Abstract

The Vavilov–Cherenkov radiation of a charge moving along the main axis of an anisotropic uniaxial nongyrotropic medium with resonant-type dispersion is analyzed. This model of the medium is typical both for crystals and for some metamaterials. The analytical results obtained using the complex plane analysis and the corresponding computed examples for the electromagnetic field components and energy patterns are given. The electromagnetic field is presented as the sum of a quasi-Coulomb field and a radiation field (the plasma oscillations are not generated in the case under consideration). The classification of media with respect to the character of the energy pattern directivity is given. It is shown that patterns of five different types can be realized. Each of them has two lobes, which can be “forward,” “reversed,” or “mixed.”

© 2011 Optical Society of America

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  1. J. V. Jelley, Čerenkov Radiation and Its Applications(Pergamon, 1958).
  2. V. P. Zrelov, Vavilov-Cherenkov Radiation in High-Energy Physics (Israel Program for Scientific Translations, 1970).
  3. I. M. Frank, Vavilov-Cherenkov Radiation: Theoretical Aspects (Nauka, 1988), in Russian.
  4. B. M. Bolotovskiy, “Theory of the Vavilov-Cerenkov effect,” Usp. Fiz. Nauk 62, 201-246 (1957).
  5. V. L. Ginzburg and V. N. Tsytovich, Transition Radiation and Transition Scattering (Hilger, 1990).
  6. V. E. Pafomov, “On transition radiation and the Vavilov-Cherenkov radiation,” Sov. Phys. JETP 9, 1321-1324 (1959).
  7. Y. O. Averkov, “Transition radiation by an electron bunch that crosses the vacuum/left-handed material interface,” Telecommun. Radio Eng. 63, 419-433 (2005).
    [CrossRef]
  8. J. Lu, T. M. Grzegorczyk, Y. Zhang, J. Pancheto, Jr., B.-I. Wu, J. A. Kong, and M. Chen, “Cerenkov radiation in materials with negative permittivity and permeability,” Opt. Express 11, 723-734 (2003).
    [CrossRef] [PubMed]
  9. 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, 194802(2009).
    [CrossRef]
  10. S. N. Galyamin and A. V. Tyukhtin, “Electromagnetic field of a moving charge in the presence of a left-handed medium,” Phys. Rev. B 81, 235134 (2010).
    [CrossRef]
  11. S. N. Galyamin and A. V. Tyukhtin, “New approach to the theory of a moving charge's radiation in dispersive medium and its application to the case of left-handed materials,” J. Phys. Conf. Ser. 236, 012003 (2010).
    [CrossRef]
  12. S. N. Galyamin and A. V. Tyukhtin, “Reversed Cherenkov transition radiation of charge entering anisotropic medium,” Tech. Phys. Lett. 37, 317-321 (2011).
    [CrossRef]
  13. C. Luo, M. Ibanescu, S. G. Johnson, and J. D. Joannopoulos, “Cerenkov radiation in photonic crystals,” Science 299, 386-371 (2003).
    [CrossRef]
  14. C. Kremers, D. N. Chigrin, and J. Kroha, “Theory of Cherenkov radiation in periodic dielectric media: emission spectrum,” Phys. Rev. A 79, 013829 (2009).
    [CrossRef]
  15. C. Kremers and D. N. Chigrin, “Spatial distribution of Cherenkov radiation in periodic dielectric media,” J. Opt. A 11, 114008(2009).
    [CrossRef]
  16. J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, “Extremely low frequency plasmons in metallic mesostructures,” Phys. Rev. Lett. 76, 4773-4776 (1996).
    [CrossRef] [PubMed]
  17. D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184-4187(2000).
    [CrossRef] [PubMed]
  18. X. Cheng, H. Chen, L. Ran, B.-I. Wu, T. M. Grzegorczyk, and J. A. Kong, “Negative refraction and cross polarization effects in metamaterial realized with bianisotropic S-ring resonator,” Phys. Rev. B 76, 024402 (2007).
    [CrossRef]
  19. Z. Y. Duan, B.-I. Wu, H. S. Chen, S. Xi, and M. Chen, “Research progress in reversed Cherenkov radiation in double-negative metamaterials,” Progress Electromagn. Res. 90, 75-87 (2009).
    [CrossRef]
  20. Z. Y. Duan, B.-I. Wu, J. Lu, J. A. Kong, and M. Chen, “Reversed Cherenkov radiation in unbounded anisotropic double-negative metamaterials,” J. Phys. D 42, 185102 (2009).
    [CrossRef]
  21. S. Antipov, L. Spentzouris, W. Liu, W. Gai, and J. G. Power, “Wakefield generation in metamaterial-loaded waveguides,” J. Appl. Phys. 102, 034906 (2007).
    [CrossRef]
  22. L. B. Felsen and N. Marcuvitz, Radiation and Scattering of Waves (Wiley Interscience, 2003).
  23. L. I. Mandelstam, “Group velocity in the crystal lattice,” Zh. Eksp. Teor. Fiz. 15, 475 (1945).
  24. B. M. Bolotovskiy and S. N. Stolyarov, “On radiation principles in medium with dispersion,” in Problems of Theoretical Physics: Collection of I. E. Tamm's Memory (Nauka, 1972), pp. 267-280.
  25. A. V. Tyukhtin and S. N. Galyamin, “Vavilov-Cherenkov radiation in passive and active media with complex resonant dispersion,” Phys. Rev. E 77, 066606 (2008).
    [CrossRef]
  26. H. Bateman and A. Erdélyi, Higher Transcendental Functions (McGraw-Hill, 1953).

