Abstract

The radiation field of relativistic charged particles moving in media with resonant dispersion is analyzed using the stationary phase method. Three medium models are considered: a model typical for dielectrics, a model typical for magnetics, and a model typical for the left-handed medium. Equations determining stationary points are obtained, and the conditions for the existence of one or two stationary points are found. A simple analytical expression for stationary points in the case of ultrarelativistic motion in resonant dielectric or magnetic materials is given. In the case of an arbitrary velocity, an algorithm for solving the stationary point equation and for computing the radiation field is developed. The results of this algorithm are compared with those obtained by computation of the field using exact formulae. Typical dependences of the field on distance from the charged particle are presented. It is shown that, for the case of the left-handed medium, the radiation field is formed at larger distances behind the charge compared with the cases of typical dielectric and magnetic materials. It is found that the radiation field can possess beats that are more pronounced in the left-handed medium.

© 2014 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. V. L. Ginzburg, V. N. Tsytovich, Transition Radiation and Transition Scattering (Hilger, 1990).
  4. I. M. Frank, Vavilov-Cherenkov Radiation: Theoretical Aspects (Nauka, 1988), in Russian.
  5. G. N. Afanasiev, Vavilov-Cherenkov and Synchrotron Radiation: Foundations and Applications (Springer, 2004).
  6. G. N. Afanasiev, V. G. Kartavenko, “Radiation of a point charge uniformly moving in a dielectric medium,” J. Phys. D 31, 2760–2776 (1998).
    [CrossRef]
  7. A. V. Tyukhtin, S. N. Galyamin, “Vavilov-Cherenkov radiation in passive and active media with complex resonant dispersion,” Phys. Rev. E 77, 066606 (2008).
    [CrossRef]
  8. S. N. Galyamin, A. V. Tyukhtin, A. Kanareykin, P. Schoessow, “Reversed Cherenkov-transition radiation by a charge crossing a left-handed medium boundary,” Phys. Rev. Lett. 103, 194802 (2009).
    [CrossRef]
  9. S. N. Galyamin, A. V. Tyukhtin, “Electromagnetic field of a moving charge in the presence of a left-handed medium,” Phys. Rev. B 81, 235134 (2010).
    [CrossRef]
  10. S. N. Galyamin, A. V. Tyukhtin, “Electromagnetic field of a charge traveling into an anisotropic medium,” Phys. Rev. E 84, 056608 (2011).
    [CrossRef]
  11. S. N. Galyamin, D. Y. Kapshtan, A. V. Tyukhtin, “Electromagnetic field of a charge moving in a cold magnetized plasma,” Phys. Rev. E 87, 013109 (2013).
    [CrossRef]
  12. S. N. Galyamin, A. A. Peshkov, A. V. Tyukhtin, “Electromagnetic field of a charge moving in a chiral isotropic medium,” Phys. Rev. E 88, 013206 (2013).
    [CrossRef]
  13. J. B. Pendry, A. J. Holden, W. J. Stewart, I. Youngs, “Extremely low frequency plasmons in metallic mesostructures,” Phys. Rev. Lett. 76, 4773–4776 (1996).
    [CrossRef]
  14. D. R. Smith, N. Kroll, “Negative refractive index in left-handed materials,” Phys. Rev. Lett. 85, 2933–2936 (2000).
    [CrossRef]
  15. C. M. Soukoulis, J. Zhou, T. Koschny, M. Kafesaki, E. N. Economou, “The science of negative index materials,” J. Phys. Condens. Matter 20, 304217 (2008).
    [CrossRef]
  16. J. Wu, B. Ng, S. P. Turaga, M. B. H. Breese, S. A. Maier, M. Hong, A. A. Bettiol, H. O. Moser, “Free-standing terahertz chiral meta-foils exhibiting strong optical activity and negative refractive index,” Appl. Phys. Lett. 103, 141106 (2013).
    [CrossRef]
  17. V. V. Vorobev, A. V. Tyukhtin, “Nondivergent Cherenkov radiation in a wire metamaterial,” Phys. Rev. Lett. 108, 184801 (2012).
    [CrossRef]
  18. D. E. Fernandes, S. I. Maslovski, M. G. Silveirinha, “Cherenkov emission in a nanowire material,” Phys. Rev. B 85, 155107 (2012).
    [CrossRef]
  19. A. V. Tyukhtin, V. V. Vorobev, “Radiation of charges moving along the boundary of a wire metamaterial,” Phys. Rev. E 89, 013202 (2014).
    [CrossRef]
  20. A. V. Tyukhtin, V. V. Vorobev, “Cherenkov radiation in a metamaterial comprised of coated wires,” J. Opt. Soc. Am. B 30, 1524–1531 (2013).
    [CrossRef]
  21. J. Lu, T. M. Grzegorczyk, Y. Zhang, J. Pacheco, B.-I. Wu, J. A. Kong, M. Chen, “Čerenkov radiation in materials with negative permittivity and permeability,” Opt. Express 11, 723–734 (2003).
    [CrossRef]
  22. Z. Y. Duan, B.-I. Wu, S. Xi, H. S. Chen, M. Chen, “Research progress in reversed Cherenkov radiation in double-negative metamaterials,” Prog. Electromagn. Res. 90, 75–87 (2009).
    [CrossRef]
  23. Z. Y. Duan, C. Guo, M. Chen, “Enhanced reversed Cherenkov radiation in a waveguide with double-negative metamaterials,” Opt. Express 19, 13825–13830 (2011).
    [CrossRef]
  24. Z. Y. Duan, B.-I. Wu, J. Lu, J. A. Kong, M. Chen, “Reversed Cherenkov radiation in unbounded anisotropic double-negative metamaterials,” J. Phys. D 42, 185102 (2009).
    [CrossRef]
  25. 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]
  26. Z. Y. Duan, C. Guo, X. Guo, M. Chen, “Double negative-metamaterial based terahertz radiation excited by a sheet beam bunch,” Phys. Plasmas 20, 093301 (2013).
    [CrossRef]
  27. D. M. French, D. Shiffler, K. Cartwright, “Electron beam coupling to a metamaterial structure,” Phys. Plasmas 20, 083116 (2013).
    [CrossRef]
  28. L. B. Felsen, N. Marcuvitz, Radiation and Scattering of Waves (Wiley Interscience, 2003).
  29. I. E. Tamm, “Radiation emitted by uniformly moving electrons,” J. Phys. 1, 439–454 (1939).

