Abstract

Unusual emission of light, called the unconventional Smith-Purcell radiation (uSPR) in this paper, was demonstrated from an electron traveling near a finite photonic crystal (PhC) at an ultra-relativistic velocity. This phenomenon is not related to the accepted mechanism of the conventional SPR and arises because the evanescent light from the electron has such a small decay constant in the ultra-relativistic regime that it works practically as a plane-wave probe entering the PhC from one end. We analyze the dependence of the SPR spectrum on the velocity of electron and on the parity of excited photonic bands and show, for PhCs made up of a finite number of cylinders, that uSPR probes the photonic band structure very faithfully.

© 2006 Optical Society of America

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    [CrossRef]
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    [CrossRef] [PubMed]
  26. 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).
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    [CrossRef]
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    [CrossRef]
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2005 (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]

2004 (3)

K. Ohtaka, J. Inoue, and S. Yamaguti, "Derivation of the density of states of leaky photonic bands," Phys. Rev. B 70, 035109 (2004).
[CrossRef]

T. Ochiai and K. Ohtaka, "Relativistic electron energy loss and induced radiation emission in two-dimensional metallic photonic crystals. I. Formalism and surface plasmon polariton," Phys. Rev. B 69, 125106 (2004).
[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]

2003 (4)

F. J. García de Abajo, A. G. Pattantyus-Abraham, N. Zabala, A. Rivacoba, M. O. Wolf, and P. M. Echenique, "Cherenkov effect as a probe of photonic nanostructures," Phys. Rev. Lett. 91, 143902 (2003).
[CrossRef]

F. J. García de Abajo, A. Rivacoba, N. Zabala, and P. M. Echenique, "Electron energy loss spectroscopy as a probe of two-dimensional photonic crystals," Phys. Rev. B 68, 205105 (2003).
[CrossRef]

C. Luo, M. Ibanescu, S. G. Johnson, and J. D. Joannopoulos, "Cerenkov radiation in photonic crystals," Science 299, 368-371 (2003).
[CrossRef] [PubMed]

F. J. García de Abajo and L. A. Blanco, "Electron energy loss and induced photon emission in photonic crystals," Phys. Rev. B 67, 125108 (2003).
[CrossRef]

2002 (1)

S. Yamaguti, J. Inoue, O. Haeberlé, and K. Ohtaka, "Photonic crystals versus diffraction gratings in Smith-Purcell radiation," Phys. Rev. B 66, 195202 (2002).
[CrossRef]

2001 (2)

K. Ohtaka and S. Yamaguti, "Theoretical study of the Smith-Purcell effect involving photonic crystals," Opt. Spectrosc. 91, 477-483 (2001).
[CrossRef]

T. Ito and K. Sakoda, "Photonic bands of metallic systems. II. Features of surface plasmon polaritons," Phys. Rev. B 64, 045117 (2001).
[CrossRef]

2000 (2)

F. J. García de Abajo, "Smith-Purcell radiation emission in aligned nanoparticles," Phys. Rev. E 61, 5743-5752 (2000).
[CrossRef]

H. van der Lem and A. Moroz, "Towards two-dimensional complete photonic bandgap structures below infrared wavelengths," J. Opt. A 2, 395-399 (2000).
[CrossRef]

1999 (1)

V. Yannopapas, A. Modinos, and N. Stefanou, "Optical properties of metallodielectric photonic crystals," Phys. Rev. B 60, 5359-5365 (1999).
[CrossRef]

1998 (2)

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," Phys. Rev. E 57, 1061-1074 (1998).
[CrossRef]

J. H. Brownell, J. Walsh, and G. Doucas, "Spontaneous Smith-Purcell radiation described through induced surface currents," Phys. Rev. E 57, 1075-1080 (1998).
[CrossRef]

1995 (1)

K. Ishi, Y. Shibata, T. Takahashi, S. Hasebe, M. Ikezawa, K. Takami, T. Matsuyama, K. Kobayashi, and Y. Fujita, "Observation of coherent Smith-Purcell radiation from short-bunched electrons," Phys. Rev. E 51, R5212-R5215 (1995).
[CrossRef]

1994 (2)

O. Haeberlé, P. Rullhusen, J. M. Salomé, and N. Maene, "Calculations of Smith-Purcell radiation generated by electrons of 1-100 Mev," Phys. Rev. E 49, 3340-3352 (1994).
[CrossRef]

J. B. Pendry and L. Martín-Moreno, "Energy-loss by charged-particles in complex media," Phys. Rev. B 50, 5062-5073 (1994).
[CrossRef]

1992 (1)

