Abstract

A novel radiation emission from traveling charged particles in vacuum is theoretically demonstrated. This radiation is conical as in the Cherenkov radiation, but emerges in backward directions of the particle trajectories. The basic mechanism of the radiation is the Smith-Purcell effect via the interaction between the charged particles and a circular-symmetric photonic wire with a one-dimensionally periodic dielectric function. The wire exhibits the photonic band structure characterized with angular momentum. The charged particle can resonantly excite the photonic band modes with particular angular momentum, depending on the particle velocity. A simple kinetics of the Smith-Purcell effect enables us to design the conical radiation emitted in backward directions. Numerical results of the backward radiation are also presented for a metallic wire with aligned air holes.

© 2010 Optical Society of America

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References

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  1. P. A. Cherenkov, “Visible Emission of Clean Liquids by Action of Radiation,” Dokl. Akad. Nauk SSSR 2, 451 (1934).
  2. L. D. Landau, E. M. Lifshitz, and L. P. Pitaevskii, Electrodynamics of Continuous Media (Butterworth-Heinemann, Oxford, 1985).
  3. V. Veselago, “The electrodynamics of substances with simultaneously negative values of ε and μ,” Sov. Phys. Usp. 10(4), 509–514 (1968).
    [CrossRef]
  4. C. Luo, M. Ibanescu, S. G. Johnson, and J. D. Joannopoulos, “Cerenkov radiation in photonic crystals,” Science 299(5605), 368–371 (2003).
    [CrossRef] [PubMed]
  5. 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(14), 143902 (2003).
    [CrossRef]
  6. T. Ochiai, and K. Ohtaka, “Electron energy loss and Smith-Purcell radiation in two- and three-dimensional photonic crystals,” Opt. Express 13(19), 7683–7698 (2005).
    [CrossRef] [PubMed]
  7. C. Kremers, D. N. Chigrin, and J. Kroha, “Theory of Cherenkov radiation in periodic dielectric media: Emission spectrum,” Phys. Rev. A 79(1), 013829 (2009).
    [CrossRef]
  8. S. N. Galyamin, A. V. Tyukhtin, A. Kanareykin, and P. Schoessow, “Reversed Cherenkov-Transition Radiation by a Charge Crossing a Left-Handed Medium Boundary,” Phys. Rev. Lett. 103(19), 194802 (2009).
    [CrossRef]
  9. R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292(5514), 77–79 (2001).
    [CrossRef] [PubMed]
  10. S. Xi, H. Chen, T. Jiang, L. Ran, J. Huangfu, B. I. Wu, J. A. Kong, and M. Chen, “Experimental Verification of Reversed Cherenkov Radiation in Left-Handed Metamaterial,” Phys. Rev. Lett. 103(19), 194801 (2009).
    [CrossRef]
  11. S. J. Smith and E. M. Purcell, “Visible light from localized surface charges moving across a grating,” Phys. Rev. 92(4–15), 1069 (1953).
    [CrossRef]
  12. F. J. García de Abajo, “Smith-Purcell radiation emission in aligned nanoparticles,” Phys. Rev. E 61(5), 5743–5752 (2000).
    [CrossRef]
  13. Y. Hara, T. Mukaiyama, K. Takeda, and M. Kuwata-Gonokami, “Heavy photon states in photonic chains of resonantly coupled cavities with supermonodispersive microspheres,” Phys. Rev. Lett. 94(20), 203905 (2005).
    [CrossRef] [PubMed]
  14. J. M. Gérard, B. Sermage, B. Gayral, B. Legrand, E. Costard, and V. Thierry-Mieg, “Enhanced spontaneous emission by quantum boxes in a monolithic optical microcavity,” Phys. Rev. Lett. 81(5), 1110–1113 (1998).
    [CrossRef]
  15. K. O. Hill, and G. Meltz, “Fiber Bragg grating technology fundamentals and overview,” J. Lightwave Technol. 15(8), 1263–1276 (1997).
    [CrossRef]
  16. A similar mechanism works in photonic crystals if they are periodic in the direction of the particle trajectory [4,6,7].
  17. K. Ohtaka, “Energy-band of photons and low-energy photon diffraction,” Phys. Rev. B 19(10), 5057–5067 (1979).
    [CrossRef]
  18. K. Ohtaka, T. Ueta, and K. Amemiya, “Calculation of photonic bands using vector cylindrical waves and reflectivity of light for an array of dielectric rods,” Phys. Rev. B 57(4), 2550–2568 (1998).
    [CrossRef]

