Electron energy loss and Smith-Purcell radiation in two- and three-dimensional photonic crystals
Optics Express, Vol. 13, Issue 19, pp. 7683-7698 (2005)
http://dx.doi.org/10.1364/OPEX.13.007683
Acrobat PDF (488 KB)
Abstract
A theoretical description of the electron energy loss and the Smith-Purcell radiation is presented for an electron moving near a two-dimensional photonic crystal slab and a three-dimensional woodpile photonic crystal. The electron energy loss and the Smith-Purcell radiation spectra are well correlated with the photonic band structures of these crystals and thus can be used as a probe of them. In particular, there is a selection rule concerning the symmetries of the photonic band modes to be excited when the electron moves in a mirror plane of the crystals. In the woodpile, a highly directional Smith-Purcell radiation is realized by using the planar defect mode inside the complete band gap.
© 2005 Optical Society of America
1. Introduction
1 . J. B. Pendry and L. Martín-Moreno , “ Energy-loss by charged-particles in complex media ,” Phys. Rev. B 50 , 5062 – 5073 ( 1994 ). [CrossRef]
2 . 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]
3 . 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]
4 . 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]
5 . 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]
6 . 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]
7 . S. J. Smith and E. M. Purcell , “ Visible light from localized surface charges moving across a grating ,” Phys. Rev. 92 , 1069 ( 1953 ). [CrossRef]
8 . E. Chow , S. Y. Lin , S. G. Johnson , P. R. Villeneuve , J. D. Joannopoulos , J. R. Wendt , G. A. Vawter , W. Zubrzycki , H. Hou , and A. Alleman , “ Three-dimensional control of light in a two-dimensional photonic crystal slab ,” Nature 407 , 983 – 986 ( 2000 ). [CrossRef] [PubMed]
9 . S. Y. Lin , J. G. Fleming , D. L. Hetherington , B. K. Smith , R. Biswas , K. M. Ho , M. M. Sigalas , W. Zubrzycki , S. R. Kurtz , and J. Bur , “ A three-dimensional photonic crystal operating at infrared wavelengths ,” Nature 394 , 251 – 253 ( 1998 ). [CrossRef]
10 . D. M. Whittaker and I. S. Culshaw , “ Scattering-matrix treatment of patterned multilayer photonic structures ,” Phys. Rev. B 60 , 2610 – 2618 ( 1999 ). [CrossRef]
11 . S. G. Tikhodeev , A. L. Yablonskii , E. A. Muljarov , N. A. Gippius , and T. Ishihara , “ Quasiguided modes and optical properties of photonic crystal slabs ,” Phys. Rev. B 66 , 045102 ( 2002 ). [CrossRef]
12 . B. Gralak , S. Enoch , and G. Tayeb , “ From scattering or impedance matrices to Bloch modes of photonic crystals ,” J. Opt. Soc. Am. A 19 , 1547 – 1554 ( 2002 ). [CrossRef]
13 . Z. Y. Li and L. L. Lin , “ Photonic band structures solved by a plane-wave-based transfer-matrix method ,” Phys. Rev. E 67 , 046607 ( 2003 ). [CrossRef]
14 . 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]
15 . A. Gover , P. Dvorkis , and U. Elisha , “ Angular radiation-pattern of Smith-Purcell radiation ,” J. Opt. Soc. Am. B 1 , 723 – 728 ( 1984 ). [CrossRef]
16 . I. Shih , W. W. Salisbury , D. L. Masters , and D. B. Chang , “ Measurements of Smith-Purcell radiation ,” J. Opt. Soc. Am. B 7 , 345 – 350 ( 1990 ). [CrossRef]
17 . 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]
18 . 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]
