Abstract

This paper presents the studies on the enhanced coherent THz Smith-Purcell superradiation excited by two pre-bunched electron beams that pass through the 1-D sub-wavelength holes array. The Smith-Purcell superradiation has been clearly observed. The radiation emitting out from the system has the radiation angle matching the 2nd harmonic frequency component of the pre-bunched electron beams. The results show that the two electron beams can be coupled with each other through the holes array so that the intensity of the radiated field has been enhanced about twice higher than that excited by one electron beam. Consequently superradiation at the frequency of 0.62 THz can be generated with 20A/cm2 current density of electron beam based on above mechanism. The advantages of low injection current density and 2nd harmonic radiation promise the potential applications in the development of electron-beam driven THz sources.

© 2012 OSA

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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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  21. H. J. Lezec and T. Thio, “Diffracted evanescent wave model for enhanced and suppressed optical transmission through subwavelength hole arrays,” Opt. Express 12(16), 3629–3651 (2004).
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    [CrossRef] [PubMed]
  23. F. J. García de Abajo, R. Gómez-Medina, and J. J. Sáenz, “Full transmission through perfect-conductor subwavelength hole arrays,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 72(1), 016608 (2005).
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    [CrossRef]

2011

S. G. Liu, M. Hu, Y. X. Zhang, W. Liu, P. Zhang, and J. Zhou, “Theoretical investigation of a tunable free-electron light source,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 83(6), 066609 (2011).
[CrossRef] [PubMed]

J. T. Donohue and J. Gardelle, “Simulation of a Smith-Purcell free-electron laser with sidewalls: copious emission at the fundamental frequency,” Appl. Phys. Lett. 99(16), 161112 (2011).
[CrossRef]

J. Xu and X. D. Zhang, “Negative electron energy loss and second-harmonic emission of nonlinear nanoparticles,” Opt. Express 19(23), 22999–23007 (2011).
[CrossRef] [PubMed]

2010

C. Prokop, P. Piot, M. C. Lin, and P. Stoltz, “Numerical modeling of a table-top tunable Smith–Purcell terahertz free-electron laser operating in the super-radiant regime,” Appl. Phys. Lett. 96(15), 151502 (2010).
[CrossRef]

2009

S. G. Liu, M. Hu, Y. X. Zhang, Y. B. Li, and R. B. Zhong, “Electromagnetic diffraction radiation of a subwavelength-hole array excited by an electron beam,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 80(3), 036602 (2009).
[CrossRef] [PubMed]

Z. Shi, Z. Yang, F. Lan, X. Gao, Z. Liang, and D. Li, “Coherent terahertz Smith–Purcell radiation from a two-section model,” Nucl. Instrum. Methods Phys. Res. A 607(2), 367–371 (2009).
[CrossRef]

J. Zhou, D. Liu, C. Liao, and Z. Li, “CHIPIC: An efficient code for electromagnetic PIC modeling and dimulation,” IEEE Trans. Plasma Sci. 37(10), 2002–2011 (2009).
[CrossRef]

2008

Y. Li and K. J. Kim, “Nonrelativistic electron bunch train for coherently enhanced terahertz radiation sources,” Appl. Phys. Lett. 92, 014101 (2008).
[CrossRef]

2007

Y. M. Shin, J. K. So, K. H. Jang, J. H. Won, A. Srivastava, and G. S. Park, “Superradiant terahertz Smith-Purcell radiation from surface plasmon excited by counterstreaming electron beam,” Appl. Phys. Lett. 90, 031502 (2007).
[CrossRef]

Y. M. Shin, J. K. So, K. H. Jang, J. H. Won, A. Srivastava, and G. S. Park, “Evanescent tunneling of an effective surface plasmon excited by convection electrons,” Phys. Rev. Lett. 99(14), 147402 (2007).
[CrossRef] [PubMed]

S. Taga, K. Inafune, and E. Sano, “Analysis of Smith-Purcell radiation in optical region,” Opt. Express 15(24), 16222–16229 (2007).
[CrossRef] [PubMed]

2006

C. A. Flory, “Analysis of super-radiant Smith-Purcell emission,” J. Appl. Phys. 99(5), 054903 (2006).
[CrossRef]

D. Li, Z. Yang, K. Imasaki, and G. S. Park, “Particle-in-cell simulation of coherent and superradiant Smith-Purcell radiation,” Phys. Rev. ST Accel. Beams 9(4), 040701 (2006).
[CrossRef]