2014 (1)

A. V. Tyukhtin, V. V. Vorobev, “Radiation of charges moving along the boundary of a wire metamaterial,” Phys. Rev. E 89, 013202 (2014).
[CrossRef]

2013 (6)

J. Wu, B. Ng, S. P. Turaga, M. B. H. Breese, S. A. Maier, M. Hong, A. A. Bettiol, H. O. Moser, “Free-standing terahertz chiral meta-foils exhibiting strong optical activity and negative refractive index,” Appl. Phys. Lett. 103, 141106 (2013).
[CrossRef]

Z. Y. Duan, C. Guo, X. Guo, M. Chen, “Double negative-metamaterial based terahertz radiation excited by a sheet beam bunch,” Phys. Plasmas 20, 093301 (2013).
[CrossRef]

D. M. French, D. Shiffler, K. Cartwright, “Electron beam coupling to a metamaterial structure,” Phys. Plasmas 20, 083116 (2013).
[CrossRef]

S. N. Galyamin, D. Y. Kapshtan, A. V. Tyukhtin, “Electromagnetic field of a charge moving in a cold magnetized plasma,” Phys. Rev. E 87, 013109 (2013).
[CrossRef]

S. N. Galyamin, A. A. Peshkov, A. V. Tyukhtin, “Electromagnetic field of a charge moving in a chiral isotropic medium,” Phys. Rev. E 88, 013206 (2013).
[CrossRef]

A. V. Tyukhtin, V. V. Vorobev, “Cherenkov radiation in a metamaterial comprised of coated wires,” J. Opt. Soc. Am. B 30, 1524–1531 (2013).
[CrossRef]