2009 (3)

C. Kremers, D. N. Chigrin, and J. Kroha, “Theory of Cherenkov radiation in periodic dielectric media: Emission spectrum,” Phys. Rev. A 79(1), 013829 (2009).
[CrossRef]

S. N. Galyamin, A. V. Tyukhtin, A. Kanareykin, and P. Schoessow, “Reversed Cherenkov-Transition Radiation by a Charge Crossing a Left-Handed Medium Boundary,” Phys. Rev. Lett. 103(19), 194802 (2009).
[CrossRef]

S. Xi, H. Chen, T. Jiang, L. Ran, J. Huangfu, B. I. Wu, J. A. Kong, and M. Chen, “Experimental Verification of Reversed Cherenkov Radiation in Left-Handed Metamaterial,” Phys. Rev. Lett. 103(19), 194801 (2009).
[CrossRef]

2005 (2)

Y. Hara, T. Mukaiyama, K. Takeda, and M. Kuwata-Gonokami, “Heavy photon states in photonic chains of resonantly coupled cavities with supermonodispersive microspheres,” Phys. Rev. Lett. 94(20), 203905 (2005).
[CrossRef] [PubMed]

T. Ochiai, and K. Ohtaka, “Electron energy loss and Smith-Purcell radiation in two- and three-dimensional photonic crystals,” Opt. Express 13(19), 7683–7698 (2005).
[CrossRef] [PubMed]

2003 (2)

C. Luo, M. Ibanescu, S. G. Johnson, and J. D. Joannopoulos, “Cerenkov radiation in photonic crystals,” Science 299(5605), 368–371 (2003).
[CrossRef] [PubMed]

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(14), 143902 (2003).
[CrossRef]

2001 (1)

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292(5514), 77–79 (2001).
[CrossRef] [PubMed]

2000 (1)

F. J. García de Abajo, “Smith-Purcell radiation emission in aligned nanoparticles,” Phys. Rev. E 61(5), 5743–5752 (2000).
[CrossRef]

1998 (2)

K. Ohtaka, T. Ueta, and K. Amemiya, “Calculation of photonic bands using vector cylindrical waves and reflectivity of light for an array of dielectric rods,” Phys. Rev. B 57(4), 2550–2568 (1998).
[CrossRef]

J. M. Gérard, B. Sermage, B. Gayral, B. Legrand, E. Costard, and V. Thierry-Mieg, “Enhanced spontaneous emission by quantum boxes in a monolithic optical microcavity,” Phys. Rev. Lett. 81(5), 1110–1113 (1998).
[CrossRef]

1997 (1)

K. O. Hill, and G. Meltz, “Fiber Bragg grating technology fundamentals and overview,” J. Lightwave Technol. 15(8), 1263–1276 (1997).
[CrossRef]

1979 (1)

K. Ohtaka, “Energy-band of photons and low-energy photon diffraction,” Phys. Rev. B 19(10), 5057–5067 (1979).
[CrossRef]

1968 (1)

V. Veselago, “The electrodynamics of substances with simultaneously negative values of ε and μ,” Sov. Phys. Usp. 10(4), 509–514 (1968).
[CrossRef]

1953 (1)

S. J. Smith and E. M. Purcell, “Visible light from localized surface charges moving across a grating,” Phys. Rev. 92(4–15), 1069 (1953).
[CrossRef]

1934 (1)

P. A. Cherenkov, “Visible Emission of Clean Liquids by Action of Radiation,” Dokl. Akad. Nauk SSSR 2, 451 (1934).

Amemiya, K.

K. Ohtaka, T. Ueta, and K. Amemiya, “Calculation of photonic bands using vector cylindrical waves and reflectivity of light for an array of dielectric rods,” Phys. Rev. B 57(4), 2550–2568 (1998).
[CrossRef]

Chen, H.

S. Xi, H. Chen, T. Jiang, L. Ran, J. Huangfu, B. I. Wu, J. A. Kong, and M. Chen, “Experimental Verification of Reversed Cherenkov Radiation in Left-Handed Metamaterial,” Phys. Rev. Lett. 103(19), 194801 (2009).
[CrossRef]

Chen, M.