D. Li, K. Imasaki, Z. Yang, and G. S. Park, “Three-dimensional simulation of super-radiation Smith-Purcell radiation,” Appl. Phys. Lett. 88(20), 201501 (2006).
[CrossRef]

2005

S. E. Korbly, A. S. Kesar, J. R. Sirigiri, and R. J. Temkin, “Observation of frequency-locked coherent terahertz Smith-Purcell radiation,” Phys. Rev. Lett. 94(5), 054803 (2005).
[CrossRef] [PubMed]

J. T. Donohue, “Simulation of Smith-Purcell radiation using a particle-in-cell code,” Phys. Rev. ST Accel. Beams 8, 060702 (2005).

F. J. García de Abajo, R. Gómez-Medina, and J. J. Sáenz, “Full transmission through perfect-conductor subwavelength hole arrays,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 72(1), 016608 (2005).
[CrossRef] [PubMed]

2004

H. J. Lezec and T. Thio, “Diffracted evanescent wave model for enhanced and suppressed optical transmission through subwavelength hole arrays,” Opt. Express 12(16), 3629–3651 (2004).
[CrossRef] [PubMed]

K. J. Koerkamp, S. Enoch, F. B. Segerink, N. F. van Hulst, and L. Kuipers, “Strong influence of hole shape on extraordinary transmission through periodic arrays of subwavelength holes,” Phys. Rev. Lett. 92(18), 183901 (2004).
[CrossRef] [PubMed]

J. B. Pendry, L. Martín-Moreno, and F. J. Garcia-Vidal, “Mimicking surface plasmons with structured surfaces,” Science 305(5685), 847–848 (2004).
[CrossRef] [PubMed]

1998

T. W. Ebbesen, H. J. Lezec, and H. F. Ghaeml, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391(6668), 667–669 (1998).
[CrossRef]

1966

K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell's equations in isotropic media,” IEEE Trans. Antenn. Propag. 14(3), 302–307 (1966).
[CrossRef]

1953

S. J. Smith and E. M. Purcell, “visible light from localized surface charges moving across a grating,” Phys. Rev. 92(4), 1069–1070 (1953).
[CrossRef]

Donohue, J. T.

J. T. Donohue and J. Gardelle, “Simulation of a Smith-Purcell free-electron laser with sidewalls: copious emission at the fundamental frequency,” Appl. Phys. Lett. 99(16), 161112 (2011).
[CrossRef]

J. T. Donohue, “Simulation of Smith-Purcell radiation using a particle-in-cell code,” Phys. Rev. ST Accel. Beams 8, 060702 (2005).

Ebbesen, T. W.

T. W. Ebbesen, H. J. Lezec, and H. F. Ghaeml, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391(6668), 667–669 (1998).
[CrossRef]

Enoch, S.

K. J. Koerkamp, S. Enoch, F. B. Segerink, N. F. van Hulst, and L. Kuipers, “Strong influence of hole shape on extraordinary transmission through periodic arrays of subwavelength holes,” Phys. Rev. Lett. 92(18), 183901 (2004).
[CrossRef] [PubMed]

Flory, C. A.

C. A. Flory, “Analysis of super-radiant Smith-Purcell emission,” J. Appl. Phys. 99(5), 054903 (2006).
[CrossRef]

Gao, X.

Z. Shi, Z. Yang, F. Lan, X. Gao, Z. Liang, and D. Li, “Coherent terahertz Smith–Purcell radiation from a two-section model,” Nucl. Instrum. Methods Phys. Res. A 607(2), 367–371 (2009).
[CrossRef]

García de Abajo, F. J.

F. J. García de Abajo, R. Gómez-Medina, and J. J. Sáenz, “Full transmission through perfect-conductor subwavelength hole arrays,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 72(1), 016608 (2005).
[CrossRef] [PubMed]

Garcia-Vidal, F. J.

J. B. Pendry, L. Martín-Moreno, and F. J. Garcia-Vidal, “Mimicking surface plasmons with structured surfaces,” Science 305(5685), 847–848 (2004).
[CrossRef] [PubMed]

Gardelle, J.

J. T. Donohue and J. Gardelle, “Simulation of a Smith-Purcell free-electron laser with sidewalls: copious emission at the fundamental frequency,” Appl. Phys. Lett. 99(16), 161112 (2011).
[CrossRef]

Ghaeml, H. F.