2012 (2)

V. V. Vorobev, A. V. Tyukhtin, “Nondivergent Cherenkov radiation in a wire metamaterial,” Phys. Rev. Lett. 108, 184801 (2012).
[CrossRef]

D. E. Fernandes, S. I. Maslovski, M. G. Silveirinha, “Cherenkov emission in a nanowire material,” Phys. Rev. B 85, 155107 (2012).
[CrossRef]

2011 (2)

S. N. Galyamin, A. V. Tyukhtin, “Electromagnetic field of a charge traveling into an anisotropic medium,” Phys. Rev. E 84, 056608 (2011).
[CrossRef]

Z. Y. Duan, C. Guo, M. Chen, “Enhanced reversed Cherenkov radiation in a waveguide with double-negative metamaterials,” Opt. Express 19, 13825–13830 (2011).
[CrossRef]

2010 (1)

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

2009 (3)

S. N. Galyamin, A. V. Tyukhtin, A. Kanareykin, 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, J. Lu, J. A. Kong, M. Chen, “Reversed Cherenkov radiation in unbounded anisotropic double-negative metamaterials,” J. Phys. D 42, 185102 (2009).
[CrossRef]

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

2008 (2)

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

C. M. Soukoulis, J. Zhou, T. Koschny, M. Kafesaki, E. N. Economou, “The science of negative index materials,” J. Phys. Condens. Matter 20, 304217 (2008).
[CrossRef]

2005 (1)

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 (1)

2000 (1)

D. R. Smith, N. Kroll, “Negative refractive index in left-handed materials,” Phys. Rev. Lett. 85, 2933–2936 (2000).
[CrossRef]

1998 (1)

G. N. Afanasiev, V. G. Kartavenko, “Radiation of a point charge uniformly moving in a dielectric medium,” J. Phys. D 31, 2760–2776 (1998).
[CrossRef]

1996 (1)

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

1939 (1)

I. E. Tamm, “Radiation emitted by uniformly moving electrons,” J. Phys. 1, 439–454 (1939).

Afanasiev, G. N.

G. N. Afanasiev, V. G. Kartavenko, “Radiation of a point charge uniformly moving in a dielectric medium,” J. Phys. D 31, 2760–2776 (1998).
[CrossRef]

G. N. Afanasiev, Vavilov-Cherenkov and Synchrotron Radiation: Foundations and Applications (Springer, 2004).

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]

Bettiol, A. A.

J. Wu, B. Ng, S. P. Turaga, M. B. H. Breese, S. A. Maier, M. Hong, A. A. Bettiol, H. O. Moser, “Free-standing terahertz chiral meta-foils exhibiting strong optical activity and negative refractive index,” Appl. Phys. Lett. 103, 141106 (2013).
[CrossRef]

Breese, M. B. H.

J. Wu, B. Ng, S. P. Turaga, M. B. H. Breese, S. A. Maier, M. Hong, A. A. Bettiol, H. O. Moser, “Free-standing terahertz chiral meta-foils exhibiting strong optical activity and negative refractive index,” Appl. Phys. Lett. 103, 141106 (2013).
[CrossRef]

Cartwright, K.

D. M. French, D. Shiffler, K. Cartwright, “Electron beam coupling to a metamaterial structure,” Phys. Plasmas 20, 083116 (2013).
[CrossRef]

Chen, H. S.

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

Chen, M.

Z. Y. Duan, C. Guo, X. Guo, M. Chen, “Double negative-metamaterial based terahertz radiation excited by a sheet beam bunch,” Phys. Plasmas 20, 093301 (2013).
[CrossRef]

Z. Y. Duan, C. Guo, M. Chen, “Enhanced reversed Cherenkov radiation in a waveguide with double-negative metamaterials,” Opt. Express 19, 13825–13830 (2011).
[CrossRef]

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

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

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

Duan, Z. Y.