G. Doucas, J. H. Mulvey, M. Omori, J. Walsh, and M. F. Kimmitt, "First observation of Smith-Purcell radiation from relativistic electrons," Phys. Rev. Lett. 69, 1761-1764 (1992).
[CrossRef] [PubMed]

1990 (1)

1984 (1)

1981 (1)

D. E. Wortman, R. P. Leavitt, H. Dropkin, and C. A. Morrison, "Generation of millimeter-wave radiation by means of a Smith-Purcell free-electron laser," Phys. Rev. A 24, 1150-1153 (1981).
[CrossRef]

1979 (1)

J. M. Wachtel, "Free-electron lasers using the Smith-Purcell effect," J. Appl. Phys. 50, 49-56 (1979).
[CrossRef]

1973 (1)

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]

1935 (1)

R. W. Wood, "Anomalous Diffraction Gratings," Phys. Rev. 48, 928-936 (1935).
[CrossRef]

Blanco, L. A.

F. J. García de Abajo and L. A. Blanco, "Electron energy loss and induced photon emission in photonic crystals," Phys. Rev. B 67, 125108 (2003).
[CrossRef]

Brownell, J. H.

J. H. Brownell, J. Walsh, and G. Doucas, "Spontaneous Smith-Purcell radiation described through induced surface currents," Phys. Rev. E 57, 1075-1080 (1998).
[CrossRef]

Chang, D. B.

Doucas, G.

J. H. Brownell, J. Walsh, and G. Doucas, "Spontaneous Smith-Purcell radiation described through induced surface currents," Phys. Rev. E 57, 1075-1080 (1998).
[CrossRef]

G. Doucas, J. H. Mulvey, M. Omori, J. Walsh, and M. F. Kimmitt, "First observation of Smith-Purcell radiation from relativistic electrons," Phys. Rev. Lett. 69, 1761-1764 (1992).
[CrossRef] [PubMed]

Dropkin, H.

D. E. Wortman, R. P. Leavitt, H. Dropkin, and C. A. Morrison, "Generation of millimeter-wave radiation by means of a Smith-Purcell free-electron laser," Phys. Rev. A 24, 1150-1153 (1981).
[CrossRef]

Dvorkis, P.

Echenique, P. M.

F. J. García de Abajo, A. Rivacoba, N. Zabala, and P. M. Echenique, "Electron energy loss spectroscopy as a probe of two-dimensional photonic crystals," Phys. Rev. B 68, 205105 (2003).
[CrossRef]

F. J. García de Abajo, A. G. Pattantyus-Abraham, N. Zabala, A. Rivacoba, M. O. Wolf, and P. M. Echenique, "Cherenkov effect as a probe of photonic nanostructures," Phys. Rev. Lett. 91, 143902 (2003).
[CrossRef]

Elisha, U.

Fujita, Y.

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," Phys. Rev. E 57, 1061-1074 (1998).
[CrossRef]

K. Ishi, Y. Shibata, T. Takahashi, S. Hasebe, M. Ikezawa, K. Takami, T. Matsuyama, K. Kobayashi, and Y. Fujita, "Observation of coherent Smith-Purcell radiation from short-bunched electrons," Phys. Rev. E 51, R5212-R5215 (1995).
[CrossRef]

García de Abajo, F. J.

F. J. García de Abajo and L. A. Blanco, "Electron energy loss and induced photon emission in photonic crystals," Phys. Rev. B 67, 125108 (2003).
[CrossRef]

F. J. García de Abajo, A. Rivacoba, N. Zabala, and P. M. Echenique, "Electron energy loss spectroscopy as a probe of two-dimensional photonic crystals," Phys. Rev. B 68, 205105 (2003).
[CrossRef]

F. J. García de Abajo, A. G. Pattantyus-Abraham, N. Zabala, A. Rivacoba, M. O. Wolf, and P. M. Echenique, "Cherenkov effect as a probe of photonic nanostructures," Phys. Rev. Lett. 91, 143902 (2003).
[CrossRef]

F. J. García de Abajo, "Smith-Purcell radiation emission in aligned nanoparticles," Phys. Rev. E 61, 5743-5752 (2000).
[CrossRef]

Gover, A.

Haeberlé, O.

S. Yamaguti, J. Inoue, O. Haeberlé, and K. Ohtaka, "Photonic crystals versus diffraction gratings in Smith-Purcell radiation," Phys. Rev. B 66, 195202 (2002).
[CrossRef]

O. Haeberlé, P. Rullhusen, J. M. Salomé, and N. Maene, "Calculations of Smith-Purcell radiation generated by electrons of 1-100 Mev," Phys. Rev. E 49, 3340-3352 (1994).
[CrossRef]

Hasebe, S.