T. W. Ebbesen, H. J. Lezec, and H. F. Ghaeml, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391(6668), 667–669 (1998).
[CrossRef]

Gómez-Medina, R.

F. J. García de Abajo, R. Gómez-Medina, and J. J. Sáenz, “Full transmission through perfect-conductor subwavelength hole arrays,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 72(1), 016608 (2005).
[CrossRef] [PubMed]

Hu, M.

S. G. Liu, M. Hu, Y. X. Zhang, W. Liu, P. Zhang, and J. Zhou, “Theoretical investigation of a tunable free-electron light source,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 83(6), 066609 (2011).
[CrossRef] [PubMed]

S. G. Liu, M. Hu, Y. X. Zhang, Y. B. Li, and R. B. Zhong, “Electromagnetic diffraction radiation of a subwavelength-hole array excited by an electron beam,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 80(3), 036602 (2009).
[CrossRef] [PubMed]

Imasaki, K.

D. Li, Z. Yang, K. Imasaki, and G. S. Park, “Particle-in-cell simulation of coherent and superradiant Smith-Purcell radiation,” Phys. Rev. ST Accel. Beams 9(4), 040701 (2006).
[CrossRef]

D. Li, K. Imasaki, Z. Yang, and G. S. Park, “Three-dimensional simulation of super-radiation Smith-Purcell radiation,” Appl. Phys. Lett. 88(20), 201501 (2006).
[CrossRef]

Inafune, K.

Jang, K. H.

Y. M. Shin, J. K. So, K. H. Jang, J. H. Won, A. Srivastava, and G. S. Park, “Superradiant terahertz Smith-Purcell radiation from surface plasmon excited by counterstreaming electron beam,” Appl. Phys. Lett. 90, 031502 (2007).
[CrossRef]

Y. M. Shin, J. K. So, K. H. Jang, J. H. Won, A. Srivastava, and G. S. Park, “Evanescent tunneling of an effective surface plasmon excited by convection electrons,” Phys. Rev. Lett. 99(14), 147402 (2007).
[CrossRef] [PubMed]

Kesar, A. S.

S. E. Korbly, A. S. Kesar, J. R. Sirigiri, and R. J. Temkin, “Observation of frequency-locked coherent terahertz Smith-Purcell radiation,” Phys. Rev. Lett. 94(5), 054803 (2005).
[CrossRef] [PubMed]

Kim, K. J.

Y. Li and K. J. Kim, “Nonrelativistic electron bunch train for coherently enhanced terahertz radiation sources,” Appl. Phys. Lett. 92, 014101 (2008).
[CrossRef]

Koerkamp, K. J.

K. J. Koerkamp, S. Enoch, F. B. Segerink, N. F. van Hulst, and L. Kuipers, “Strong influence of hole shape on extraordinary transmission through periodic arrays of subwavelength holes,” Phys. Rev. Lett. 92(18), 183901 (2004).
[CrossRef] [PubMed]

Korbly, S. E.

S. E. Korbly, A. S. Kesar, J. R. Sirigiri, and R. J. Temkin, “Observation of frequency-locked coherent terahertz Smith-Purcell radiation,” Phys. Rev. Lett. 94(5), 054803 (2005).
[CrossRef] [PubMed]

Kuipers, L.

K. J. Koerkamp, S. Enoch, F. B. Segerink, N. F. van Hulst, and L. Kuipers, “Strong influence of hole shape on extraordinary transmission through periodic arrays of subwavelength holes,” Phys. Rev. Lett. 92(18), 183901 (2004).
[CrossRef] [PubMed]

Lan, F.

Z. Shi, Z. Yang, F. Lan, X. Gao, Z. Liang, and D. Li, “Coherent terahertz Smith–Purcell radiation from a two-section model,” Nucl. Instrum. Methods Phys. Res. A 607(2), 367–371 (2009).
[CrossRef]

Lezec, H. J.

H. J. Lezec and T. Thio, “Diffracted evanescent wave model for enhanced and suppressed optical transmission through subwavelength hole arrays,” Opt. Express 12(16), 3629–3651 (2004).
[CrossRef] [PubMed]

T. W. Ebbesen, H. J. Lezec, and H. F. Ghaeml, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391(6668), 667–669 (1998).
[CrossRef]

Li, D.