Z. Y. Duan, C. Guo, X. Guo, M. Chen, “Double negative-metamaterial based terahertz radiation excited by a sheet beam bunch,” Phys. Plasmas 20, 093301 (2013).
[CrossRef]

Z. Y. Duan, C. Guo, M. Chen, “Enhanced reversed Cherenkov radiation in a waveguide with double-negative metamaterials,” Opt. Express 19, 13825–13830 (2011).
[CrossRef]

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

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

Economou, E. N.

C. M. Soukoulis, J. Zhou, T. Koschny, M. Kafesaki, E. N. Economou, “The science of negative index materials,” J. Phys. Condens. Matter 20, 304217 (2008).
[CrossRef]

Felsen, L. B.

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

Fernandes, D. E.

D. E. Fernandes, S. I. Maslovski, M. G. Silveirinha, “Cherenkov emission in a nanowire material,” Phys. Rev. B 85, 155107 (2012).
[CrossRef]

Frank, I. M.

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

French, D. M.

D. M. French, D. Shiffler, K. Cartwright, “Electron beam coupling to a metamaterial structure,” Phys. Plasmas 20, 083116 (2013).
[CrossRef]

Galyamin, S. N.

S. N. Galyamin, A. A. Peshkov, A. V. Tyukhtin, “Electromagnetic field of a charge moving in a chiral isotropic medium,” Phys. Rev. E 88, 013206 (2013).
[CrossRef]

S. N. Galyamin, D. Y. Kapshtan, A. V. Tyukhtin, “Electromagnetic field of a charge moving in a cold magnetized plasma,” Phys. Rev. E 87, 013109 (2013).
[CrossRef]

S. N. Galyamin, A. V. Tyukhtin, “Electromagnetic field of a charge traveling into an anisotropic medium,” Phys. Rev. E 84, 056608 (2011).
[CrossRef]

S. N. Galyamin, 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, 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, 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, V. N. Tsytovich, Transition Radiation and Transition Scattering (Hilger, 1990).

Grzegorczyk, T. M.

Guo, C.

Z. Y. Duan, C. Guo, X. Guo, M. Chen, “Double negative-metamaterial based terahertz radiation excited by a sheet beam bunch,” Phys. Plasmas 20, 093301 (2013).
[CrossRef]

Z. Y. Duan, C. Guo, M. Chen, “Enhanced reversed Cherenkov radiation in a waveguide with double-negative metamaterials,” Opt. Express 19, 13825–13830 (2011).
[CrossRef]

Guo, X.

Z. Y. Duan, C. Guo, X. Guo, M. Chen, “Double negative-metamaterial based terahertz radiation excited by a sheet beam bunch,” Phys. Plasmas 20, 093301 (2013).
[CrossRef]

Holden, A. J.

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

Hong, M.

J. Wu, B. Ng, S. P. Turaga, M. B. H. Breese, S. A. Maier, M. Hong, A. A. Bettiol, H. O. Moser, “Free-standing terahertz chiral meta-foils exhibiting strong optical activity and negative refractive index,” Appl. Phys. Lett. 103, 141106 (2013).
[CrossRef]

Jelley, J. V.

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

Kafesaki, M.

C. M. Soukoulis, J. Zhou, T. Koschny, M. Kafesaki, E. N. Economou, “The science of negative index materials,” J. Phys. Condens. Matter 20, 304217 (2008).
[CrossRef]

Kanareykin, A.

S. N. Galyamin, A. V. Tyukhtin, A. Kanareykin, P. Schoessow, “Reversed Cherenkov-transition radiation by a charge crossing a left-handed medium boundary,” Phys. Rev. Lett. 103, 194802 (2009).
[CrossRef]

Kapshtan, D. Y.

S. N. Galyamin, D. Y. Kapshtan, A. V. Tyukhtin, “Electromagnetic field of a charge moving in a cold magnetized plasma,” Phys. Rev. E 87, 013109 (2013).
[CrossRef]

Kartavenko, V. G.