19 . 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]
20 . Y. Shibata , S. Hasebe , K. Ishi , S. Ono , M. Ikezawa , T. Nakazato , M. Oyamada , S. Urasawa , T. Takahashi , T. Mat-suyama , 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]
1 . J. B. Pendry and L. Martín-Moreno , “ Energy-loss by charged-particles in complex media ,” Phys. Rev. B 50 , 5062 – 5073 ( 1994 ). [CrossRef]
5 . 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]
6 . 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]
1 . J. B. Pendry and L. Martín-Moreno , “ Energy-loss by charged-particles in complex media ,” Phys. Rev. B 50 , 5062 – 5073 ( 1994 ). [CrossRef]
21 . F. J. García de Abajo , “ Smith-Purcell radiation emission in aligned nanoparticles ,” Phys. Rev. E 61 , 5743 – 5752 ( 2000 ). [CrossRef]
22 . K. Ohtaka and S. Yamaguti , “ Theoretical study of the Smith-Purcell effect involving photonic crystals ,” Opt. Spectrosc. 91 , 477 – 483 ( 2001 ). [CrossRef]
23 . 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]
24 . 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 ( 2004 ). [CrossRef]
25 . S. P. Ogawa , M. Imada , S. Yoshimoto , M. Okano , and S. Noda , “ Control of light emission by 3D photonic crystals ,” Science 305 , 227 – 229 ( 2004 ). [CrossRef] [PubMed]
26 . M. Okano and S. Noda , “ Analysis of multimode point-defect cavities in three-dimensional photonic crystals using group theory in frequency and time domains ,” Phys. Rev. B 70 , 125105 ( 2004 ). [CrossRef]
2. Formalism
10 . D. M. Whittaker and I. S. Culshaw , “ Scattering-matrix treatment of patterned multilayer photonic structures ,” Phys. Rev. B 60 , 2610 – 2618 ( 1999 ). [CrossRef]
11 . S. G. Tikhodeev , A. L. Yablonskii , E. A. Muljarov , N. A. Gippius , and T. Ishihara , “ Quasiguided modes and optical properties of photonic crystal slabs ,” Phys. Rev. B 66 , 045102 ( 2002 ). [CrossRef]
12 . B. Gralak , S. Enoch , and G. Tayeb , “ From scattering or impedance matrices to Bloch modes of photonic crystals ,” J. Opt. Soc. Am. A 19 , 1547 – 1554 ( 2002 ). [CrossRef]
13 . Z. Y. Li and L. L. Lin , “ Photonic band structures solved by a plane-wave-based transfer-matrix method ,” Phys. Rev. E 67 , 046607 ( 2003 ). [CrossRef]
29 . T. Ueta , K. Ohtaka , N. Kawai , and K. Sakoda , “ Limits on quality factors of localized defect modes in photonic crystals due to dielectric loss ,” J. Appl. Phys. 84 , 6299 – 6304 ( 1998 ). [CrossRef]
3. Two-dimensional photonic crystal slab
30 . T. Ochiai and K. Sakoda , “ Dispersion relation and optical transmittance of a hexagonal photonic crystal slab ,” Phys. Rev. B 63 , 125107 ( 2001 ). [CrossRef]
31 . T. Ochiai and K. Sakoda , “ Nearly free-photon approximation for two-dimensional photonic crystal slabs ,” Phys. Rev. B 64 , 045108 ( 2001 ). [CrossRef]
11 . S. G. Tikhodeev , A. L. Yablonskii , E. A. Muljarov , N. A. Gippius , and T. Ishihara , “ Quasiguided modes and optical properties of photonic crystal slabs ,” Phys. Rev. B 66 , 045102 ( 2002 ). [CrossRef]
32 . K. Ohtaka , J. Inoue , and S. Yamaguti , “ Derivation of the density of states of leaky photonic bands ,” Phys. Rev. B 70 , 035 ,109 ( 2004 ). [CrossRef]
33 . P. Paddon and J. F. Young , “ Two-dimensional vector-coupled-mode theory for textured planar waveguides ,” Phys. Rev. B 61 , 2090 – 2101 ( 2000 ). [CrossRef]
4. Three-dimensional woodpile photonic crystal