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," Phys. Rev. E 57, 1061-1074 (1998).
[CrossRef]

K. Ishi, Y. Shibata, T. Takahashi, S. Hasebe, M. Ikezawa, K. Takami, T. Matsuyama, K. Kobayashi, and Y. Fujita, "Observation of coherent Smith-Purcell radiation from short-bunched electrons," Phys. Rev. E 51, R5212-R5215 (1995).
[CrossRef]

Hess, M.

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]

Ibanescu, M.

C. Luo, M. Ibanescu, S. G. Johnson, and J. D. Joannopoulos, "Cerenkov radiation in photonic crystals," Science 299, 368-371 (2003).
[CrossRef] [PubMed]

Ikezawa, M.

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," Phys. Rev. E 57, 1061-1074 (1998).
[CrossRef]

K. Ishi, Y. Shibata, T. Takahashi, S. Hasebe, M. Ikezawa, K. Takami, T. Matsuyama, K. Kobayashi, and Y. Fujita, "Observation of coherent Smith-Purcell radiation from short-bunched electrons," Phys. Rev. E 51, R5212-R5215 (1995).
[CrossRef]

Inoue, J.

K. Ohtaka, J. Inoue, and S. Yamaguti, "Derivation of the density of states of leaky photonic bands," Phys. Rev. B 70, 035109 (2004).
[CrossRef]

S. Yamaguti, J. Inoue, O. Haeberlé, and K. Ohtaka, "Photonic crystals versus diffraction gratings in Smith-Purcell radiation," Phys. Rev. B 66, 195202 (2002).
[CrossRef]

Ishi, K.

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," Phys. Rev. E 57, 1061-1074 (1998).
[CrossRef]

K. Ishi, Y. Shibata, T. Takahashi, S. Hasebe, M. Ikezawa, K. Takami, T. Matsuyama, K. Kobayashi, and Y. Fujita, "Observation of coherent Smith-Purcell radiation from short-bunched electrons," Phys. Rev. E 51, R5212-R5215 (1995).
[CrossRef]

Ito, T.

T. Ito and K. Sakoda, "Photonic bands of metallic systems. II. Features of surface plasmon polaritons," Phys. Rev. B 64, 045117 (2001).
[CrossRef]

Joannopoulos, J. D.

C. Luo, M. Ibanescu, S. G. Johnson, and J. D. Joannopoulos, "Cerenkov radiation in photonic crystals," Science 299, 368-371 (2003).
[CrossRef] [PubMed]

Johnson, S. G.

C. Luo, M. Ibanescu, S. G. Johnson, and J. D. Joannopoulos, "Cerenkov radiation in photonic crystals," Science 299, 368-371 (2003).
[CrossRef] [PubMed]

Kesar, A. S.

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]

Kimmitt, M. F.

G. Doucas, J. H. Mulvey, M. Omori, J. Walsh, and M. F. Kimmitt, "First observation of Smith-Purcell radiation from relativistic electrons," Phys. Rev. Lett. 69, 1761-1764 (1992).
[CrossRef] [PubMed]

Kobayashi, K.

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," Phys. Rev. E 57, 1061-1074 (1998).
[CrossRef]

K. Ishi, Y. Shibata, T. Takahashi, S. Hasebe, M. Ikezawa, K. Takami, T. Matsuyama, K. Kobayashi, and Y. Fujita, "Observation of coherent Smith-Purcell radiation from short-bunched electrons," Phys. Rev. E 51, R5212-R5215 (1995).
[CrossRef]

Korbly, S. E.

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]

Leavitt, R. P.

D. E. Wortman, R. P. Leavitt, H. Dropkin, and C. A. Morrison, "Generation of millimeter-wave radiation by means of a Smith-Purcell free-electron laser," Phys. Rev. A 24, 1150-1153 (1981).
[CrossRef]

Luo, C.

C. Luo, M. Ibanescu, S. G. Johnson, and J. D. Joannopoulos, "Cerenkov radiation in photonic crystals," Science 299, 368-371 (2003).
[CrossRef] [PubMed]

Maene, N.

O. Haeberlé, P. Rullhusen, J. M. Salomé, and N. Maene, "Calculations of Smith-Purcell radiation generated by electrons of 1-100 Mev," Phys. Rev. E 49, 3340-3352 (1994).
[CrossRef]

Martín-Moreno, L.

J. B. Pendry and L. Martín-Moreno, "Energy-loss by charged-particles in complex media," Phys. Rev. B 50, 5062-5073 (1994).
[CrossRef]

Masters, D. L.

