Abstract

Smith-Purcell radiation (SPR), emitted when an electron beam is traveling above a metallic grating, has attracted a lot of attention as a source of electromagnetic (EM) radiation in the millimeter to visible spectrum. We conducted a theoretical investigation of SPR in the optical region using a two-dimensional finite-difference time-domain (FDTD) method. The permittivity of metal was represented using the Drude model. During the simulation, we observed three types of EM radiations when an electron bunch passes above a metal grating. We think these three types of EM radiation were basic SPR, original surface plasmon polariton (SPP), and mimic-SPP, caused by the periodic grating structure. Our observations were in accordance with analytical models of original SPP and mimic-SPP EM radiation.

© 2007 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |

  1. S. J. Smith and E. M. Purcell, "Visible light from localized surface charges moving across a grating," Phys Rev. 92, 1069 (1953).
    [CrossRef]
  2. P. M. van den Berg, "Smith-Purcell radiation from a line charge moving parallel to a reflection grating," J. Opt. Soc. Am. 63, 689-698 (1973).
    [CrossRef]
  3. P. M. van den Berg, "Smith-Purcell radiation from a point charge moving to a parallel reflection grating," J. Opt. Soc. Am. 63, 1589-1597 (1973).
  4. A. S. Kesar, M. Hess, S. E. Korbly, and R. J. Temkin, "Time-and frequency-domain models for Smith-Purcell radiation from a two-dimensional charge moving above a finite length grating," Phys. Rev. E 71, 016501 (2005).
    [CrossRef]
  5. J. Urata, M. Goldstein, M. F. Kimmitt, A. Naumov, C. Platt, and J. E. Walsh, "Superradiant Smith-Purcell emission," Phys. Rev. Lett. 80, 516-519 (1998).
    [CrossRef]
  6. L. Schachter and A. Ron, "Smith-Purcell free-electron laser," Phys Rev. A 40, 876- 896 (1989).
    [CrossRef] [PubMed]
  7. H. L. Andrews, C. A. Brau, "Gain of a Smith-Purcell free-electron laser," Phys. Rev. Special Topics 7, 070701 (2004).
  8. H. L. Andrews, C. A. Brau, and J. D. Jarvis, "Superradiant emission of Smith-Purcell radiation," Phys. Rev. Special Topics 8, 110702 (2005).
  9. Y. Shibata, S. Hasebe, K. Ishi, S. Ono, M. Ikezawa, T. Nakazato, M. Oyamada, S. Urasawa, T. Takahashi, T. Matsuyama, K. Kobayashi, and Y. Fujita, "Coherent Smith-Purcell radiation in the millimeter-wave region from a short-bunch beam of relativistic electrons," Phy. Rev. E 57, 1061-1074 (1998).
    [CrossRef]
  10. I. Shih, W. W. Salisbury, D. L. Masters, and D. B. Chang, "Measurement of Smith-Purcell radiation," J. Opt. Soc. Am. B 7, 345-350 (1990).
    [CrossRef]
  11. J. B. Pendry, L. Martin-Moreno, F. J. Garcia-Vidal, "Mimicking surface plasmons with structured surfaces," Science 305, 847-848 (2004).
    [CrossRef] [PubMed]
  12. D. Li, Z. Yang, K. Imasaki, and G.-S. Park, "Particle-in-cell simulation of coherent and superradiant Smith-Purcell radiation," Phys. Rev. Special Topics 9, 040701 (2006).
  13. J. T. Donohue, "Simulation of Smith-Purcell radiation using a particle-in-cell code," Phys Pev.Special Topics 8, 060702 (2005).
  14. 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, 054803 (2005).
    [CrossRef] [PubMed]
  15. T. Ochiai and K. Ohtaka, "Electron energy loss and Smith-Purcell radiation in two- and three-dimentional photonic crystals," Opt. Express 13, 7683-7697 (2005).
    [CrossRef] [PubMed]
  16. T. Ochiai and K. Ohtaka, "Relativistic electron energy loss and induced radiation emission in two-dimensional metallic photonic crystals. II. photonic band effects," Phys. Rev. B 69, 125107 (2004).
    [CrossRef]
  17. M. Moskovits, I. Srnova-Sloufova, B. Vlckova, "Bimetallic Ag-Au nanoparticles: Extracting meaningful optical constants from the surface-plasmon extinction spectrum," J. Chem. Phys. 116, 10435-10446 (2002).
    [CrossRef]
  18. L. Cao, N. C. Panoiu and R. M. OsgoodJr., "Surface second-harmonic generation from surface plasmon waves scattered by metallic nanostructures," Phys. Rev. B 75, 205401 (2007).
    [CrossRef]
  19. J. Cesario, M. U. Gonzalez, S. Cheylan, W. L. Barnes, S. Enoch, and R. Quidant, "Coupling localized and extended plasmons to improve the light extraction through metal films," Opt. Express 15, 10533-10539 (2007).
    [CrossRef] [PubMed]

2007 (2)