2011

S. N. Galyamin and A. V. Tyukhtin, “Reversed Cherenkov transition radiation of charge entering anisotropic medium,” Tech. Phys. Lett. 37, 317-321 (2011).
[CrossRef]

2010

S. N. Galyamin and A. V. Tyukhtin, “Electromagnetic field of a moving charge in the presence of a left-handed medium,” Phys. Rev. B 81, 235134 (2010).
[CrossRef]

S. N. Galyamin and A. V. Tyukhtin, “New approach to the theory of a moving charge's radiation in dispersive medium and its application to the case of left-handed materials,” J. Phys. Conf. Ser. 236, 012003 (2010).
[CrossRef]

2009

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

C. Kremers and D. N. Chigrin, “Spatial distribution of Cherenkov radiation in periodic dielectric media,” J. Opt. A 11, 114008(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, 194802(2009).
[CrossRef]

Z. Y. Duan, B.-I. Wu, H. S. Chen, S. Xi, and M. Chen, “Research progress in reversed Cherenkov radiation in double-negative metamaterials,” Progress Electromagn. Res. 90, 75-87 (2009).
[CrossRef]

Z. Y. Duan, B.-I. Wu, J. Lu, J. A. Kong, and M. Chen, “Reversed Cherenkov radiation in unbounded anisotropic double-negative metamaterials,” J. Phys. D 42, 185102 (2009).
[CrossRef]

2008

A. V. Tyukhtin and S. N. Galyamin, “Vavilov-Cherenkov radiation in passive and active media with complex resonant dispersion,” Phys. Rev. E 77, 066606 (2008).
[CrossRef]

2007

X. Cheng, H. Chen, L. Ran, B.-I. Wu, T. M. Grzegorczyk, and J. A. Kong, “Negative refraction and cross polarization effects in metamaterial realized with bianisotropic S-ring resonator,” Phys. Rev. B 76, 024402 (2007).
[CrossRef]

S. Antipov, L. Spentzouris, W. Liu, W. Gai, and J. G. Power, “Wakefield generation in metamaterial-loaded waveguides,” J. Appl. Phys. 102, 034906 (2007).
[CrossRef]

2005

Y. O. Averkov, “Transition radiation by an electron bunch that crosses the vacuum/left-handed material interface,” Telecommun. Radio Eng. 63, 419-433 (2005).
[CrossRef]

2003

2000

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184-4187(2000).
[CrossRef] [PubMed]

1996

J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, “Extremely low frequency plasmons in metallic mesostructures,” Phys. Rev. Lett. 76, 4773-4776 (1996).
[CrossRef] [PubMed]

1959

V. E. Pafomov, “On transition radiation and the Vavilov-Cherenkov radiation,” Sov. Phys. JETP 9, 1321-1324 (1959).

1957

B. M. Bolotovskiy, “Theory of the Vavilov-Cerenkov effect,” Usp. Fiz. Nauk 62, 201-246 (1957).

1945

L. I. Mandelstam, “Group velocity in the crystal lattice,” Zh. Eksp. Teor. Fiz. 15, 475 (1945).

Antipov, S.