Z. Shi, Z. Yang, F. Lan, X. Gao, Z. Liang, and D. Li, “Coherent terahertz Smith–Purcell radiation from a two-section model,” Nucl. Instrum. Methods Phys. Res. A 607(2), 367–371 (2009).
[CrossRef]

D. Li, K. Imasaki, Z. Yang, and G. S. Park, “Three-dimensional simulation of super-radiation Smith-Purcell radiation,” Appl. Phys. Lett. 88(20), 201501 (2006).
[CrossRef]

D. Li, Z. Yang, K. Imasaki, and G. S. Park, “Particle-in-cell simulation of coherent and superradiant Smith-Purcell radiation,” Phys. Rev. ST Accel. Beams 9(4), 040701 (2006).
[CrossRef]

Li, Y.

Y. Li and K. J. Kim, “Nonrelativistic electron bunch train for coherently enhanced terahertz radiation sources,” Appl. Phys. Lett. 92, 014101 (2008).
[CrossRef]

Li, Y. B.

S. G. Liu, M. Hu, Y. X. Zhang, Y. B. Li, and R. B. Zhong, “Electromagnetic diffraction radiation of a subwavelength-hole array excited by an electron beam,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 80(3), 036602 (2009).
[CrossRef] [PubMed]

Li, Z.

J. Zhou, D. Liu, C. Liao, and Z. Li, “CHIPIC: An efficient code for electromagnetic PIC modeling and dimulation,” IEEE Trans. Plasma Sci. 37(10), 2002–2011 (2009).
[CrossRef]

Liang, Z.

Z. Shi, Z. Yang, F. Lan, X. Gao, Z. Liang, and D. Li, “Coherent terahertz Smith–Purcell radiation from a two-section model,” Nucl. Instrum. Methods Phys. Res. A 607(2), 367–371 (2009).
[CrossRef]

Liao, C.

J. Zhou, D. Liu, C. Liao, and Z. Li, “CHIPIC: An efficient code for electromagnetic PIC modeling and dimulation,” IEEE Trans. Plasma Sci. 37(10), 2002–2011 (2009).
[CrossRef]

Lin, M. C.

C. Prokop, P. Piot, M. C. Lin, and P. Stoltz, “Numerical modeling of a table-top tunable Smith–Purcell terahertz free-electron laser operating in the super-radiant regime,” Appl. Phys. Lett. 96(15), 151502 (2010).
[CrossRef]

Liu, D.

J. Zhou, D. Liu, C. Liao, and Z. Li, “CHIPIC: An efficient code for electromagnetic PIC modeling and dimulation,” IEEE Trans. Plasma Sci. 37(10), 2002–2011 (2009).
[CrossRef]

Liu, S. G.

S. G. Liu, M. Hu, Y. X. Zhang, W. Liu, P. Zhang, and J. Zhou, “Theoretical investigation of a tunable free-electron light source,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 83(6), 066609 (2011).
[CrossRef] [PubMed]

S. G. Liu, M. Hu, Y. X. Zhang, Y. B. Li, and R. B. Zhong, “Electromagnetic diffraction radiation of a subwavelength-hole array excited by an electron beam,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 80(3), 036602 (2009).
[CrossRef] [PubMed]

Liu, W.

S. G. Liu, M. Hu, Y. X. Zhang, W. Liu, P. Zhang, and J. Zhou, “Theoretical investigation of a tunable free-electron light source,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 83(6), 066609 (2011).
[CrossRef] [PubMed]

Martín-Moreno, L.

J. B. Pendry, L. Martín-Moreno, and F. J. Garcia-Vidal, “Mimicking surface plasmons with structured surfaces,” Science 305(5685), 847–848 (2004).
[CrossRef] [PubMed]

Park, G. S.

Y. M. Shin, J. K. So, K. H. Jang, J. H. Won, A. Srivastava, and G. S. Park, “Superradiant terahertz Smith-Purcell radiation from surface plasmon excited by counterstreaming electron beam,” Appl. Phys. Lett. 90, 031502 (2007).
[CrossRef]

Y. M. Shin, J. K. So, K. H. Jang, J. H. Won, A. Srivastava, and G. S. Park, “Evanescent tunneling of an effective surface plasmon excited by convection electrons,” Phys. Rev. Lett. 99(14), 147402 (2007).
[CrossRef] [PubMed]

D. Li, Z. Yang, K. Imasaki, and G. S. Park, “Particle-in-cell simulation of coherent and superradiant Smith-Purcell radiation,” Phys. Rev. ST Accel. Beams 9(4), 040701 (2006).
[CrossRef]

D. Li, K. Imasaki, Z. Yang, and G. S. Park, “Three-dimensional simulation of super-radiation Smith-Purcell radiation,” Appl. Phys. Lett. 88(20), 201501 (2006).
[CrossRef]

Pendry, J. B.