G. N. Afanasiev, V. G. Kartavenko, “Radiation of a point charge uniformly moving in a dielectric medium,” J. Phys. D 31, 2760–2776 (1998).
[CrossRef]

Kong, J. A.

Z. Y. Duan, B.-I. Wu, J. Lu, J. A. Kong, 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. Pacheco, B.-I. Wu, J. A. Kong, M. Chen, “Čerenkov radiation in materials with negative permittivity and permeability,” Opt. Express 11, 723–734 (2003).
[CrossRef]

Koschny, T.

C. M. Soukoulis, J. Zhou, T. Koschny, M. Kafesaki, E. N. Economou, “The science of negative index materials,” J. Phys. Condens. Matter 20, 304217 (2008).
[CrossRef]

Kroll, N.

D. R. Smith, N. Kroll, “Negative refractive index in left-handed materials,” Phys. Rev. Lett. 85, 2933–2936 (2000).
[CrossRef]

Lu, J.

Z. Y. Duan, B.-I. Wu, J. Lu, J. A. Kong, 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. Pacheco, B.-I. Wu, J. A. Kong, M. Chen, “Čerenkov radiation in materials with negative permittivity and permeability,” Opt. Express 11, 723–734 (2003).
[CrossRef]

Maier, S. A.

J. Wu, B. Ng, S. P. Turaga, M. B. H. Breese, S. A. Maier, M. Hong, A. A. Bettiol, H. O. Moser, “Free-standing terahertz chiral meta-foils exhibiting strong optical activity and negative refractive index,” Appl. Phys. Lett. 103, 141106 (2013).
[CrossRef]

Marcuvitz, N.

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

Maslovski, S. I.

D. E. Fernandes, S. I. Maslovski, M. G. Silveirinha, “Cherenkov emission in a nanowire material,” Phys. Rev. B 85, 155107 (2012).
[CrossRef]

Moser, H. O.

J. Wu, B. Ng, S. P. Turaga, M. B. H. Breese, S. A. Maier, M. Hong, A. A. Bettiol, H. O. Moser, “Free-standing terahertz chiral meta-foils exhibiting strong optical activity and negative refractive index,” Appl. Phys. Lett. 103, 141106 (2013).
[CrossRef]

Ng, B.

J. Wu, B. Ng, S. P. Turaga, M. B. H. Breese, S. A. Maier, M. Hong, A. A. Bettiol, H. O. Moser, “Free-standing terahertz chiral meta-foils exhibiting strong optical activity and negative refractive index,” Appl. Phys. Lett. 103, 141106 (2013).
[CrossRef]

Pacheco, J.

Pendry, J. B.

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

Peshkov, A. A.

S. N. Galyamin, A. A. Peshkov, A. V. Tyukhtin, “Electromagnetic field of a charge moving in a chiral isotropic medium,” Phys. Rev. E 88, 013206 (2013).
[CrossRef]

Schoessow, P.

S. N. Galyamin, A. V. Tyukhtin, A. Kanareykin, P. Schoessow, “Reversed Cherenkov-transition radiation by a charge crossing a left-handed medium boundary,” Phys. Rev. Lett. 103, 194802 (2009).
[CrossRef]

Shiffler, D.

D. M. French, D. Shiffler, K. Cartwright, “Electron beam coupling to a metamaterial structure,” Phys. Plasmas 20, 083116 (2013).
[CrossRef]

Silveirinha, M. G.

D. E. Fernandes, S. I. Maslovski, M. G. Silveirinha, “Cherenkov emission in a nanowire material,” Phys. Rev. B 85, 155107 (2012).
[CrossRef]

Smith, D. R.

D. R. Smith, N. Kroll, “Negative refractive index in left-handed materials,” Phys. Rev. Lett. 85, 2933–2936 (2000).
[CrossRef]

Soukoulis, C. M.

C. M. Soukoulis, J. Zhou, T. Koschny, M. Kafesaki, E. N. Economou, “The science of negative index materials,” J. Phys. Condens. Matter 20, 304217 (2008).
[CrossRef]

Stewart, W. J.

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

Tamm, I. E.