34 . B. Gralak , M. de Dood , G. Tayeb , S. Enoch , and D. Maystre , “ Theoretical study of photonic band gaps in woodpile crystals ,” Phys. Rev. E 67 , 066601 ( 2003 ). [CrossRef]
29 . T. Ueta , K. Ohtaka , N. Kawai , and K. Sakoda , “ Limits on quality factors of localized defect modes in photonic crystals due to dielectric loss ,” J. Appl. Phys. 84 , 6299 – 6304 ( 1998 ). [CrossRef]
Acknowledgments
References and links
1 . | J. B. Pendry and L. Martín-Moreno , “ Energy-loss by charged-particles in complex media ,” Phys. Rev. B 50 , 5062 – 5073 ( 1994 ). [CrossRef] |
2 . | 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] |
3 . | 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] |
4 . | 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] |
5 . | 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] |
6 . | 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] |
7 . | S. J. Smith and E. M. Purcell , “ Visible light from localized surface charges moving across a grating ,” Phys. Rev. 92 , 1069 ( 1953 ). [CrossRef] |
8 . | E. Chow , S. Y. Lin , S. G. Johnson , P. R. Villeneuve , J. D. Joannopoulos , J. R. Wendt , G. A. Vawter , W. Zubrzycki , H. Hou , and A. Alleman , “ Three-dimensional control of light in a two-dimensional photonic crystal slab ,” Nature 407 , 983 – 986 ( 2000 ). [CrossRef] [PubMed] |
9 . | S. Y. Lin , J. G. Fleming , D. L. Hetherington , B. K. Smith , R. Biswas , K. M. Ho , M. M. Sigalas , W. Zubrzycki , S. R. Kurtz , and J. Bur , “ A three-dimensional photonic crystal operating at infrared wavelengths ,” Nature 394 , 251 – 253 ( 1998 ). [CrossRef] |
10 . | D. M. Whittaker and I. S. Culshaw , “ Scattering-matrix treatment of patterned multilayer photonic structures ,” Phys. Rev. B 60 , 2610 – 2618 ( 1999 ). [CrossRef] |
11 . | S. G. Tikhodeev , A. L. Yablonskii , E. A. Muljarov , N. A. Gippius , and T. Ishihara , “ Quasiguided modes and optical properties of photonic crystal slabs ,” Phys. Rev. B 66 , 045102 ( 2002 ). [CrossRef] |
12 . | B. Gralak , S. Enoch , and G. Tayeb , “ From scattering or impedance matrices to Bloch modes of photonic crystals ,” J. Opt. Soc. Am. A 19 , 1547 – 1554 ( 2002 ). [CrossRef] |
13 . | Z. Y. Li and L. L. Lin , “ Photonic band structures solved by a plane-wave-based transfer-matrix method ,” Phys. Rev. E 67 , 046607 ( 2003 ). [CrossRef] |
14 . | 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] |
15 . | A. Gover , P. Dvorkis , and U. Elisha , “ Angular radiation-pattern of Smith-Purcell radiation ,” J. Opt. Soc. Am. B 1 , 723 – 728 ( 1984 ). [CrossRef] |
16 . | I. Shih , W. W. Salisbury , D. L. Masters , and D. B. Chang , “ Measurements of Smith-Purcell radiation ,” J. Opt. Soc. Am. B 7 , 345 – 350 ( 1990 ). [CrossRef] |
17 . | 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] |
18 . | 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] |
19 . | 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] |
20 . | Y. Shibata , S. Hasebe , K. Ishi , S. Ono , M. Ikezawa , T. Nakazato , M. Oyamada , S. Urasawa , T. Takahashi , T. Mat-suyama , 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] |
21 . | F. J. García de Abajo , “ Smith-Purcell radiation emission in aligned nanoparticles ,” Phys. Rev. E 61 , 5743 – 5752 ( 2000 ). [CrossRef] |
22 . | K. Ohtaka and S. Yamaguti , “ Theoretical study of the Smith-Purcell effect involving photonic crystals ,” Opt. Spectrosc. 91 , 477 – 483 ( 2001 ). [CrossRef] |