Matsuyama, T.

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," Phys. Rev. E 57, 1061-1074 (1998).
[CrossRef]

K. Ishi, Y. Shibata, T. Takahashi, S. Hasebe, M. Ikezawa, K. Takami, T. Matsuyama, K. Kobayashi, and Y. Fujita, "Observation of coherent Smith-Purcell radiation from short-bunched electrons," Phys. Rev. E 51, R5212-R5215 (1995).
[CrossRef]

Modinos, A.

V. Yannopapas, A. Modinos, and N. Stefanou, "Optical properties of metallodielectric photonic crystals," Phys. Rev. B 60, 5359-5365 (1999).
[CrossRef]

Moroz, A.

H. van der Lem and A. Moroz, "Towards two-dimensional complete photonic bandgap structures below infrared wavelengths," J. Opt. A 2, 395-399 (2000).
[CrossRef]

Morrison, C. A.

D. E. Wortman, R. P. Leavitt, H. Dropkin, and C. A. Morrison, "Generation of millimeter-wave radiation by means of a Smith-Purcell free-electron laser," Phys. Rev. A 24, 1150-1153 (1981).
[CrossRef]

Mulvey, J. H.

G. Doucas, J. H. Mulvey, M. Omori, J. Walsh, and M. F. Kimmitt, "First observation of Smith-Purcell radiation from relativistic electrons," Phys. Rev. Lett. 69, 1761-1764 (1992).
[CrossRef] [PubMed]

Nakazato, T.

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," Phys. Rev. E 57, 1061-1074 (1998).
[CrossRef]

Ochiai, T.

T. Ochiai and K. Ohtaka, "Relativistic electron energy loss and induced radiation emission in two-dimensional metallic photonic crystals. I. Formalism and surface plasmon polariton," Phys. Rev. B 69, 125106 (2004).
[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]

Ohtaka, K.

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]

T. Ochiai and K. Ohtaka, "Relativistic electron energy loss and induced radiation emission in two-dimensional metallic photonic crystals. I. Formalism and surface plasmon polariton," Phys. Rev. B 69, 125106 (2004).
[CrossRef]

K. Ohtaka, J. Inoue, and S. Yamaguti, "Derivation of the density of states of leaky photonic bands," Phys. Rev. B 70, 035109 (2004).
[CrossRef]

S. Yamaguti, J. Inoue, O. Haeberlé, and K. Ohtaka, "Photonic crystals versus diffraction gratings in Smith-Purcell radiation," Phys. Rev. B 66, 195202 (2002).
[CrossRef]

K. Ohtaka and S. Yamaguti, "Theoretical study of the Smith-Purcell effect involving photonic crystals," Opt. Spectrosc. 91, 477-483 (2001).
[CrossRef]

Omori, M.

G. Doucas, J. H. Mulvey, M. Omori, J. Walsh, and M. F. Kimmitt, "First observation of Smith-Purcell radiation from relativistic electrons," Phys. Rev. Lett. 69, 1761-1764 (1992).
[CrossRef] [PubMed]

Ono, S.

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," Phys. Rev. E 57, 1061-1074 (1998).
[CrossRef]

Oyamada, M.

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," Phys. Rev. E 57, 1061-1074 (1998).
[CrossRef]

Pattantyus-Abraham, A. G.

F. J. García de Abajo, A. G. Pattantyus-Abraham, N. Zabala, A. Rivacoba, M. O. Wolf, and P. M. Echenique, "Cherenkov effect as a probe of photonic nanostructures," Phys. Rev. Lett. 91, 143902 (2003).
[CrossRef]

Pendry, J. B.

J. B. Pendry and L. Martín-Moreno, "Energy-loss by charged-particles in complex media," Phys. Rev. B 50, 5062-5073 (1994).
[CrossRef]

Purcell, E. M.

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

Rivacoba, A.

F. J. García de Abajo, A. G. Pattantyus-Abraham, N. Zabala, A. Rivacoba, M. O. Wolf, and P. M. Echenique, "Cherenkov effect as a probe of photonic nanostructures," Phys. Rev. Lett. 91, 143902 (2003).
[CrossRef]

F. J. García de Abajo, A. Rivacoba, N. Zabala, and P. M. Echenique, "Electron energy loss spectroscopy as a probe of two-dimensional photonic crystals," Phys. Rev. B 68, 205105 (2003).
[CrossRef]

Rullhusen, P.

