29 287 (in Chinese) [王振林 2009 物理学进展 29 287]
[4] Gu B Y 2007 Physical Review 36 280 (in Chinese) [顾本源 2007 物理评述 36 280]
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[8] Gramotnev D K, Pile D F P 2004 Appl. Phys. Lett. 85 6323
[9] Moreno E, Rodrigo S G, Bozhevolnyi S I, Martín-Moreno L, Garcia-Vidal F J 2008 Phys. Rev. Lett. 100 023901
[10] Catrysse P B, Veronis G, Shin H, Shen J T, Fan S H 2006 Appl. Phys. Lett. 88 031101
[11] Zhu W Q, Agrawal A, Nahata A 2008 Opt. Express 16 6216
[12] Li J Y, Qiu K S, Ma H Q 2014 Chin. Phys. B 23 106804
[13] Wang Y, He X J, Wu Y M, Wu Q, Mei J S, Li L W, Yang F X, Zhao T, Li L W 2011 Acta Phys. Sin. 60 107301 (in Chinese) [王玥, 贺训军, 吴昱明, 吴群, 梅金硕, 李龙威, 杨福杏, 赵拓, 李乐为 2011 60 107301]
[14] Garcia-Vidal F J, Martín-Moreno L, Pendry J B 2005 J. Opt. A: Pure Appl. Opt. 7 S97
[15] Zayats A V, Smolyaninov I I 2003 J. Opt. A: Pure Appl. Opt. 5 S16
[16] McVey B D, Basten M A, Booske J H, Joe J, Scharer J E 1994 IEEE Trans. Microw. Theory Tech. 42 995
[17] Mehrany K, Rashidian B 2003 IEEE Trans. Elec. Dev. 50 1562
[18] Freund H P, Abu- Elfadl T M 2004 IEEE Trans. Plasmas Sci. 32 1015
[19] Joe J, Louis L J, Scharer J E, Booske J H, Basten M A 1997 Phys. Plasmas 4 2707
[20] Carlsten B E 2002 Phys. Plasmas 9 5088
[21] Joe J, Scharer J, Booske J, McVey B 1994 Phys. Plasmas 1 176
[22] Donohue J T, Gardelle J 2011 Phys. Rev. ST Accel. Beams 14 060709
[23] Cao M M, Liu W X, Wang Y, Li K 2014 Acta Phys. Sin. 63 024101 (in Chinese) [曹苗苗, 刘文鑫, 王勇, 李科 2014 63 024101]
[24] Mineo M, Paoloni C 2010 IEEE Trans. Elec. Dev. 57 1481
[25] Kong L B, Huang C P, Du C H, Liu P K, Yin X G 2015 Sci. Rep. 5 8772
[26] Shin Y M, Barnett L R, Luhmann N C 2009 IEEE Trans. Elec. Dev. 56 706
[27] Shin Y M, Baig A, Barnett L R, Tsai W C, Luhmann N C, 2012 IEEE Trans. Elec. Dev. 59 234
[28] Liu Q L, Wang Z C, Liu P K, Dong F 2012 Acta Phys. Sin. 61 244102 (in Chinese) [刘青伦, 王自成, 刘濮鲲, 董芳 2012 61 244102]
[29] Shen L F, Chen X D, Yang T J 2008 Opt. Express 16 3326
[30] Zhang K Q, Li D J 2001 Electromagnetic Theory for Microwaves and Optoelectronics (The Second Edition) (Beijing: Electronic Industry Press) p405 (in Chinese) [张克潜, 李德杰 2001 微波与光电子学中的电磁理论(第二版) (北京: 电子工业出版社) 第405页]
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[1] Barnes W L, Dereux A, Ebbesen T W 2003 Nature 424 824
[2] Pendry J B, Martín-Moreno L, Garcia-Vidal F J 2004 Science 305 847
[3] Wang Z L 2009 Progress in Physics 29 287 (in Chinese) [王振林 2009 物理学进展 29 287]