23 . | 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] |
24 . | 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 ( 2004 ). [CrossRef] |
25 . | S. P. Ogawa , M. Imada , S. Yoshimoto , M. Okano , and S. Noda , “ Control of light emission by 3D photonic crystals ,” Science 305 , 227 – 229 ( 2004 ). [CrossRef] [PubMed] |
26 . | M. Okano and S. Noda , “ Analysis of multimode point-defect cavities in three-dimensional photonic crystals using group theory in frequency and time domains ,” Phys. Rev. B 70 , 125105 ( 2004 ). [CrossRef] |
27 . | C. Luo , M. Ibanescu , S. G. Johnson , and J. D. Joannopoulos , Science 299 , 368 – 371 ( 2003 ). [CrossRef] [PubMed] |
28 . | J. Pendry , Low Energy Electron Diffraction ( Academic, London , 1974 ). |
29 . | T. Ueta , K. Ohtaka , N. Kawai , and K. Sakoda , “ Limits on quality factors of localized defect modes in photonic crystals due to dielectric loss ,” J. Appl. Phys. 84 , 6299 – 6304 ( 1998 ). [CrossRef] |
30 . | T. Ochiai and K. Sakoda , “ Dispersion relation and optical transmittance of a hexagonal photonic crystal slab ,” Phys. Rev. B 63 , 125107 ( 2001 ). [CrossRef] |
31 . | T. Ochiai and K. Sakoda , “ Nearly free-photon approximation for two-dimensional photonic crystal slabs ,” Phys. Rev. B 64 , 045108 ( 2001 ). [CrossRef] |
32 . | K. Ohtaka , J. Inoue , and S. Yamaguti , “ Derivation of the density of states of leaky photonic bands ,” Phys. Rev. B 70 , 035 ,109 ( 2004 ). [CrossRef] |
33 . | P. Paddon and J. F. Young , “ Two-dimensional vector-coupled-mode theory for textured planar waveguides ,” Phys. Rev. B 61 , 2090 – 2101 ( 2000 ). [CrossRef] |
34 . | B. Gralak , M. de Dood , G. Tayeb , S. Enoch , and D. Maystre , “ Theoretical study of photonic band gaps in woodpile crystals ,” Phys. Rev. E 67 , 066601 ( 2003 ). [CrossRef] |
OCIS Codes
(230.3990) Optical devices : Micro-optical devices
(230.4170) Optical devices : Multilayers
(300.2140) Spectroscopy : Emission
ToC Category:
Research Papers
History
Original Manuscript: August 11, 2005
Revised Manuscript: September 14, 2005
Published: September 19, 2005
Citation
Tetsuyuki Ochiai and Kazuo Ohtaka, "Electron energy loss and Smith-Purcell radiation in two- and three-dimensional photonic crystals," Opt. Express 13, 7683-7698 (2005)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-13-19-7683
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References
- J. B. Pendry and L. Martín-Moreno, �??Energy-loss by charged-particles in complex media,�?? Phys. Rev. B 50, 5062�??5073 (1994). [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]
- 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]
- 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]
- S. J. Smith and E. M. Purcell, �??Visible light from localized surface charges moving across a grating,�?? Phys. Rev. 92, 1069 (1953). [CrossRef]
- E. Chow, S. Y. Lin, S. G. Johnson, P. R. Villeneuve, J. D. Joannopoulos, J. R.Wendt, G. A. Vawter,W. Zubrzycki, H. Hou, and A. Alleman, �??Three-dimensional control of light in a two-dimensional photonic crystal slab,�?? Nature 407, 983�??986 (2000). [CrossRef] [PubMed]
- S. Y. Lin, J. G. Fleming, D. L. Hetherington, B. K. Smith, R. Biswas, K. M. Ho, M. M. Sigalas, W. Zubrzycki, S. R. Kurtz, and J. Bur, �??A three-dimensional photonic crystal operating at infrared wavelengths,�?? Nature 394, 251�??253 (1998). [CrossRef]