S. Xi, H. Chen, T. Jiang, L. Ran, J. Huangfu, B. I. Wu, J. A. Kong, and M. Chen, “Experimental Verification of Reversed Cherenkov Radiation in Left-Handed Metamaterial,” Phys. Rev. Lett. 103(19), 194801 (2009).
[CrossRef]

Cherenkov, P. A.

P. A. Cherenkov, “Visible Emission of Clean Liquids by Action of Radiation,” Dokl. Akad. Nauk SSSR 2, 451 (1934).

Chigrin, D. N.

C. Kremers, D. N. Chigrin, and J. Kroha, “Theory of Cherenkov radiation in periodic dielectric media: Emission spectrum,” Phys. Rev. A 79(1), 013829 (2009).
[CrossRef]

Costard, E.

J. M. Gérard, B. Sermage, B. Gayral, B. Legrand, E. Costard, and V. Thierry-Mieg, “Enhanced spontaneous emission by quantum boxes in a monolithic optical microcavity,” Phys. Rev. Lett. 81(5), 1110–1113 (1998).
[CrossRef]

Echenique, P. M.

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(14), 143902 (2003).
[CrossRef]

Galyamin, S. N.

S. N. Galyamin, A. V. Tyukhtin, A. Kanareykin, and P. Schoessow, “Reversed Cherenkov-Transition Radiation by a Charge Crossing a Left-Handed Medium Boundary,” Phys. Rev. Lett. 103(19), 194802 (2009).
[CrossRef]

García de Abajo, F. J.

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(14), 143902 (2003).
[CrossRef]

F. J. García de Abajo, “Smith-Purcell radiation emission in aligned nanoparticles,” Phys. Rev. E 61(5), 5743–5752 (2000).
[CrossRef]

Gayral, B.

J. M. Gérard, B. Sermage, B. Gayral, B. Legrand, E. Costard, and V. Thierry-Mieg, “Enhanced spontaneous emission by quantum boxes in a monolithic optical microcavity,” Phys. Rev. Lett. 81(5), 1110–1113 (1998).
[CrossRef]

Gérard, J. M.

J. M. Gérard, B. Sermage, B. Gayral, B. Legrand, E. Costard, and V. Thierry-Mieg, “Enhanced spontaneous emission by quantum boxes in a monolithic optical microcavity,” Phys. Rev. Lett. 81(5), 1110–1113 (1998).
[CrossRef]

Hara, Y.

Y. Hara, T. Mukaiyama, K. Takeda, and M. Kuwata-Gonokami, “Heavy photon states in photonic chains of resonantly coupled cavities with supermonodispersive microspheres,” Phys. Rev. Lett. 94(20), 203905 (2005).
[CrossRef] [PubMed]

Hill, K. O.

K. O. Hill, and G. Meltz, “Fiber Bragg grating technology fundamentals and overview,” J. Lightwave Technol. 15(8), 1263–1276 (1997).
[CrossRef]

Huangfu, J.

S. Xi, H. Chen, T. Jiang, L. Ran, J. Huangfu, B. I. Wu, J. A. Kong, and M. Chen, “Experimental Verification of Reversed Cherenkov Radiation in Left-Handed Metamaterial,” Phys. Rev. Lett. 103(19), 194801 (2009).
[CrossRef]

Ibanescu, M.

C. Luo, M. Ibanescu, S. G. Johnson, and J. D. Joannopoulos, “Cerenkov radiation in photonic crystals,” Science 299(5605), 368–371 (2003).
[CrossRef] [PubMed]

Jiang, T.

S. Xi, H. Chen, T. Jiang, L. Ran, J. Huangfu, B. I. Wu, J. A. Kong, and M. Chen, “Experimental Verification of Reversed Cherenkov Radiation in Left-Handed Metamaterial,” Phys. Rev. Lett. 103(19), 194801 (2009).
[CrossRef]

Joannopoulos, J. D.

C. Luo, M. Ibanescu, S. G. Johnson, and J. D. Joannopoulos, “Cerenkov radiation in photonic crystals,” Science 299(5605), 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(5605), 368–371 (2003).
[CrossRef] [PubMed]

Kanareykin, A.