J. B. Pendry, L. Martín-Moreno, and F. J. Garcia-Vidal, “Mimicking surface plasmons with structured surfaces,” Science 305(5685), 847–848 (2004).
[CrossRef] [PubMed]

Piot, P.

C. Prokop, P. Piot, M. C. Lin, and P. Stoltz, “Numerical modeling of a table-top tunable Smith–Purcell terahertz free-electron laser operating in the super-radiant regime,” Appl. Phys. Lett. 96(15), 151502 (2010).
[CrossRef]

Prokop, C.

C. Prokop, P. Piot, M. C. Lin, and P. Stoltz, “Numerical modeling of a table-top tunable Smith–Purcell terahertz free-electron laser operating in the super-radiant regime,” Appl. Phys. Lett. 96(15), 151502 (2010).
[CrossRef]

Purcell, E. M.

S. J. Smith and E. M. Purcell, “visible light from localized surface charges moving across a grating,” Phys. Rev. 92(4), 1069–1070 (1953).
[CrossRef]

Sáenz, J. J.

F. J. García de Abajo, R. Gómez-Medina, and J. J. Sáenz, “Full transmission through perfect-conductor subwavelength hole arrays,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 72(1), 016608 (2005).
[CrossRef] [PubMed]

Sano, E.

Segerink, F. B.

K. J. Koerkamp, S. Enoch, F. B. Segerink, N. F. van Hulst, and L. Kuipers, “Strong influence of hole shape on extraordinary transmission through periodic arrays of subwavelength holes,” Phys. Rev. Lett. 92(18), 183901 (2004).
[CrossRef] [PubMed]

Shi, Z.

Z. Shi, Z. Yang, F. Lan, X. Gao, Z. Liang, and D. Li, “Coherent terahertz Smith–Purcell radiation from a two-section model,” Nucl. Instrum. Methods Phys. Res. A 607(2), 367–371 (2009).
[CrossRef]

Shin, Y. M.

Y. M. Shin, J. K. So, K. H. Jang, J. H. Won, A. Srivastava, and G. S. Park, “Superradiant terahertz Smith-Purcell radiation from surface plasmon excited by counterstreaming electron beam,” Appl. Phys. Lett. 90, 031502 (2007).
[CrossRef]

Y. M. Shin, J. K. So, K. H. Jang, J. H. Won, A. Srivastava, and G. S. Park, “Evanescent tunneling of an effective surface plasmon excited by convection electrons,” Phys. Rev. Lett. 99(14), 147402 (2007).
[CrossRef] [PubMed]

Sirigiri, J. R.

S. E. Korbly, A. S. Kesar, J. R. Sirigiri, and R. J. Temkin, “Observation of frequency-locked coherent terahertz Smith-Purcell radiation,” Phys. Rev. Lett. 94(5), 054803 (2005).
[CrossRef] [PubMed]

Smith, S. J.

S. J. Smith and E. M. Purcell, “visible light from localized surface charges moving across a grating,” Phys. Rev. 92(4), 1069–1070 (1953).
[CrossRef]

So, J. K.

Y. M. Shin, J. K. So, K. H. Jang, J. H. Won, A. Srivastava, and G. S. Park, “Superradiant terahertz Smith-Purcell radiation from surface plasmon excited by counterstreaming electron beam,” Appl. Phys. Lett. 90, 031502 (2007).
[CrossRef]

Y. M. Shin, J. K. So, K. H. Jang, J. H. Won, A. Srivastava, and G. S. Park, “Evanescent tunneling of an effective surface plasmon excited by convection electrons,” Phys. Rev. Lett. 99(14), 147402 (2007).
[CrossRef] [PubMed]

Srivastava, A.