I. E. Tamm, “Radiation emitted by uniformly moving electrons,” J. Phys. 1, 439–454 (1939).

Tsytovich, V. N.

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

Turaga, S. P.

J. Wu, B. Ng, S. P. Turaga, M. B. H. Breese, S. A. Maier, M. Hong, A. A. Bettiol, H. O. Moser, “Free-standing terahertz chiral meta-foils exhibiting strong optical activity and negative refractive index,” Appl. Phys. Lett. 103, 141106 (2013).
[CrossRef]

Tyukhtin, A. V.

A. V. Tyukhtin, V. V. Vorobev, “Radiation of charges moving along the boundary of a wire metamaterial,” Phys. Rev. E 89, 013202 (2014).
[CrossRef]

S. N. Galyamin, A. A. Peshkov, A. V. Tyukhtin, “Electromagnetic field of a charge moving in a chiral isotropic medium,” Phys. Rev. E 88, 013206 (2013).
[CrossRef]

A. V. Tyukhtin, V. V. Vorobev, “Cherenkov radiation in a metamaterial comprised of coated wires,” J. Opt. Soc. Am. B 30, 1524–1531 (2013).
[CrossRef]

S. N. Galyamin, D. Y. Kapshtan, A. V. Tyukhtin, “Electromagnetic field of a charge moving in a cold magnetized plasma,” Phys. Rev. E 87, 013109 (2013).
[CrossRef]

V. V. Vorobev, A. V. Tyukhtin, “Nondivergent Cherenkov radiation in a wire metamaterial,” Phys. Rev. Lett. 108, 184801 (2012).
[CrossRef]

S. N. Galyamin, A. V. Tyukhtin, “Electromagnetic field of a charge traveling into an anisotropic medium,” Phys. Rev. E 84, 056608 (2011).
[CrossRef]

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

Vorobev, V. V.

A. V. Tyukhtin, V. V. Vorobev, “Radiation of charges moving along the boundary of a wire metamaterial,” Phys. Rev. E 89, 013202 (2014).
[CrossRef]

A. V. Tyukhtin, V. V. Vorobev, “Cherenkov radiation in a metamaterial comprised of coated wires,” J. Opt. Soc. Am. B 30, 1524–1531 (2013).
[CrossRef]

V. V. Vorobev, A. V. Tyukhtin, “Nondivergent Cherenkov radiation in a wire metamaterial,” Phys. Rev. Lett. 108, 184801 (2012).
[CrossRef]

Wu, B.-I.

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

Z. Y. Duan, B.-I. Wu, S. Xi, H. S. Chen, M. Chen, “Research progress in reversed Cherenkov radiation in double-negative metamaterials,” Prog. Electromagn. Res. 90, 75–87 (2009).
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J. Wu, B. Ng, S. P. Turaga, M. B. H. Breese, S. A. Maier, M. Hong, A. A. Bettiol, H. O. Moser, “Free-standing terahertz chiral meta-foils exhibiting strong optical activity and negative refractive index,” Appl. Phys. Lett. 103, 141106 (2013).
[CrossRef]

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[CrossRef]

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Opt. Express (2)

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[CrossRef]

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S. N. Galyamin, A. V. Tyukhtin, “Electromagnetic field of a charge traveling into an anisotropic medium,” Phys. Rev. E 84, 056608 (2011).
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S. N. Galyamin, D. Y. Kapshtan, A. V. Tyukhtin, “Electromagnetic field of a charge moving in a cold magnetized plasma,” Phys. Rev. E 87, 013109 (2013).
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Z. Y. Duan, B.-I. Wu, S. Xi, H. S. Chen, M. Chen, “Research progress in reversed Cherenkov radiation in double-negative metamaterials,” Prog. Electromagn. Res. 90, 75–87 (2009).
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Figures (3)

Fig. 1.
Fig. 1.

Dependence of the function d s / d ω on ω in the case of right-handed electric and magnetic resonant media when β < β c (solid red line), right-handed electric and magnetic resonant media when β > β c (blue-dotted line) and left-handed media with resonant permeability and plasma-like permittivity (green dash–dotted line) ( ω is in terms of ω r , and d s ( ω ) / d ω is in terms of c 1 ).