S. N. Galyamin, A. V. Tyukhtin, A. Kanareykin, and P. Schoessow, “Reversed Cherenkov-Transition Radiation by a Charge Crossing a Left-Handed Medium Boundary,” Phys. Rev. Lett. 103(19), 194802 (2009).
[CrossRef]

Kong, J. A.

S. Xi, H. Chen, T. Jiang, L. Ran, J. Huangfu, B. I. Wu, J. A. Kong, and M. Chen, “Experimental Verification of Reversed Cherenkov Radiation in Left-Handed Metamaterial,” Phys. Rev. Lett. 103(19), 194801 (2009).
[CrossRef]

Kremers, C.

C. Kremers, D. N. Chigrin, and J. Kroha, “Theory of Cherenkov radiation in periodic dielectric media: Emission spectrum,” Phys. Rev. A 79(1), 013829 (2009).
[CrossRef]

Kroha, J.

C. Kremers, D. N. Chigrin, and J. Kroha, “Theory of Cherenkov radiation in periodic dielectric media: Emission spectrum,” Phys. Rev. A 79(1), 013829 (2009).
[CrossRef]

Kuwata-Gonokami, M.

Y. Hara, T. Mukaiyama, K. Takeda, and M. Kuwata-Gonokami, “Heavy photon states in photonic chains of resonantly coupled cavities with supermonodispersive microspheres,” Phys. Rev. Lett. 94(20), 203905 (2005).
[CrossRef] [PubMed]

Legrand, B.

J. M. Gérard, B. Sermage, B. Gayral, B. Legrand, E. Costard, and V. Thierry-Mieg, “Enhanced spontaneous emission by quantum boxes in a monolithic optical microcavity,” Phys. Rev. Lett. 81(5), 1110–1113 (1998).
[CrossRef]

Luo, C.

C. Luo, M. Ibanescu, S. G. Johnson, and J. D. Joannopoulos, “Cerenkov radiation in photonic crystals,” Science 299(5605), 368–371 (2003).
[CrossRef] [PubMed]

Meltz, G.

K. O. Hill, and G. Meltz, “Fiber Bragg grating technology fundamentals and overview,” J. Lightwave Technol. 15(8), 1263–1276 (1997).
[CrossRef]

Mukaiyama, T.

Y. Hara, T. Mukaiyama, K. Takeda, and M. Kuwata-Gonokami, “Heavy photon states in photonic chains of resonantly coupled cavities with supermonodispersive microspheres,” Phys. Rev. Lett. 94(20), 203905 (2005).
[CrossRef] [PubMed]

Ochiai, T.

Ohtaka, K.

T. Ochiai, and K. Ohtaka, “Electron energy loss and Smith-Purcell radiation in two- and three-dimensional photonic crystals,” Opt. Express 13(19), 7683–7698 (2005).
[CrossRef] [PubMed]

K. Ohtaka, T. Ueta, and K. Amemiya, “Calculation of photonic bands using vector cylindrical waves and reflectivity of light for an array of dielectric rods,” Phys. Rev. B 57(4), 2550–2568 (1998).
[CrossRef]

K. Ohtaka, “Energy-band of photons and low-energy photon diffraction,” Phys. Rev. B 19(10), 5057–5067 (1979).
[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(14), 143902 (2003).
[CrossRef]

Purcell, E. M.

S. J. Smith and E. M. Purcell, “Visible light from localized surface charges moving across a grating,” Phys. Rev. 92(4–15), 1069 (1953).
[CrossRef]

Ran, L.

S. Xi, H. Chen, T. Jiang, L. Ran, J. Huangfu, B. I. Wu, J. A. Kong, and M. Chen, “Experimental Verification of Reversed Cherenkov Radiation in Left-Handed Metamaterial,” Phys. Rev. Lett. 103(19), 194801 (2009).
[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(14), 143902 (2003).
[CrossRef]

Schoessow, P.

S. N. Galyamin, A. V. Tyukhtin, A. Kanareykin, and P. Schoessow, “Reversed Cherenkov-Transition Radiation by a Charge Crossing a Left-Handed Medium Boundary,” Phys. Rev. Lett. 103(19), 194802 (2009).
[CrossRef]

Schultz, S.

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292(5514), 77–79 (2001).
[CrossRef] [PubMed]

Sermage, B.