L. Cao, N. C. Panoiu and R. M. OsgoodJr., "Surface second-harmonic generation from surface plasmon waves scattered by metallic nanostructures," Phys. Rev. B 75, 205401 (2007).
[CrossRef]

J. Cesario, M. U. Gonzalez, S. Cheylan, W. L. Barnes, S. Enoch, and R. Quidant, "Coupling localized and extended plasmons to improve the light extraction through metal films," Opt. Express 15, 10533-10539 (2007).
[CrossRef] [PubMed]

2006 (1)

D. Li, Z. Yang, K. Imasaki, and G.-S. Park, "Particle-in-cell simulation of coherent and superradiant Smith-Purcell radiation," Phys. Rev. Special Topics 9, 040701 (2006).

2005 (5)

J. T. Donohue, "Simulation of Smith-Purcell radiation using a particle-in-cell code," Phys Pev.Special Topics 8, 060702 (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, 054803 (2005).
[CrossRef] [PubMed]

A. S. Kesar, M. Hess, S. E. Korbly, and R. J. Temkin, "Time-and frequency-domain models for Smith-Purcell radiation from a two-dimensional charge moving above a finite length grating," Phys. Rev. E 71, 016501 (2005).
[CrossRef]

H. L. Andrews, C. A. Brau, and J. D. Jarvis, "Superradiant emission of Smith-Purcell radiation," Phys. Rev. Special Topics 8, 110702 (2005).

T. Ochiai and K. Ohtaka, "Electron energy loss and Smith-Purcell radiation in two- and three-dimentional photonic crystals," Opt. Express 13, 7683-7697 (2005).
[CrossRef] [PubMed]

2004 (3)

J. B. Pendry, L. Martin-Moreno, F. J. Garcia-Vidal, "Mimicking surface plasmons with structured surfaces," Science 305, 847-848 (2004).
[CrossRef] [PubMed]

H. L. Andrews, C. A. Brau, "Gain of a Smith-Purcell free-electron laser," Phys. Rev. Special Topics 7, 070701 (2004).

T. Ochiai and K. Ohtaka, "Relativistic electron energy loss and induced radiation emission in two-dimensional metallic photonic crystals. II. photonic band effects," Phys. Rev. B 69, 125107 (2004).
[CrossRef]

2002 (1)

M. Moskovits, I. Srnova-Sloufova, B. Vlckova, "Bimetallic Ag-Au nanoparticles: Extracting meaningful optical constants from the surface-plasmon extinction spectrum," J. Chem. Phys. 116, 10435-10446 (2002).
[CrossRef]

1998 (2)

J. Urata, M. Goldstein, M. F. Kimmitt, A. Naumov, C. Platt, and J. E. Walsh, "Superradiant Smith-Purcell emission," Phys. Rev. Lett. 80, 516-519 (1998).
[CrossRef]

Y. Shibata, S. Hasebe, K. Ishi, S. Ono, M. Ikezawa, T. Nakazato, M. Oyamada, S. Urasawa, T. Takahashi, T. Matsuyama, K. Kobayashi, and Y. Fujita, "Coherent Smith-Purcell radiation in the millimeter-wave region from a short-bunch beam of relativistic electrons," Phy. Rev. E 57, 1061-1074 (1998).
[CrossRef]

1990 (1)

1989 (1)

L. Schachter and A. Ron, "Smith-Purcell free-electron laser," Phys Rev. A 40, 876- 896 (1989).
[CrossRef] [PubMed]

1973 (2)

P. M. van den Berg, "Smith-Purcell radiation from a point charge moving to a parallel reflection grating," J. Opt. Soc. Am. 63, 1589-1597 (1973).

P. M. van den Berg, "Smith-Purcell radiation from a line charge moving parallel to a reflection grating," J. Opt. Soc. Am. 63, 689-698 (1973).
[CrossRef]

1953 (1)

S. J. Smith and E. M. Purcell, "Visible light from localized surface charges moving across a grating," Phys Rev. 92, 1069 (1953).
[CrossRef]

J. Chem. Phys. (1)

M. Moskovits, I. Srnova-Sloufova, B. Vlckova, "Bimetallic Ag-Au nanoparticles: Extracting meaningful optical constants from the surface-plasmon extinction spectrum," J. Chem. Phys. 116, 10435-10446 (2002).
[CrossRef]

J. Opt. Soc. Am. (2)

P. M. van den Berg, "Smith-Purcell radiation from a line charge moving parallel to a reflection grating," J. Opt. Soc. Am. 63, 689-698 (1973).
[CrossRef]

P. M. van den Berg, "Smith-Purcell radiation from a point charge moving to a parallel reflection grating," J. Opt. Soc. Am. 63, 1589-1597 (1973).