S. Antipov, L. Spentzouris, W. Liu, W. Gai, and J. G. Power, “Wakefield generation in metamaterial-loaded waveguides,” J. Appl. Phys. 102, 034906 (2007).
[CrossRef]

Averkov, Y. O.

Y. O. Averkov, “Transition radiation by an electron bunch that crosses the vacuum/left-handed material interface,” Telecommun. Radio Eng. 63, 419-433 (2005).
[CrossRef]

Bateman, H.

H. Bateman and A. Erdélyi, Higher Transcendental Functions (McGraw-Hill, 1953).

Bolotovskiy, B. M.

B. M. Bolotovskiy, “Theory of the Vavilov-Cerenkov effect,” Usp. Fiz. Nauk 62, 201-246 (1957).

B. M. Bolotovskiy and S. N. Stolyarov, “On radiation principles in medium with dispersion,” in Problems of Theoretical Physics: Collection of I. E. Tamm's Memory (Nauka, 1972), pp. 267-280.

Chen, H.

X. Cheng, H. Chen, L. Ran, B.-I. Wu, T. M. Grzegorczyk, and J. A. Kong, “Negative refraction and cross polarization effects in metamaterial realized with bianisotropic S-ring resonator,” Phys. Rev. B 76, 024402 (2007).
[CrossRef]

Chen, H. S.

Z. Y. Duan, B.-I. Wu, H. S. Chen, S. Xi, and M. Chen, “Research progress in reversed Cherenkov radiation in double-negative metamaterials,” Progress Electromagn. Res. 90, 75-87 (2009).
[CrossRef]

Chen, M.

Z. Y. Duan, B.-I. Wu, H. S. Chen, S. Xi, and M. Chen, “Research progress in reversed Cherenkov radiation in double-negative metamaterials,” Progress Electromagn. Res. 90, 75-87 (2009).
[CrossRef]

Z. Y. Duan, B.-I. Wu, J. Lu, J. A. Kong, and M. Chen, “Reversed Cherenkov radiation in unbounded anisotropic double-negative metamaterials,” J. Phys. D 42, 185102 (2009).
[CrossRef]

J. Lu, T. M. Grzegorczyk, Y. Zhang, J. Pancheto, Jr., B.-I. Wu, J. A. Kong, and M. Chen, “Cerenkov radiation in materials with negative permittivity and permeability,” Opt. Express 11, 723-734 (2003).
[CrossRef] [PubMed]

Cheng, X.

X. Cheng, H. Chen, L. Ran, B.-I. Wu, T. M. Grzegorczyk, and J. A. Kong, “Negative refraction and cross polarization effects in metamaterial realized with bianisotropic S-ring resonator,” Phys. Rev. B 76, 024402 (2007).
[CrossRef]

Chigrin, D. N.

C. Kremers and D. N. Chigrin, “Spatial distribution of Cherenkov radiation in periodic dielectric media,” J. Opt. A 11, 114008(2009).
[CrossRef]

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

Duan, Z. Y.

Z. Y. Duan, B.-I. Wu, H. S. Chen, S. Xi, and M. Chen, “Research progress in reversed Cherenkov radiation in double-negative metamaterials,” Progress Electromagn. Res. 90, 75-87 (2009).
[CrossRef]

Z. Y. Duan, B.-I. Wu, J. Lu, J. A. Kong, and M. Chen, “Reversed Cherenkov radiation in unbounded anisotropic double-negative metamaterials,” J. Phys. D 42, 185102 (2009).
[CrossRef]

Erdélyi, A.

H. Bateman and A. Erdélyi, Higher Transcendental Functions (McGraw-Hill, 1953).

Felsen, L. B.

L. B. Felsen and N. Marcuvitz, Radiation and Scattering of Waves (Wiley Interscience, 2003).

Frank, I. M.