O. Haeberlé, P. Rullhusen, J. M. Salomé, and N. Maene, "Calculations of Smith-Purcell radiation generated by electrons of 1-100 Mev," Phys. Rev. E 49, 3340-3352 (1994).
[CrossRef]

Sakoda, K.

T. Ito and K. Sakoda, "Photonic bands of metallic systems. II. Features of surface plasmon polaritons," Phys. Rev. B 64, 045117 (2001).
[CrossRef]

Salisbury, W. W.

Salomé, J. M.

O. Haeberlé, P. Rullhusen, J. M. Salomé, and N. Maene, "Calculations of Smith-Purcell radiation generated by electrons of 1-100 Mev," Phys. Rev. E 49, 3340-3352 (1994).
[CrossRef]

Shibata, Y.

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," Phys. Rev. E 57, 1061-1074 (1998).
[CrossRef]

K. Ishi, Y. Shibata, T. Takahashi, S. Hasebe, M. Ikezawa, K. Takami, T. Matsuyama, K. Kobayashi, and Y. Fujita, "Observation of coherent Smith-Purcell radiation from short-bunched electrons," Phys. Rev. E 51, R5212-R5215 (1995).
[CrossRef]

Shih, I.

Smith, S. J.

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

Stefanou, N.

V. Yannopapas, A. Modinos, and N. Stefanou, "Optical properties of metallodielectric photonic crystals," Phys. Rev. B 60, 5359-5365 (1999).
[CrossRef]

Takahashi, T.

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," Phys. Rev. E 57, 1061-1074 (1998).
[CrossRef]

K. Ishi, Y. Shibata, T. Takahashi, S. Hasebe, M. Ikezawa, K. Takami, T. Matsuyama, K. Kobayashi, and Y. Fujita, "Observation of coherent Smith-Purcell radiation from short-bunched electrons," Phys. Rev. E 51, R5212-R5215 (1995).
[CrossRef]

Takami, K.

K. Ishi, Y. Shibata, T. Takahashi, S. Hasebe, M. Ikezawa, K. Takami, T. Matsuyama, K. Kobayashi, and Y. Fujita, "Observation of coherent Smith-Purcell radiation from short-bunched electrons," Phys. Rev. E 51, R5212-R5215 (1995).
[CrossRef]

Temkin, R. J.

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]

Urasawa, S.

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," Phys. Rev. E 57, 1061-1074 (1998).
[CrossRef]

van den Berg, P. M.

van der Lem, H.

H. van der Lem and A. Moroz, "Towards two-dimensional complete photonic bandgap structures below infrared wavelengths," J. Opt. A 2, 395-399 (2000).
[CrossRef]

Wachtel, J. M.

J. M. Wachtel, "Free-electron lasers using the Smith-Purcell effect," J. Appl. Phys. 50, 49-56 (1979).
[CrossRef]

Walsh, J.

J. H. Brownell, J. Walsh, and G. Doucas, "Spontaneous Smith-Purcell radiation described through induced surface currents," Phys. Rev. E 57, 1075-1080 (1998).
[CrossRef]

G. Doucas, J. H. Mulvey, M. Omori, J. Walsh, and M. F. Kimmitt, "First observation of Smith-Purcell radiation from relativistic electrons," Phys. Rev. Lett. 69, 1761-1764 (1992).
[CrossRef] [PubMed]

Wolf, M. O.

F. J. García de Abajo, A. G. Pattantyus-Abraham, N. Zabala, A. Rivacoba, M. O. Wolf, and P. M. Echenique, "Cherenkov effect as a probe of photonic nanostructures," Phys. Rev. Lett. 91, 143902 (2003).
[CrossRef]

Wood, R. W.

R. W. Wood, "Anomalous Diffraction Gratings," Phys. Rev. 48, 928-936 (1935).
[CrossRef]

Wortman, D. E.

D. E. Wortman, R. P. Leavitt, H. Dropkin, and C. A. Morrison, "Generation of millimeter-wave radiation by means of a Smith-Purcell free-electron laser," Phys. Rev. A 24, 1150-1153 (1981).
[CrossRef]

Yamaguti, S.

K. Ohtaka, J. Inoue, and S. Yamaguti, "Derivation of the density of states of leaky photonic bands," Phys. Rev. B 70, 035109 (2004).
[CrossRef]

S. Yamaguti, J. Inoue, O. Haeberlé, and K. Ohtaka, "Photonic crystals versus diffraction gratings in Smith-Purcell radiation," Phys. Rev. B 66, 195202 (2002).
[CrossRef]

K. Ohtaka and S. Yamaguti, "Theoretical study of the Smith-Purcell effect involving photonic crystals," Opt. Spectrosc. 91, 477-483 (2001).
[CrossRef]

Yannopapas, V.