J. Opt. Soc. Am. B (1)

Opt. Express (2)

Phy. Rev. E (1)

Y. Shibata, S. Hasebe, K. Ishi, S. Ono, M. Ikezawa, T. Nakazato, M. Oyamada, S. Urasawa, T. Takahashi, T. Matsuyama, K. Kobayashi, and Y. Fujita, "Coherent Smith-Purcell radiation in the millimeter-wave region from a short-bunch beam of relativistic electrons," Phy. Rev. E 57, 1061-1074 (1998).
[CrossRef]

Phys Rev. (1)

S. J. Smith and E. M. Purcell, "Visible light from localized surface charges moving across a grating," Phys Rev. 92, 1069 (1953).
[CrossRef]

Phys Rev. A (1)

L. Schachter and A. Ron, "Smith-Purcell free-electron laser," Phys Rev. A 40, 876- 896 (1989).
[CrossRef] [PubMed]

Phys. Rev. B (2)

L. Cao, N. C. Panoiu and R. M. OsgoodJr., "Surface second-harmonic generation from surface plasmon waves scattered by metallic nanostructures," Phys. Rev. B 75, 205401 (2007).
[CrossRef]

T. Ochiai and K. Ohtaka, "Relativistic electron energy loss and induced radiation emission in two-dimensional metallic photonic crystals. II. photonic band effects," Phys. Rev. B 69, 125107 (2004).
[CrossRef]

Phys. Rev. E (1)

A. S. Kesar, M. Hess, S. E. Korbly, and R. J. Temkin, "Time-and frequency-domain models for Smith-Purcell radiation from a two-dimensional charge moving above a finite length grating," Phys. Rev. E 71, 016501 (2005).
[CrossRef]

Phys. Rev. Lett. (2)

J. Urata, M. Goldstein, M. F. Kimmitt, A. Naumov, C. Platt, and J. E. Walsh, "Superradiant Smith-Purcell emission," Phys. Rev. Lett. 80, 516-519 (1998).
[CrossRef]

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, 054803 (2005).
[CrossRef] [PubMed]

Phys. Rev. Special Topics (3)

H. L. Andrews, C. A. Brau, "Gain of a Smith-Purcell free-electron laser," Phys. Rev. Special Topics 7, 070701 (2004).

H. L. Andrews, C. A. Brau, and J. D. Jarvis, "Superradiant emission of Smith-Purcell radiation," Phys. Rev. Special Topics 8, 110702 (2005).

D. Li, Z. Yang, K. Imasaki, and G.-S. Park, "Particle-in-cell simulation of coherent and superradiant Smith-Purcell radiation," Phys. Rev. Special Topics 9, 040701 (2006).

Science (1)

J. B. Pendry, L. Martin-Moreno, F. J. Garcia-Vidal, "Mimicking surface plasmons with structured surfaces," Science 305, 847-848 (2004).
[CrossRef] [PubMed]

Special Topics (1)

J. T. Donohue, "Simulation of Smith-Purcell radiation using a particle-in-cell code," Phys Pev.Special Topics 8, 060702 (2005).

Supplementary Material (2)

» Media 1: GIF (2372 KB)     
» Media 2: GIF (2480 KB)     

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (7)

Fig.1.
Fig.1.

Geometry used for simulations.

Fig. 2.
Fig. 2.

(a) Transient waveform of Hz observed at observation point with θ=-10°. (b) FFT spectrum.

Fig. 3.
Fig. 3.

FFT spectrum for Hz (a) before and (b) after 86 fs.

Fig. 4.
Fig. 4.

(a) (2.31MB) Film of the magnetic field behavior from 40 to 49 fs [Media 1]. (b) (2.42MB) Film of the magnetic field behavior from 71 to 80 fs [Media 2].

Fig. 5.
Fig. 5.

FFT spectrum for Hz as function of observation angle θ.

Fig. 6.
Fig. 6.

Relationship between SPP wavelength and velocity of electron bunch.

Fig. 7.
Fig. 7.

(a) D ispersion relation between M-SPP and electron bunch (l=200 nm, a=100n, h=200nm). (b) Groove depth dependence of mimic-SPP.

Tables (1)

Tables Icon

Table 1. Main parameters for the simulation.

Equations (11)

Equations on this page are rendered with MathJax. Learn more.

λ = l n ( β 1 sin θ )
ε r ( ω ) = 1 + ω p 2 ω ( j Γ ω ) = 1 + χ ( ω )
χ ( ω ) = ω p 2 ω ( j Γ ω )
n e = N 0 exp { ( x x 0 ) 2 + ( y y 0 ) 2 2 σ 2 }
d p dt = q ( E + ν × B )
p = m e ν 1 ν 2 c 2
j = n e q ν
k sp = ω c ( ε r ε d ε r + ε d ) 1 2
R 00 1 + χ 0 S 00 = 0
R 00 = tanh ( κ 0 h ) 1 + δ 00 p = 1 1 κ 0 a α p l 4 ( k + pK ) 2 a 2 × cos [ ( k + pK ) a ] 1
S 00 = tanh ( κ 0 h ) 1 + δ 00 κ 0 a α 0 l 4 k 2 a 2 × cos [ ka ] 1

Metrics