I. M. Frank, Vavilov-Cherenkov Radiation: Theoretical Aspects (Nauka, 1988), in Russian.

Gai, W.

S. Antipov, L. Spentzouris, W. Liu, W. Gai, and J. G. Power, “Wakefield generation in metamaterial-loaded waveguides,” J. Appl. Phys. 102, 034906 (2007).
[CrossRef]

Galyamin, S. N.

S. N. Galyamin and A. V. Tyukhtin, “Reversed Cherenkov transition radiation of charge entering anisotropic medium,” Tech. Phys. Lett. 37, 317-321 (2011).
[CrossRef]

S. N. Galyamin and A. V. Tyukhtin, “New approach to the theory of a moving charge's radiation in dispersive medium and its application to the case of left-handed materials,” J. Phys. Conf. Ser. 236, 012003 (2010).
[CrossRef]

S. N. Galyamin and A. V. Tyukhtin, “Electromagnetic field of a moving charge in the presence of a left-handed medium,” Phys. Rev. B 81, 235134 (2010).
[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, 194802(2009).
[CrossRef]

A. V. Tyukhtin and S. N. Galyamin, “Vavilov-Cherenkov radiation in passive and active media with complex resonant dispersion,” Phys. Rev. E 77, 066606 (2008).
[CrossRef]

Ginzburg, V. L.

V. L. Ginzburg and V. N. Tsytovich, Transition Radiation and Transition Scattering (Hilger, 1990).

Grzegorczyk, T. M.

X. Cheng, H. Chen, L. Ran, B.-I. Wu, T. M. Grzegorczyk, and J. A. Kong, “Negative refraction and cross polarization effects in metamaterial realized with bianisotropic S-ring resonator,” Phys. Rev. B 76, 024402 (2007).
[CrossRef]

J. Lu, T. M. Grzegorczyk, Y. Zhang, J. Pancheto, Jr., B.-I. Wu, J. A. Kong, and M. Chen, “Cerenkov radiation in materials with negative permittivity and permeability,” Opt. Express 11, 723-734 (2003).
[CrossRef] [PubMed]

Holden, A. J.

J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, “Extremely low frequency plasmons in metallic mesostructures,” Phys. Rev. Lett. 76, 4773-4776 (1996).
[CrossRef] [PubMed]

Ibanescu, M.

C. Luo, M. Ibanescu, S. G. Johnson, and J. D. Joannopoulos, “Cerenkov radiation in photonic crystals,” Science 299, 386-371 (2003).
[CrossRef]

Jelley, J. V.

J. V. Jelley, Čerenkov Radiation and Its Applications(Pergamon, 1958).

Joannopoulos, J. D.

C. Luo, M. Ibanescu, S. G. Johnson, and J. D. Joannopoulos, “Cerenkov radiation in photonic crystals,” Science 299, 386-371 (2003).
[CrossRef]

Johnson, S. G.

C. Luo, M. Ibanescu, S. G. Johnson, and J. D. Joannopoulos, “Cerenkov radiation in photonic crystals,” Science 299, 386-371 (2003).
[CrossRef]

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, 194802(2009).
[CrossRef]

Kong, J. A.

Z. Y. Duan, B.-I. Wu, J. Lu, J. A. Kong, and M. Chen, “Reversed Cherenkov radiation in unbounded anisotropic double-negative metamaterials,” J. Phys. D 42, 185102 (2009).
[CrossRef]

X. Cheng, H. Chen, L. Ran, B.-I. Wu, T. M. Grzegorczyk, and J. A. Kong, “Negative refraction and cross polarization effects in metamaterial realized with bianisotropic S-ring resonator,” Phys. Rev. B 76, 024402 (2007).
[CrossRef]

J. Lu, T. M. Grzegorczyk, Y. Zhang, J. Pancheto, Jr., B.-I. Wu, J. A. Kong, and M. Chen, “Cerenkov radiation in materials with negative permittivity and permeability,” Opt. Express 11, 723-734 (2003).
[CrossRef] [PubMed]

Kremers, C.

C. Kremers and D. N. Chigrin, “Spatial distribution of Cherenkov radiation in periodic dielectric media,” J. Opt. A 11, 114008(2009).
[CrossRef]

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

Liu, W.