Fig. 2.
Fig. 2.

Dependence of the magnetic field H φ (in terms of q ω r 2 c 2 ) on ζ = z υ t (in terms of c ω r 1 ) in the case of right-handed electric or magnetic resonance medium (top row) and left-handed medium (bottom row) with ε ( ω ) = 4 for β = 0.6 (left column) and β = 0.99 (right column). Other parameters are ρ = 3 c / ω r and ω p = 0.6 ω r .

Fig. 3.
Fig. 3.

Asymptotic (solid line) and exact (dashed line) results for the magnetic field H φ (in terms of q c 1 ω r 2 ) in the case of right-handed dielectric resonant media: β = 0.6 , ρ = 3 c / ω r , and ω p = 0.6 ω r .

Equations (32)

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{ E ρ , E z , H φ } = + { E ρ ω , E z ω , H φ ω } exp ( i ω ζ υ 1 ) d ω ,
E ρ ω = i q 2 β c s ( ω ) ε ( ω ) H 1 ( 1 ) ( s ( ω ) ρ ) , E z ω = q 2 ω s 2 ( ω ) ε ( ω ) H 0 ( 1 ) ( s ( ω ) ρ ) , H φ ω = i q 2 c s ( ω ) H 1 ( 1 ) ( s ( ω ) ρ ) ,
s 2 ( ω ) = ω 2 υ 2 ( n 2 β 2 1 ) ,
E ρ ω ( ω * ) = E ρ ω * ( ω ) , E z ω ( ω * ) = E z ω * ( ω ) , H φ ω ( ω * ) = H φ ω * ( ω ) .
+ { E ρ ω , E z ω , H φ ω } exp ( i ω ζ υ ) d ω = 2 0 + Re ( { E ρ ω , E z ω , H φ ω } exp ( i ω ζ υ ) ) d ω .
ε ( ω ) = ε ( ω ) , ε ( ω ) = ε ( ω ) , μ ( ω ) = μ ( ω ) , μ ( ω ) = μ ( ω ) .
s 2 ( ω ) = ω 2 υ 2 ( ε μ β 2 ε μ β 2 + i ( ε μ + ε μ ) ) .
ε = 1 + ω p e 2 ω r e 2 2 i ω d e ω ω 2 , μ = 1 ;
ε = 1 , μ = 1 + ω p m 2 ω r m 2 2 i ω d m ω ω 2 ;
ε = 1 ω p e 2 ω 2 + 2 i ω d e ω , μ = 1 + ω p m 2 ω r m 2 2 i ω d m ω ω 2 .
{ ω c e , m , if ω c e , m 2 > 0 0 , if ω c e , m 2 < 0 } < ω < ω r e , m
{ E ρ , E z , H φ } = 2 0 + { E ˜ ρ ω , E ˜ z ω , H ˜ φ ω } exp ( i f ( ω ) ) d ω ,
E ˜ ρ ω = i q ε ( ω ) β c s ( ω ) 2 π ρ exp ( 3 π i 4 ) , E ˜ z ω = q ω ε ( ω ) 1 2 π ρ s ( ω ) s 2 ( ω ) exp ( i π 4 ) , H ˜ φ ω = i q c s ( ω ) 2 π ρ exp ( 3 π i 4 ) , f ( ω ) = s ( ω ) ρ + ω ζ υ .