Y. M. Shin, J. K. So, K. H. Jang, J. H. Won, A. Srivastava, and G. S. Park, “Evanescent tunneling of an effective surface plasmon excited by convection electrons,” Phys. Rev. Lett. 99(14), 147402 (2007).
[CrossRef] [PubMed]

Y. M. Shin, J. K. So, K. H. Jang, J. H. Won, A. Srivastava, and G. S. Park, “Superradiant terahertz Smith-Purcell radiation from surface plasmon excited by counterstreaming electron beam,” Appl. Phys. Lett. 90, 031502 (2007).
[CrossRef]

Stoltz, P.

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Zhang, Y. X.

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S. G. Liu, M. Hu, Y. X. Zhang, Y. B. Li, and R. B. Zhong, “Electromagnetic diffraction radiation of a subwavelength-hole array excited by an electron beam,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 80(3), 036602 (2009).
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[CrossRef]

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[CrossRef] [PubMed]

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[CrossRef] [PubMed]

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[CrossRef] [PubMed]

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D. Li, Z. Yang, K. Imasaki, and G. S. Park, “Particle-in-cell simulation of coherent and superradiant Smith-Purcell radiation,” Phys. Rev. ST Accel. Beams 9(4), 040701 (2006).
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Figures (8)

Fig. 1
Fig. 1

(a) The 3-D geometry. (b) the 2-D sketch map.(c) the Smith-Purcell radiation when two electron bunches pass close over the holes array.(d) the comparison of theoretical SP law and simulation results.

Fig. 2
Fig. 2

(a) the structure of bi-grating (b) dispersion Brillouin diagram: the blue line is the calculated dispersion curve of the bi-grating, the red cross line is the beam line with beam energy 50kV and the point P is the interaction point of the dispersion curve. The area between P1 and P2 is the radiation area of the SHA.

Fig. 3
Fig. 3

Simulation of interaction in bi-grating structure.(a)The e-beams phasespace in bi-grating. (b)The time evolution of the electric field Ez(t). (c)The associated FFT of the Ez(t). (d)The contour map of Ez.

Fig. 4
Fig. 4

The simulation model of superradiation excited by ideal periodical electron bunches

Fig. 5
Fig. 5

The simulation results of ideal electron beam bunches superradiation.(a)Distribution of superradiation frequency and it’s Bx(t) field amplitude.(b)Contour map when the periodic electron bunches passing over the 1-D holes array.(c)Time evolution of the Ez(t) field at the radiation angle and associated FFT.

Fig. 6
Fig. 6

The simulation model of superradiation in the whole system

Fig. 7
Fig. 7

The simulation results of two pre-bunched electron beams superradiation. (a).The process of two well bunched electron beam passing over the 1-D holes array. (b)The contour map at 4.245ns when bunched electron beam passing over the holes array.(c)Time evolution of the Ey(t) field at the radiation angle and associated FFT.

Fig. 8
Fig. 8

(a) the comparison of the intensites of Ez(t) field excited by one pre-bunched beam and two beams (b) contour map of the field in the holes array (c) the frequency spectrum of radiation excited by one beam (d) the frequency spectrum of radiation excited by two beams

Tables (1)

Tables Icon

Table 1 Main parameters of the simulation

Equations (5)

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λ=L/| n |(1/βcosθ)
E z Ι =Q Ι sin k cx ( A 2 + D 1 x) sin k cx ( A 2 + D 1 ) sin( k y y); H y Ι = jωε k cx Q Ι cos k cx ( A 2 + D 1 x) sin k cx ( A 2 + D 1 ) sin( k y y)
{ E z ΙΙ = n= [ Q ΙΙ n cosh( k xn x)+ P ΙΙ n sinh( k xn x) ]sin( k y y) e j k zn z H y ΙΙ = n= jωε k xn k 2 zn k 2 [ Q ΙΙ n sinh( k xn x)+ P ΙΙ n cosh( k xn x) ]sin( k y y) e j k zn z
E z ΙΙΙ =Q ΙΙΙ sin k cx ( A 2 + D 1 +x) sin k cx ( A 2 + D 1 ) sin( k y y); H y ΙΙΙ =- jωε k cx Q ΙΙΙ cos k cx ( A 2 + D 1 +x) sin k cx ( A 2 + D 1 ) sin( k y y)
cot( k 0 D 1 ) k 0 = W L 1 n= sin c 2 ( k zn W 2 ) k yn k 2 zn k 2 0 tanh( k yn A 2 )

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