S. Antipov, L. Spentzouris, W. Liu, W. Gai, and J. G. Power, “Wakefield generation in metamaterial-loaded waveguides,” J. Appl. Phys. 102, 034906 (2007).
[CrossRef]

Lu, J.

Z. Y. Duan, B.-I. Wu, J. Lu, J. A. Kong, and M. Chen, “Reversed Cherenkov radiation in unbounded anisotropic double-negative metamaterials,” J. Phys. D 42, 185102 (2009).
[CrossRef]

J. Lu, T. M. Grzegorczyk, Y. Zhang, J. Pancheto, Jr., B.-I. Wu, J. A. Kong, and M. Chen, “Cerenkov radiation in materials with negative permittivity and permeability,” Opt. Express 11, 723-734 (2003).
[CrossRef] [PubMed]

Luo, C.

C. Luo, M. Ibanescu, S. G. Johnson, and J. D. Joannopoulos, “Cerenkov radiation in photonic crystals,” Science 299, 386-371 (2003).
[CrossRef]

Mandelstam, L. I.

L. I. Mandelstam, “Group velocity in the crystal lattice,” Zh. Eksp. Teor. Fiz. 15, 475 (1945).

Marcuvitz, N.

L. B. Felsen and N. Marcuvitz, Radiation and Scattering of Waves (Wiley Interscience, 2003).

Nemat-Nasser, S. C.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184-4187(2000).
[CrossRef] [PubMed]

Padilla, W. J.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184-4187(2000).
[CrossRef] [PubMed]

Pafomov, V. E.

V. E. Pafomov, “On transition radiation and the Vavilov-Cherenkov radiation,” Sov. Phys. JETP 9, 1321-1324 (1959).

Pancheto, J.

Pendry, J. B.

J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, “Extremely low frequency plasmons in metallic mesostructures,” Phys. Rev. Lett. 76, 4773-4776 (1996).
[CrossRef] [PubMed]

Power, J. G.

S. Antipov, L. Spentzouris, W. Liu, W. Gai, and J. G. Power, “Wakefield generation in metamaterial-loaded waveguides,” J. Appl. Phys. 102, 034906 (2007).
[CrossRef]

Ran, L.

X. Cheng, H. Chen, L. Ran, B.-I. Wu, T. M. Grzegorczyk, and J. A. Kong, “Negative refraction and cross polarization effects in metamaterial realized with bianisotropic S-ring resonator,” Phys. Rev. B 76, 024402 (2007).
[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, 194802(2009).
[CrossRef]

Schultz, S.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184-4187(2000).
[CrossRef] [PubMed]

Smith, D. R.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184-4187(2000).
[CrossRef] [PubMed]

Spentzouris, L.

S. Antipov, L. Spentzouris, W. Liu, W. Gai, and J. G. Power, “Wakefield generation in metamaterial-loaded waveguides,” J. Appl. Phys. 102, 034906 (2007).
[CrossRef]

Stewart, W. J.

J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, “Extremely low frequency plasmons in metallic mesostructures,” Phys. Rev. Lett. 76, 4773-4776 (1996).
[CrossRef] [PubMed]

Stolyarov, S. N.

B. M. Bolotovskiy and S. N. Stolyarov, “On radiation principles in medium with dispersion,” in Problems of Theoretical Physics: Collection of I. E. Tamm's Memory (Nauka, 1972), pp. 267-280.

Tsytovich, V. N.

V. L. Ginzburg and V. N. Tsytovich, Transition Radiation and Transition Scattering (Hilger, 1990).

Tyukhtin, A. V.