V. Yannopapas, A. Modinos, and N. Stefanou, "Optical properties of metallodielectric photonic crystals," Phys. Rev. B 60, 5359-5365 (1999).
[CrossRef]

Zabala, N.

F. J. García de Abajo, A. G. Pattantyus-Abraham, N. Zabala, A. Rivacoba, M. O. Wolf, and P. M. Echenique, "Cherenkov effect as a probe of photonic nanostructures," Phys. Rev. Lett. 91, 143902 (2003).
[CrossRef]

F. J. García de Abajo, A. Rivacoba, N. Zabala, and P. M. Echenique, "Electron energy loss spectroscopy as a probe of two-dimensional photonic crystals," Phys. Rev. B 68, 205105 (2003).
[CrossRef]

J. Appl. Phys. (1)

J. M. Wachtel, "Free-electron lasers using the Smith-Purcell effect," J. Appl. Phys. 50, 49-56 (1979).
[CrossRef]

J. Opt. A (1)

H. van der Lem and A. Moroz, "Towards two-dimensional complete photonic bandgap structures below infrared wavelengths," J. Opt. A 2, 395-399 (2000).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. B (2)

Opt. Spectrosc. (1)

K. Ohtaka and S. Yamaguti, "Theoretical study of the Smith-Purcell effect involving photonic crystals," Opt. Spectrosc. 91, 477-483 (2001).
[CrossRef]

Phys. Rev. (2)

R. W. Wood, "Anomalous Diffraction Gratings," Phys. Rev. 48, 928-936 (1935).
[CrossRef]

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)

D. E. Wortman, R. P. Leavitt, H. Dropkin, and C. A. Morrison, "Generation of millimeter-wave radiation by means of a Smith-Purcell free-electron laser," Phys. Rev. A 24, 1150-1153 (1981).
[CrossRef]

Phys. Rev. B (9)

K. Ohtaka, J. Inoue, and S. Yamaguti, "Derivation of the density of states of leaky photonic bands," Phys. Rev. B 70, 035109 (2004).
[CrossRef]

V. Yannopapas, A. Modinos, and N. Stefanou, "Optical properties of metallodielectric photonic crystals," Phys. Rev. B 60, 5359-5365 (1999).
[CrossRef]

J. B. Pendry and L. Martín-Moreno, "Energy-loss by charged-particles in complex media," Phys. Rev. B 50, 5062-5073 (1994).
[CrossRef]

S. Yamaguti, J. Inoue, O. Haeberlé, and K. Ohtaka, "Photonic crystals versus diffraction gratings in Smith-Purcell radiation," Phys. Rev. B 66, 195202 (2002).
[CrossRef]

F. J. García de Abajo and L. A. Blanco, "Electron energy loss and induced photon emission in photonic crystals," Phys. Rev. B 67, 125108 (2003).
[CrossRef]

T. Ochiai and K. Ohtaka, "Relativistic electron energy loss and induced radiation emission in two-dimensional metallic photonic crystals. I. Formalism and surface plasmon polariton," Phys. Rev. B 69, 125106 (2004).
[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]

T. Ito and K. Sakoda, "Photonic bands of metallic systems. II. Features of surface plasmon polaritons," Phys. Rev. B 64, 045117 (2001).
[CrossRef]

F. J. García de Abajo, A. Rivacoba, N. Zabala, and P. M. Echenique, "Electron energy loss spectroscopy as a probe of two-dimensional photonic crystals," Phys. Rev. B 68, 205105 (2003).
[CrossRef]

Phys. Rev. E (6)

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]

F. J. García de Abajo, "Smith-Purcell radiation emission in aligned nanoparticles," Phys. Rev. E 61, 5743-5752 (2000).
[CrossRef]

O. Haeberlé, P. Rullhusen, J. M. Salomé, and N. Maene, "Calculations of Smith-Purcell radiation generated by electrons of 1-100 Mev," Phys. Rev. E 49, 3340-3352 (1994).
[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," Phys. Rev. E 57, 1061-1074 (1998).
[CrossRef]

J. H. Brownell, J. Walsh, and G. Doucas, "Spontaneous Smith-Purcell radiation described through induced surface currents," Phys. Rev. E 57, 1075-1080 (1998).
[CrossRef]

K. Ishi, Y. Shibata, T. Takahashi, S. Hasebe, M. Ikezawa, K. Takami, T. Matsuyama, K. Kobayashi, and Y. Fujita, "Observation of coherent Smith-Purcell radiation from short-bunched electrons," Phys. Rev. E 51, R5212-R5215 (1995).
[CrossRef]