J. M. Gérard, B. Sermage, B. Gayral, B. Legrand, E. Costard, and V. Thierry-Mieg, “Enhanced spontaneous emission by quantum boxes in a monolithic optical microcavity,” Phys. Rev. Lett. 81(5), 1110–1113 (1998).
[CrossRef]

Shelby, R. A.

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292(5514), 77–79 (2001).
[CrossRef] [PubMed]

Smith, D. R.

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292(5514), 77–79 (2001).
[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(4–15), 1069 (1953).
[CrossRef]

Takeda, K.

Y. Hara, T. Mukaiyama, K. Takeda, and M. Kuwata-Gonokami, “Heavy photon states in photonic chains of resonantly coupled cavities with supermonodispersive microspheres,” Phys. Rev. Lett. 94(20), 203905 (2005).
[CrossRef] [PubMed]

Thierry-Mieg, V.

J. M. Gérard, B. Sermage, B. Gayral, B. Legrand, E. Costard, and V. Thierry-Mieg, “Enhanced spontaneous emission by quantum boxes in a monolithic optical microcavity,” Phys. Rev. Lett. 81(5), 1110–1113 (1998).
[CrossRef]

Tyukhtin, A. V.

S. N. Galyamin, A. V. Tyukhtin, A. Kanareykin, and P. Schoessow, “Reversed Cherenkov-Transition Radiation by a Charge Crossing a Left-Handed Medium Boundary,” Phys. Rev. Lett. 103(19), 194802 (2009).
[CrossRef]

Ueta, T.

K. Ohtaka, T. Ueta, and K. Amemiya, “Calculation of photonic bands using vector cylindrical waves and reflectivity of light for an array of dielectric rods,” Phys. Rev. B 57(4), 2550–2568 (1998).
[CrossRef]

Veselago, V.

V. Veselago, “The electrodynamics of substances with simultaneously negative values of ε and μ,” Sov. Phys. Usp. 10(4), 509–514 (1968).
[CrossRef]

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(14), 143902 (2003).
[CrossRef]

Wu, B. I.

S. Xi, H. Chen, T. Jiang, L. Ran, J. Huangfu, B. I. Wu, J. A. Kong, and M. Chen, “Experimental Verification of Reversed Cherenkov Radiation in Left-Handed Metamaterial,” Phys. Rev. Lett. 103(19), 194801 (2009).
[CrossRef]

Xi, S.

S. Xi, H. Chen, T. Jiang, L. Ran, J. Huangfu, B. I. Wu, J. A. Kong, and M. Chen, “Experimental Verification of Reversed Cherenkov Radiation in Left-Handed Metamaterial,” Phys. Rev. Lett. 103(19), 194801 (2009).
[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(14), 143902 (2003).
[CrossRef]

Dokl. Akad. Nauk SSSR (1)

P. A. Cherenkov, “Visible Emission of Clean Liquids by Action of Radiation,” Dokl. Akad. Nauk SSSR 2, 451 (1934).

J. Lightwave Technol. (1)

K. O. Hill, and G. Meltz, “Fiber Bragg grating technology fundamentals and overview,” J. Lightwave Technol. 15(8), 1263–1276 (1997).
[CrossRef]

Opt. Express (1)

Phys. Rev. (1)

S. J. Smith and E. M. Purcell, “Visible light from localized surface charges moving across a grating,” Phys. Rev. 92(4–15), 1069 (1953).
[CrossRef]

Phys. Rev. A (1)

C. Kremers, D. N. Chigrin, and J. Kroha, “Theory of Cherenkov radiation in periodic dielectric media: Emission spectrum,” Phys. Rev. A 79(1), 013829 (2009).
[CrossRef]

Phys. Rev. B (2)

K. Ohtaka, “Energy-band of photons and low-energy photon diffraction,” Phys. Rev. B 19(10), 5057–5067 (1979).
[CrossRef]

K. Ohtaka, T. Ueta, and K. Amemiya, “Calculation of photonic bands using vector cylindrical waves and reflectivity of light for an array of dielectric rods,” Phys. Rev. B 57(4), 2550–2568 (1998).
[CrossRef]

Phys. Rev. E (1)

F. J. García de Abajo, “Smith-Purcell radiation emission in aligned nanoparticles,” Phys. Rev. E 61(5), 5743–5752 (2000).
[CrossRef]