S. N. Galyamin and A. V. Tyukhtin, “Reversed Cherenkov transition radiation of charge entering anisotropic medium,” Tech. Phys. Lett. 37, 317-321 (2011).
[CrossRef]

S. N. Galyamin and A. V. Tyukhtin, “New approach to the theory of a moving charge's radiation in dispersive medium and its application to the case of left-handed materials,” J. Phys. Conf. Ser. 236, 012003 (2010).
[CrossRef]

S. N. Galyamin and A. V. Tyukhtin, “Electromagnetic field of a moving charge in the presence of a left-handed medium,” Phys. Rev. B 81, 235134 (2010).
[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, 194802(2009).
[CrossRef]

A. V. Tyukhtin and S. N. Galyamin, “Vavilov-Cherenkov radiation in passive and active media with complex resonant dispersion,” Phys. Rev. E 77, 066606 (2008).
[CrossRef]

Vier, D. C.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184-4187(2000).
[CrossRef] [PubMed]

Wu, B.-I.

Z. Y. Duan, B.-I. Wu, H. S. Chen, S. Xi, and M. Chen, “Research progress in reversed Cherenkov radiation in double-negative metamaterials,” Progress Electromagn. Res. 90, 75-87 (2009).
[CrossRef]

Z. Y. Duan, B.-I. Wu, J. Lu, J. A. Kong, and M. Chen, “Reversed Cherenkov radiation in unbounded anisotropic double-negative metamaterials,” J. Phys. D 42, 185102 (2009).
[CrossRef]

X. Cheng, H. Chen, L. Ran, B.-I. Wu, T. M. Grzegorczyk, and J. A. Kong, “Negative refraction and cross polarization effects in metamaterial realized with bianisotropic S-ring resonator,” Phys. Rev. B 76, 024402 (2007).
[CrossRef]

J. Lu, T. M. Grzegorczyk, Y. Zhang, J. Pancheto, Jr., B.-I. Wu, J. A. Kong, and M. Chen, “Cerenkov radiation in materials with negative permittivity and permeability,” Opt. Express 11, 723-734 (2003).
[CrossRef] [PubMed]

Xi, S.

Z. Y. Duan, B.-I. Wu, H. S. Chen, S. Xi, and M. Chen, “Research progress in reversed Cherenkov radiation in double-negative metamaterials,” Progress Electromagn. Res. 90, 75-87 (2009).
[CrossRef]

Youngs, I.

J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, “Extremely low frequency plasmons in metallic mesostructures,” Phys. Rev. Lett. 76, 4773-4776 (1996).
[CrossRef] [PubMed]

Zhang, Y.

Zrelov, V. P.

V. P. Zrelov, Vavilov-Cherenkov Radiation in High-Energy Physics (Israel Program for Scientific Translations, 1970).

J. Appl. Phys.

S. Antipov, L. Spentzouris, W. Liu, W. Gai, and J. G. Power, “Wakefield generation in metamaterial-loaded waveguides,” J. Appl. Phys. 102, 034906 (2007).
[CrossRef]

J. Opt. A

C. Kremers and D. N. Chigrin, “Spatial distribution of Cherenkov radiation in periodic dielectric media,” J. Opt. A 11, 114008(2009).
[CrossRef]

J. Phys. Conf. Ser.

S. N. Galyamin and A. V. Tyukhtin, “New approach to the theory of a moving charge's radiation in dispersive medium and its application to the case of left-handed materials,” J. Phys. Conf. Ser. 236, 012003 (2010).
[CrossRef]

J. Phys. D

Z. Y. Duan, B.-I. Wu, J. Lu, J. A. Kong, and M. Chen, “Reversed Cherenkov radiation in unbounded anisotropic double-negative metamaterials,” J. Phys. D 42, 185102 (2009).
[CrossRef]

Opt. Express

Phys. Rev. A

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

Phys. Rev. B

S. N. Galyamin and A. V. Tyukhtin, “Electromagnetic field of a moving charge in the presence of a left-handed medium,” Phys. Rev. B 81, 235134 (2010).
[CrossRef]

X. Cheng, H. Chen, L. Ran, B.-I. Wu, T. M. Grzegorczyk, and J. A. Kong, “Negative refraction and cross polarization effects in metamaterial realized with bianisotropic S-ring resonator,” Phys. Rev. B 76, 024402 (2007).
[CrossRef]

Phys. Rev. E

A. V. Tyukhtin and S. N. Galyamin, “Vavilov-Cherenkov radiation in passive and active media with complex resonant dispersion,” Phys. Rev. E 77, 066606 (2008).
[CrossRef]

Phys. Rev. Lett.