Phys. Rev. Lett. (2)

F. J. García de Abajo, A. G. Pattantyus-Abraham, N. Zabala, A. Rivacoba, M. O. Wolf, and P. M. Echenique, "Cherenkov effect as a probe of photonic nanostructures," Phys. Rev. Lett. 91, 143902 (2003).
[CrossRef]

G. Doucas, J. H. Mulvey, M. Omori, J. Walsh, and M. F. Kimmitt, "First observation of Smith-Purcell radiation from relativistic electrons," Phys. Rev. Lett. 69, 1761-1764 (1992).
[CrossRef] [PubMed]

Science (1)

C. Luo, M. Ibanescu, S. G. Johnson, and J. D. Joannopoulos, "Cerenkov radiation in photonic crystals," Science 299, 368-371 (2003).
[CrossRef] [PubMed]

Other (6)

K. Sakoda, Optical Properties of Photonic Crystals (Springer, Berlin, 2001).

M. A. Kumakhov and G. Shirner, Atomic Collisions in Crystals (Gordon and Breach Science Publishers, New York, 1989).

L. D. Landau, E. M. Lifshitz, and L. P. Pitaevskii, Electrodynamics of Continuous Media, p. 408 (Butterworth- Heinemann, Oxford, 1985).

K. Yamamoto, R. Sakakibara, S. Yano, Y. Segawa, Y. Shibata, K. Ishi, T. Ohsaka, T. Hara, Y. Kondo, H. Miyazaki, F. Hinode, T. Matsuyama, S. Yamaguti, and K. Ohtaka, "Observation of millimeter-wave radiation generated by the interaction between an electron beam and a photonic crystal," Phys. Rev. E 69, 045601(R) (2004).
[CrossRef]

N. Horiuchi, T. Ochiai, J. Inoue, Y. Segawa, Y. Shibata, K. Ishi, Y. Kondo, M. Kanbe, H. Miyazaki, F. Hinode, S. Yamaguti, and K. Ohtaka, "Exotic radiation from a photonic crystal excited by an ultra-relativistic electron beam," cond-mat/0604624.

V. P. Shestopalov, The Smith-Purcell effect (Nova Science, New York, 1998).

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Figures (13)

Fig. 1.
Fig. 1.

Schematic illustration of the system under study. An electron travels with constant velocity v and impact parameter b below the one-dimensional periodic array of dielectric or metallic cylinders. The cylinders are arrayed periodically with axes in the z direction with radius r, dielectric constant ε and the lattice constant a. The trajectory of the electron is parallel to the direction of the periodicity. Angles θ and ϕ are the polar angles of the SPR signals. This PhC has a mirror plane indicated by dotted line in the right panel.

Fig. 2.
Fig. 2.

Schematic illustration of the input evanescent light yielding conventional (left panel) and unconventional (right panel) SPRs. The conventional SPR is produced when the evanescent wave has an appreciable decay constant. The incident light enters the PhC from below. The unconventional case arises when the incident evanescent light has a negligible decay constant and is regarded as a plane wave entering the PhC from its left edge. In this case, the evanescent wave is almost symmetric with respect to the mirror plane, inducing the even-parity selection rule in the PhB excitation.

Fig. 3.
Fig. 3.

PhB structure of the monolayer of low-index cylinders in contact (ε = 2.05). The modes of TE polarization of kz = 0 are plotted as a function of kx . The PhB modes are classified according to the parity with respect to the mirror plane bisecting the monolayer. The light line ω= ±ckx is indicated by thick solid lines, the shifted v lines of v = 0.5c by thin solid lines, and those of v = 0.99999c by dashed lines. The horizontal arrows (six for v = 0.99999c and four for v = 0.5c) are drawn at the intersections between the shifted v lines and the PhB dispersion curves. They correspond to those of Figs. 4 and 7.

Fig. 4.
Fig. 4.

Reflected intensity of cSPR on the shifted v lines of v = 0.99999c for ε= 2.05 and b = 3.33a. Perfect periodicity ranging from x = -∞ to x = ∞ of the monolayer cylinders is assumed. The arrows are drawn at the peak positions and agree with those of Fig. 3, which were assigned to the crossing points between the shifted v line and the band structure.

Fig. 5.
Fig. 5.

Reflected SPR intensity map from a finite (N = 21) monolayer of the contact cylinders with a low index dielectric constant. The signals appearing off the shifted v lines characterize the uSPR. Except for N, the same parameters as in Fig. 4 were used.