Phys. Rev. Lett. (5)

Y. Hara, T. Mukaiyama, K. Takeda, and M. Kuwata-Gonokami, “Heavy photon states in photonic chains of resonantly coupled cavities with supermonodispersive microspheres,” Phys. Rev. Lett. 94(20), 203905 (2005).
[CrossRef] [PubMed]

J. M. Gérard, B. Sermage, B. Gayral, B. Legrand, E. Costard, and V. Thierry-Mieg, “Enhanced spontaneous emission by quantum boxes in a monolithic optical microcavity,” Phys. Rev. Lett. 81(5), 1110–1113 (1998).
[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(14), 143902 (2003).
[CrossRef]

S. Xi, H. Chen, T. Jiang, L. Ran, J. Huangfu, B. I. Wu, J. A. Kong, and M. Chen, “Experimental Verification of Reversed Cherenkov Radiation in Left-Handed Metamaterial,” Phys. Rev. Lett. 103(19), 194801 (2009).
[CrossRef]

S. N. Galyamin, A. V. Tyukhtin, A. Kanareykin, and P. Schoessow, “Reversed Cherenkov-Transition Radiation by a Charge Crossing a Left-Handed Medium Boundary,” Phys. Rev. Lett. 103(19), 194802 (2009).
[CrossRef]

Science (2)

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292(5514), 77–79 (2001).
[CrossRef] [PubMed]

C. Luo, M. Ibanescu, S. G. Johnson, and J. D. Joannopoulos, “Cerenkov radiation in photonic crystals,” Science 299(5605), 368–371 (2003).
[CrossRef] [PubMed]

Sov. Phys. Usp. (1)

V. Veselago, “The electrodynamics of substances with simultaneously negative values of ε and μ,” Sov. Phys. Usp. 10(4), 509–514 (1968).
[CrossRef]

Other (2)

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

A similar mechanism works in photonic crystals if they are periodic in the direction of the particle trajectory [4,6,7].

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Figures (5)

Fig. 1.
Fig. 1.

Schematic illustration of the system under study. It consists of a periodic arrangement of spherical air holes with lattice constant a, embedded in a infinitely-long circular cylinder. A charged particle travels with impact parameter b, outside the cylinder. The particle trajectory is parallel to the cylindrical axis (taken to be the z axis). The charged particle can induce the radiation emission that can be detected at a far-field observation point of solid angle Ω = (θ,ϕ).

Fig. 2.
Fig. 2.

The photonic band diagram of the metallic wire with periodic arrangement of air holes inside. The radius and the dielectric constant of the wire are given by 0.5a and ε = 1−(ωp /ω)2, respectively, where ωpa/(2πc) is fixed to be 1. The air-hole radius is taken to be 0.3a. The photonic bands are classified according to angular momentum m (indicated in the legend) with respect to the wire axis. The light line ω = c|kz | and the shifted v-line ω = v(kz + G) with v = 0.7c are also shown by dashed and solid lines, respectively.

Fig. 3.
Fig. 3.

The Smith-Purcell radiation spectra Γ(ω) for dissipation-less (η = 0, black curve) and dissipative (ηa/(2πc) = 0.01, red curve) metallic wire. The following parameters are used: v = 0.7c and b = a. For comparison, the Cherenkov radiation spectrum ΓCR(ω) is also shown (by blue curve) for a medium with refractive index n = 2.

Fig. 4.
Fig. 4.

The azimuthal angle distribution of the induced radiation emission at the lowest three peaks in Fig. 3. Black, red, and blue curves stand for ωa/(2πc) = 0.447,0.508, and 0.580, respectively.

Fig. 5.
Fig. 5.

The radiation energy density and the Poynting vector flow in the zx plane (y = 0) at ωa/2πc = 0.447. The Poynting vector flow below x/a = 1.4 is omitted and the maximal energy density is normalized to be 1. The electron trajectory is at (x,y) = (a,0), and is indicated by the green arrow.

Equations (3)

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θ G = cos 1 ( c ν cG ω ) .
W = 0 d ω h ¯ ω Γ ( ω ) ,
Γ CR ( ω ) = μ 0 e 2 2 h ( 1 ( c nv ) 2 ) ,

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