[4] Gu B Y 2007 Physical Review 36 280 (in Chinese) [顾本源 2007 物理评述 36 280]
[5] Maier S A, Andrews S R, Martín-Moreno L, Garcia-Vidal F J 2006 Phys. Rev. Lett. 97 176805
[6] Gan Q Q, Fu Z, Ding Y J, Bartoli F J 2008 Phys. Rev. Lett. 100 256803
[7] Li X, Jiang T, Shen L F, Deng X H 2013 Appl. Phys. Lett. 102 031606
[8] Gramotnev D K, Pile D F P 2004 Appl. Phys. Lett. 85 6323
[9] Moreno E, Rodrigo S G, Bozhevolnyi S I, Martín-Moreno L, Garcia-Vidal F J 2008 Phys. Rev. Lett. 100 023901
[10] Catrysse P B, Veronis G, Shin H, Shen J T, Fan S H 2006 Appl. Phys. Lett. 88 031101
[11] Zhu W Q, Agrawal A, Nahata A 2008 Opt. Express 16 6216
[12] Li J Y, Qiu K S, Ma H Q 2014 Chin. Phys. B 23 106804
[13] Wang Y, He X J, Wu Y M, Wu Q, Mei J S, Li L W, Yang F X, Zhao T, Li L W 2011 Acta Phys. Sin. 60 107301 (in Chinese) [王玥, 贺训军, 吴昱明, 吴群, 梅金硕, 李龙威, 杨福杏, 赵拓, 李乐为 2011 60 107301]
[14] Garcia-Vidal F J, Martín-Moreno L, Pendry J B 2005 J. Opt. A: Pure Appl. Opt. 7 S97
[15] Zayats A V, Smolyaninov I I 2003 J. Opt. A: Pure Appl. Opt. 5 S16
[16] McVey B D, Basten M A, Booske J H, Joe J, Scharer J E 1994 IEEE Trans. Microw. Theory Tech. 42 995
[17] Mehrany K, Rashidian B 2003 IEEE Trans. Elec. Dev. 50 1562
[18] Freund H P, Abu- Elfadl T M 2004 IEEE Trans. Plasmas Sci. 32 1015
[19] Joe J, Louis L J, Scharer J E, Booske J H, Basten M A 1997 Phys. Plasmas 4 2707
[20] Carlsten B E 2002 Phys. Plasmas 9 5088
[21] Joe J, Scharer J, Booske J, McVey B 1994 Phys. Plasmas 1 176
[22] Donohue J T, Gardelle J 2011 Phys. Rev. ST Accel. Beams 14 060709
[23] Cao M M, Liu W X, Wang Y, Li K 2014 Acta Phys. Sin. 63 024101 (in Chinese) [曹苗苗, 刘文鑫, 王勇, 李科 2014 63 024101]
[24] Mineo M, Paoloni C 2010 IEEE Trans. Elec. Dev. 57 1481
[25] Kong L B, Huang C P, Du C H, Liu P K, Yin X G 2015 Sci. Rep. 5 8772
[26] Shin Y M, Barnett L R, Luhmann N C 2009 IEEE Trans. Elec. Dev. 56 706
[27] Shin Y M, Baig A, Barnett L R, Tsai W C, Luhmann N C, 2012 IEEE Trans. Elec. Dev. 59 234
[28] Liu Q L, Wang Z C, Liu P K, Dong F 2012 Acta Phys. Sin. 61 244102 (in Chinese) [刘青伦, 王自成, 刘濮鲲, 董芳 2012 61 244102]
[29] Shen L F, Chen X D, Yang T J 2008 Opt. Express 16 3326
[30] Zhang K Q, Li D J 2001 Electromagnetic Theory for Microwaves and Optoelectronics (The Second Edition) (Beijing: Electronic Industry Press) p405 (in Chinese) [张克潜, 李德杰 2001 微波与光电子学中的电磁理论(第二版) (北京: 电子工业出版社) 第405页]
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