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, 194802(2009).
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

Schematic view of the complex plane ω for real ω c (left) and imaginary ω c (right) (the figure shows only the right half-plane because of symmetry with respect to the imaginary axis). The bold solid lines are cuts, γ 0 is an initial integration path, and γ + and γ are contours used for numerical calculations in the domains ζ > 0 and ζ < 0 , respectively.

Fig. 2
Fig. 2

Polar pattern for w ( θ w ) (in units q 2 ω p 2 c 3 ) and magnetic field component H φ (in units q ω p 2 c 2 ) in the case of (top)  ω p > ω p and (bottom)  ω p < ω p . Parameters: ω p = 2 ω p (top), ω p = 0.5 ω p (bottom), ω d = ω d = 10 2 ω p , ρ = 10 c ω p 1 , β = 0.5 .

Fig. 3
Fig. 3

(left) Domains of FR (+) and RR (−) and (right) the typical polar patterns for w ( θ w ) in units q 2 ω p 2 c 3 in different cases determined by the inequalities in Eq. (23). The values of the plasma and resonant frequencies (in units ω p ) used for computation of w ( θ w ) are the following: ω r = 1 , ω p = 1.3 , ω r = 1.6 (a, b); ω r = 0.7 , ω p = 0.5 , ω r = 0.9 (c); ω r = 1.7 , ω p = 1 , ω r = 1.2 (d); ω r = 0.5 , ω p = 0.9 , ω r = 0.4 (e); ω r = 1.3 , ω p = 1.5 , ω r = 0.9 (f); for all cases ω d = ω d = 10 2 ω p , ω c = [ ω r 2 β 2 ( 1 β 2 ) 1 ω p 2 ] 1 / 2 , ρ = 10 c ω p 1 , β = 0.5 .

Fig. 4
Fig. 4

The magnetic field H φ (in units q ω p 2 c 2 ) depending on distance ζ (in units c ω p 1 ) for the same cases as in Fig. 3.

Equations (34)