- D. M. Whittaker and I. S. Culshaw, �??Scattering-matrix treatment of patterned multilayer photonic structures,�?? Phys. Rev. B 60, 2610�??2618 (1999). [CrossRef]
- S. G. Tikhodeev, A. L. Yablonskii, E. A. Muljarov, N. A. Gippius, and T. Ishihara, �??Quasiguided modes and optical properties of photonic crystal slabs,�?? Phys. Rev. B 66, 045102 (2002). [CrossRef]
- B. Gralak, S. Enoch, and G. Tayeb, �??From scattering or impedance matrices to Bloch modes of photonic crystals,�?? J. Opt. Soc. Am. A 19, 1547�??1554 (2002). [CrossRef]
- Z. Y. Li and L. L. Lin, �??Photonic band structures solved by a plane-wave-based transfer-matrix method,�?? Phys. Rev. E 67, 046607 (2003). [CrossRef]
- 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]
- A. Gover, P. Dvorkis, and U. Elisha, �??Angular radiation-pattern of Smith-Purcell radiation,�?? J. Opt. Soc. Am. B 1, 723�??728 (1984). [CrossRef]
- I. Shih, W. W. Salisbury, D. L. Masters, and D. B. Chang, �??Measurements of Smith-Purcell radiation,�?? J. Opt. Soc. Am. B 7, 345�??350 (1990). [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]
- 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]
- 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]
- 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]
- F. J. García de Abajo, �??Smith-Purcell radiation emission in aligned nanoparticles,�?? Phys. Rev. E 61, 5743�??5752 (2000). [CrossRef]
- K. Ohtaka and S. Yamaguti, �??Theoretical study of the Smith-Purcell effect involving photonic crystals,�?? Opt. Spectrosc. 91, 477�??483 (2001). [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. 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 (2004). [CrossRef]
- S. P. Ogawa, M. Imada, S. Yoshimoto, M. Okano, and S. Noda, �??Control of light emission by 3D photonic crystals,�?? Science 305, 227�??229 (2004). [CrossRef] [PubMed]
- M. Okano and S. Noda, �??Analysis of multimode point-defect cavities in three-dimensional photonic crystals using group theory in frequency and time domains,�?? Phys. Rev. B 70, 125105 (2004). [CrossRef]
- C. Luo, M. Ibanescu, S. G. Johnson, and J. D. Joannopoulos, Science 299, 368�??371 (2003). [CrossRef] [PubMed]
- J. Pendry, Low Energy Electron Diffraction (Academic, London, 1974).
- T. Ueta, K. Ohtaka, N. Kawai, and K. Sakoda, �??Limits on quality factors of localized defect modes in photonic crystals due to dielectric loss,�?? J. Appl. Phys. 84, 6299�??6304 (1998). [CrossRef]
- T. Ochiai and K. Sakoda, �??Dispersion relation and optical transmittance of a hexagonal photonic crystal slab,�?? Phys. Rev. B 63, 125107 (2001). [CrossRef]
- T. Ochiai and K. Sakoda, �??Nearly free-photon approximation for two-dimensional photonic crystal slabs,�?? Phys. Rev. B 64, 045108 (2001). [CrossRef]
- K. Ohtaka, J. Inoue, and S. Yamaguti, �??Derivation of the density of states of leaky photonic bands,�?? Phys. Rev. B 70, 035,109 (2004). [CrossRef]
- P. Paddon and J. F. Young, �??Two-dimensional vector-coupled-mode theory for textured planar waveguides,�?? Phys. Rev. B 61, 2090�??2101 (2000). [CrossRef]
- B. Gralak, M. de Dood, G. Tayeb, S. Enoch, and D. Maystre, �??Theoretical study of photonic band gaps in woodpile crystals,�?? Phys. Rev. E 67, 066601 (2003). [CrossRef]
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