E 1 ρ = ( 1 ) α 2 q c β s ( ω 1 ) ε ( ω 1 ) sin ( γ π 2 α ) ρ | s ( ω 1 ) | | f ¨ ( ω 1 ) | , E 1 z = ( 1 ) α + 1 2 q ω 1 s 2 ( ω 1 ) ε ( ω 1 ) sin ( γ π 2 α ) ρ | s ( ω 1 ) | | f ¨ ( ω 1 ) | , H 1 φ = 2 q c | s ( ω 1 ) | ρ | f ¨ ( ω 1 ) | sin ( γ π 2 α ) ,
γ = f ( ω 1 ) π 4 + π 4 sgn ( d 2 f ( ω ) d ω 2 ) | ω = ω 1 ,
d s d ω = ζ ρ υ .
d s d ω ˜ = ( 1 β 2 ) ( ω ˜ 4 2 ω ˜ 2 ) 1 + β 2 ( 1 + ω ˜ p e 2 ) ω ˜ 2 ( 1 β 2 ) + β 2 ω ˜ p e 2 + β 2 1 ( 1 ω ˜ 2 ) β c ( ω ˜ 2 1 ) 2 ,
{ ω ˜ c e , if ω ˜ c e 2 > 0 0 if ω ˜ c e 2 < 0 } < ω ˜ < 1 ,
d 2 s d ω ˜ 2 = β ω ˜ ω ˜ p e 2 c ω r e ( ω ˜ 2 1 ) 4 ( ω ˜ 2 ( 1 β 2 ) + β 2 ω ˜ p e 2 + β 2 1 1 ω ˜ 2 ) 3 / 2 × [ ( 1 β 2 ) ( ω ˜ 4 + 2 ω ˜ 2 ) + 3 ( β 2 ω ˜ p e 2 + β 2 1 ) ] .
ω ˜ 4 ( β 2 1 ) 2 ω ˜ 2 ( 1 β 2 ) 3 ( β 2 ω ˜ p e 2 + β 2 1 ) = 0 .
ω ˜ 1 2 = 1 1 + 3 ω ˜ c e 2 ; ω ˜ 2 2 = 1 + 1 + 3 ω ˜ c e 2 .
d s d ω ˜ | ω ˜ = 0 = | ζ min | ρ υ .
d s d ω ˜ | ω ˜ = 1 + 1 + 3 ω ˜ c e 2 = | ζ min | ρ υ .
ω 6 ( ζ 2 ω p e 2 ) + ω 4 ( 3 ζ 2 ω r e 2 ω p e 2 ) + ω 2 ( 3 ζ 2 ω r e 4 ω p e 2 ) + ζ 2 ρ 2 ω r e 6 ω p e 2 ρ 2 ω r e 4 ω p e 4 = 0 .
ω 1 2 = ω r e 2 ( ρ 2 ω r e 4 ω p e 2 ζ 2 ) 1 / 3 .
ω 1 2 = ω r m 2 ( ρ 2 ω r m 4 ω p m 2 ζ 2 ) 1 / 3 .
d s d ω ˜ = ( 1 ε β 2 ) ( ω ˜ 4 2 ω ˜ 2 ) ε β 2 ( ω ˜ p m 2 + 1 ) + 1 β c ( ω ˜ 2 1 ) 2 ε β 2 ( ω ˜ p m 2 ω ˜ 2 1 1 ) 1 .
ω ˜ 4 ( 1 ε β 2 ) 2 ω ˜ 2 ( 1 ε β 2 ) ε β 2 ω ˜ p m 2 ε β 2 + 1 = 0 .
d 2 s d ω ˜ 2 = ε β ω ˜ ω ˜ p m 2 c ω r m ( ω ˜ 2 1 ) 4 [ ε β 2 ( ω ˜ p m 2 1 ω ˜ 2 + 1 ) 1 ] 3 / 2 × [ ( 1 ε β 2 ) ( ω ˜ 4 + 2 ω ˜ 2 ) + 3 ( ε β 2 ω ˜ p m 2 + ε β 2 1 ) ] .
( 1 ε β 2 ) ( ω ˜ 4 + 2 ω ˜ 2 ) + 3 ( ε β 2 ω ˜ p m 2 + ε β 2 1 ) = 0 .
ω ˜ 1 2 = 1 1 + 3 ω ˜ c m 2 , ω ˜ 2 2 = 1 + 1 + 3 ω ˜ c m 2 ,
d s d ω ˜ | ω ˜ = ω ˜ 2 = | ζ min | ρ υ .

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