Fig. 6.
Fig. 6.

Figure 5 of the intensity overlaid with the PhB structure of the even parity (indicated by red circles). The shifted v lines are indicated by solid lines.

Fig. 7.
Fig. 7.

The reflected cSPR intensity from the infinite monolayer (N = ∞) of the low-index contact cylinders. The parameters v = 0.5c and b = 0.2a were assumed for the electron beam. Four arrows are assigned to the peak positions and coincide with those of Fig. 3.

Fig. 8.
Fig. 8.

Reflected SPR spectrum from a finite (N = 21) monolayer of low-index cylinders in contact. The intensity profile is overlaid with the corresponding PhB structure of N = ∞. The PhB modes with even (odd) parity are indicated by red (green) circles. The parameters v = 0.5c and b = 0.2a were assumed for the electron beam.

Fig. 9.
Fig. 9.

Dependence of the reflected SPR spectra on electron velocity. The result for a finite monolayer (N = 21) of contact cylinders is shown for ε = 2.05. Panels (a) and (b) are the results for v = 0.7c, and panels (c) and (d) are those for v = 0.99c. Panels (b) and (d) are reproductions of (a) and (c), respectively, overlaid with the PhB structure of N = ∞. The PhB modes with even (odd) parity are indicated by red (green) circles. See text for the impact parameter b used in the calculation.

Fig. 10.
Fig. 10.

Reflected SPRs from the monolayers of contact cylinders of various dielectric constants. Panel (a) shows the result of dielectric cylinders of ε = 4.41 and r = 0.5a, panel (c) is the result of metallic cylinders of Drude dielectric constant ω = 1 - ωp2/ω 2 with ωpa/2ωc = 1, and panel (e) shows the result of cylinders of perfect metal, i.e., r = 0.5a and ε = - ∞. Panels (a) and (c) are reproduced in panels (b) and (d), respectively, with the corresponding PhB superposed. The same parameters as in Fig. 4 were used for the electron beam.

Fig. 11.
Fig. 11.

The reflected SPR intensity spectra at (θ,ϕ) = (60°,180°) from finite-size PhCs of various N. The same parameters as in Fig. 4 were used except for N.

Fig. 12.
Fig. 12.

Reflected SPR intensity map of various PhCs of cylinders. Panel (a) shows the result of the double-layer system of contact low-index cylinders (N = 21 and Nl = 2). Panel (b) is produced from panel (a) by overlaying the even-parity PhBs. The mirror plane of the parity lies in between the double-layers. Panel (c) shows the result for a multi-layer PhC of square lattice of contact low-index cylinders (N = 8 and Nl = 20). Panel (d) is a reproduction of panel (c), overlaid with the PhB structure along the Γ-X direction. Only the even-parity modes with respect to the mirror plane relevant to Γ - X are shown. The same parameters as in Fig. 4 were used for the electron beam.

Fig. 13.
Fig. 13.

Reflected SPR intensity off the xy plane. Spectra from the monolayer of contact low-index cylinders are shown. (a) Intensity in the (kx) plane at ϕ = 15°. (b) Intensity in the (kz) plane at θ = 90°. For the electron beam, the same parameters are used as in Fig. 4.

Equations (13)

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

K ± = ( ω ν , ± Γ , k z ) , Γ = ( ω c ) 2 ( ω ν ) 2 k z 2 ,
K h ± = ( ω ν h , ± Γ h , k z ) , Γ h = ( ω c ) 2 ( ω ν h ) 2 k z 2 .
K h ± = ω c ( cos θ , sin θ cos ϕ , sin θ sin ϕ ) ,
v = ( v x , 0 , v z ) = v ( cos α , 0 , sin α ) ,
ω = v x ( k x h ) + v z k z , k z = v z v 2 ω , ω = ω n ( k x , k z ) ,
W = dωd k z π 2 P em ( ω , k z ) ,
P em = ( ω , k z ) b = e 2 Γ ( b b 0 ) P em ( ω , k z ) b 0 ,
b = 0.01 βγa , with β = v c , γ = 1 1 β 2 ,
k x = ± ( ω c ) 2 h 2 ,
W ω Ω = q q 2 k z 2 4 π μ 0 ω ( f M ( θ′ ) 2 + f N ( θ′ ) 2 ) ,
k z = q sin θ sin ϕ , q = ω c ,
θ′ = i log ( cos θ + i sin θ cos ϕ 1 sin 2 θ sin 2 ϕ ) .
Γ = ( ω c ) 2 ( ω v ) 2 ( ω c sin θ sin ϕ ) 2 iq sin θ sin ϕ .

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