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ε ^ = ( ε 0 0 0 ε 0 0 0 ε )
{ E ρ , E z , H φ } = q 2 c + { e ρ ( ω ) , e z ( ω ) , h φ ( ω ) } exp ( i ω V 1 ζ ) d ω ,
e ρ ( ω ) = i s ( ω ) β ε ( ω ) H 1 ( 1 ) ( s ( ω ) ρ ) , e z ( ω ) = 1 c 1 β 2 ε ( ω ) ε ( ω ) β 2 H 0 ( 1 ) ( s ( ω ) ρ ) ω , h φ ( ω ) = i s ( ω ) H 1 ( 1 ) ( s ( ω ) ρ ) .
s ( ω ) = 1 c β ε ( ω ) ε ( ω ) ω 2 ( ε ( ω ) β 2 1 ) .
Im s ( ω ) > 0 .
V g ρ = ( d ω d k ) ρ = d ω d s = ( d s d ω ) 1 > 0 .
Γ f ( ω ) exp ( i ω ζ V 1 ) d ω = 2 Re Γ + f ( ω ) exp ( i ω ζ V 1 ) d ω ,
s ( ω ) | ω | V 1 1 β 2 i ω sgn ( Re ω ) ,
Im ω > | Re ω | ρ 1 β 2 / ζ for     ζ > 0 , Im ω < | Re ω | ρ 1 β 2 / | ζ | for     ζ < 0 .
ρ 1 β 2 Im ω = ζ | Re ω | + const .
ε = 1 + ω p 2 ω r 2 2 i ω d ω ω 2 , ε = 1 + ω p 2 ω r 2 2 i ω d ω ω 2 ,
s 2 ( ω ) = ( 1 β 2 ) ω 2 c 2 β 2 ω 2 ω Σ 2 ω 2 ω Σ 2 ω 2 ω c 2 ω 2 ω r 2 ,
{ e ρ , e z , h φ } exp ( i ω V 1 ζ ) exp ( i s ( ω ) ρ + i ω V 1 z i ω t ) ,
E ρ = E ρ C + E ρ W , E z = E z C + E z W , H φ = H φ C + H φ W ,
( E ρ C E z C H φ C ) = q c ω 0 + ( | s ( i ω ˜ ) | [ β ε ( i ω ˜ ) ] 1 J 1 ( | s ( i ω ˜ ) | ρ ) ( 1 β 2 ε ( i ω ˜ ) ) ω ˜ [ c β 2 ε ( i ω ˜ ) ] 1 J 0 ( | s ( i ω ˜ ) | ρ ) sgn ( ζ ) | s ( i ω ˜ ) | J 1 ( | s ( i ω ˜ ) | ρ ) ) exp ( ω ˜ V | ζ | ) d ω ˜ ,
( E ρ W E z W H φ W ) = 2 q c i = 1 , 3 ω i i ω i + 1 ϰ i ( s ( ω ) [ β ε ( ω ) ] 1 J 1 ( s ( ω ) ρ ) sin ( V 1 ω ζ ) ( β 2 ε ( ω ) 1 ) [ c β 2 ε ( ω ) ] 1 ω J 0 ( s ( ω ) ρ ) cos ( V 1 ω ζ ) s ( ω ) J 1 ( s ( ω ) ρ ) sin ( V 1 ω ζ ) ) d ω Θ ( ζ ) ,
ϰ 1 = [ + 1 , if     ω 1 = ω Σ , or ω 1 = ω r , 1 , if     ω 1 = ω Σ , or ω 1 = ω c , or ω 1 = 0 , ϰ 3 = [ + 1 , if     ω 4 = ω Σ , or ω 4 = ω c , 1 , if     ω 4 = ω Σ , or ω 4 = ω r ,
ω Σ ω Σ + Δ cos ( α ρ ( ω ω Σ ) 1 / 2 π / 4 ) ( ω ω Σ ) 3 / 4 d ω 1 / Δ + cos ( α ρ ξ π / 4 ) ξ 3 / 2 d ξ Δ 0 0 ,
Re s β 0 ω ( c β ) 1 | ε / ε | sgn ( ε ε ε ε ) , Im s β 0 | ω | ( 2 c β ) 1 | ε / ε | · | ε / ε ε / ε | ,
{ W z W ρ } = q 2 16 π c + + + { e ρ ( ω ) h φ ( ω ˜ ) e z ( ω ) h φ ( ω ˜ ) } d ω d ω ˜ d ζ .
{ W z W ρ } = 0 + { w z w ρ } d ω ,
w z = q 2 4 c Re [ e ρ ( ω ) h φ * ( ω ) ] = q 2 4 β c Re [ | s ( ω ) | 2 ε ( ω ) | H 1 ( 1 ) ( s ( ω ) ρ ) | 2 ] , w ρ = q 2 4 c Re [ e z ( ω ) h φ * ( ω ) ] = q 2 4 Im [ | s ( ω ) | 2 s ( ω ) ε ( ω ) ω H 0 ( 1 ) ( s ( ω ) ρ ) ( H 1 ( 1 ) ( s ( ω ) ρ ) ) * ] ,
w z q 2 2 π c β ρ Re ( | s | ε exp ( 2 s ρ ) ) , w ρ q 2 2 π ρ Re ( s | s | ω ε exp ( 2 s ρ ) ) ,
w z q 2 | s | 2 π c β ρ ε , w ρ q 2 s | s | 2 π ρ ω ε ,
Δ ( ω , k ) = k x 2 / ε + k z 2 / ε ω 2 / c 2 = 0 .
V g = d ω d k = Δ / k Δ / ω , { V g x V g z } = ( Δ ω ) 1 { 2 k x / ε 2 k z / ε } ,
ε = 1 ω p 2 2 i ω d ω + ω 2 , ε = 1 ω p 2 2 i ω d ω + ω 2 .
s 2 ( ω ) = β 2 1 c 2 β 2 ω 2 ω p 2 ω 2 ω p 2 ( ω 2 ω p 2 1 β 2 ) .
ω r < ω Σ < ω r < ω Σ ,
ω r < ω r < ω Σ < ω Σ ,
ω r < ω r < ω Σ < ω Σ ,
ω r < ω Σ < ω r < ω Σ ,
ω r < ω r < ω Σ < ω Σ ,
ω r < ω r < ω Σ < ω Σ .

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