Abstract

The electromagnetic field of a point charge moving in a “wire metamaterial” parallel to the wires is investigated. The metamaterial under consideration is a periodic structure of perfect conductors with a dielectric or magnetic coating. The spacing of the structure is assumed to be much less than the typical wavelengths; therefore, the structure can be described as an anisotropic medium that exhibits both frequency and spatial dispersions. In this paper, the general expressions for the field components have been obtained. A comparison with the charge field in a cold plasma has been performed. The charge is shown to radiate when its velocity is greater than a threshold determined by the wire coating parameters. The properties of the Cherenkov radiation in the metamaterial under consideration differ radically from those in an ordinary isotropic medium. In particular, the spectral density of the radiation energy decreases with the frequency. The maximum of the radiation pattern falls in the direction of the charge motion (if the losses in the medium are negligible) or in some close direction (if the losses are considered). For the ultrarelativistic case, the radiation pattern is very narrow, and the charge energy loss is small.

© 2013 Optical Society of America

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    [CrossRef]
  7. 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).
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  8. Z. Duan, B.-I. Wu, S. Xi, H. S. Chen, and M. Chen, “Research progress in reversed Cherenkov radiation in double-negative metamaterials,” Prog. Electromagn. Res. 90, 75–87 (2009).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  13. M. A. Shapiro, S. Trendafilov, Y. Urzhumov, A. Alu, R. J. Temkin, and G. Shvets, “Active negative-index metamaterial powered by an electron beam,” Phys. Rev. B 86, 085132 (2012).
    [CrossRef]
  14. Z. Y. Duan, C. Guo, J. Zhou, J. C. Lu, and M. Chen, “Novel electromagnetic radiation in a semi-infinite space filled with a double-negative metamaterial,” Phys. Plasmas 19, 013112 (2012).
    [CrossRef]
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    [CrossRef]
  21. S. I. Maslovski, S. A. Tretyakov, and P. A. Belov, “Wire media with negative effective permittivity: a quasi-static model,” Microw. Opt. Technol. Lett. 35, 47–51 (2002).
    [CrossRef]
  22. P. A. Belov, S. Tretyakov, and A. J. Viitanen, “Dispersion and reflection properties of artificial media formed by regular lattices of ideally conducting wires,” J. Electromagn. Waves Appl. 16, 1153–1170 (2002).
    [CrossRef]
  23. G. Dewar, “Complex mediums V: light and complexity,” Proc. SPIE 5508, 158–166 (2004).
    [CrossRef]
  24. A. P. Prudnikov, Y. Brychkov, and O. I. Marichev, Integrals and Series. Special Functions (Nauka, 1983).
  25. V. M. Agranovich and V. L. Ginzburg, Spatial Dispersion in Crystal Optics and the Theory of Excitons (Interscience, 1966).
  26. M. G. Silveirinha, “Poynting vector, heating rate, and stored energy in structured materials: a first-principles derivation,” Phys. Rev. B 80, 235120 (2009).
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    [CrossRef]

2012

M. A. Shapiro, S. Trendafilov, Y. Urzhumov, A. Alu, R. J. Temkin, and G. Shvets, “Active negative-index metamaterial powered by an electron beam,” Phys. Rev. B 86, 085132 (2012).
[CrossRef]

Z. Y. Duan, C. Guo, J. Zhou, J. C. Lu, and M. Chen, “Novel electromagnetic radiation in a semi-infinite space filled with a double-negative metamaterial,” Phys. Plasmas 19, 013112 (2012).
[CrossRef]

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

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

M. G. Silveirinha and S. I. Maslovski, “Radiation from elementary sources in a uniaxial wire medium,” Phys. Rev. B 85, 155125 (2012).
[CrossRef]

2011

A. V. Tyukhtin and E. G. Doilnitsina, “Effective permittivity of a metamaterial from coated wires,” J. Phys. D 44, 265401 (2011).
[CrossRef]

E. S. Belonogaya, S. N. Galyamin, and A. V. Tyukhtin, “Properties of Vavilov-Cherenkov radiation in an anisotropic medium with a resonant dispersion of permittivity,” J. Opt. Soc. Am. B 28, 2871–2878 (2011).
[CrossRef]

S. N. Galyamin and A. V. Tyukhtin, “Reversed Cherenkov transition radiation of charge entering anisotropic medium,” Phys. Rev. E 84, 056608 (2011).
[CrossRef]

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

A. Kanareykin, “Cherenkov radiation and dielectric based accelerating structures: Wakefield generation, power extraction and energy transfer efficiency,” J. Phys. Conf. Ser. 236, 012032 (2010).
[CrossRef]

2009

Y. O. Averkov, A. V. Kats, and V. M. Yakovenko, “Electron beam excitation of left-handed surface electromagnetic waves at artificial interfaces,” Phys. Rev. B 79, 193402 (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. Duan, B.-I. Wu, S. Xi, H. S. Chen, and M. Chen, “Research progress in reversed Cherenkov radiation in double-negative metamaterials,” Prog. Electromagn. Res. 90, 75–87 (2009).
[CrossRef]

M. G. Silveirinha, “Poynting vector, heating rate, and stored energy in structured materials: a first-principles derivation,” Phys. Rev. B 80, 235120 (2009).
[CrossRef]

2008

M. C. Thompson, H. Badakov, A. Cook, J. B. Rosenzweig, R. Tikhoplav, G. Travish, I. Blumenfeld, M. J. Hogan, R. Ischebeck, N. Kirby, R. Siemann, D. Walz, P. Muggli, A. Scott, and R. B. Yoder, “Breakdown limits on gigavolt-per-meter electron-beam-drivenWakefields in dielectric structures,” Phys. Rev. Lett. 100, 214801 (2008).
[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]

A. Demetriadou and J. B. Pendry, “Taming spatial dispersion in wire metamaterial,” J. Phys. Condens. Matter 20, 295222 (2008).
[CrossRef]

2004

G. Dewar, “Complex mediums V: light and complexity,” Proc. SPIE 5508, 158–166 (2004).
[CrossRef]

2003

P. A. Belov, R. Marqu’es, S. I. Maslovski, I. S. Nefedov, M. Silveirinha, C. R. Simovski, and S. A. Tretyakov, “Strong spatial dispersion in wire media in the very large wavelength limit,” Phys. Rev. B 67, 113103 (2003).
[CrossRef]

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

2002

S. I. Maslovski, S. A. Tretyakov, and P. A. Belov, “Wire media with negative effective permittivity: a quasi-static model,” Microw. Opt. Technol. Lett. 35, 47–51 (2002).
[CrossRef]

P. A. Belov, S. Tretyakov, and A. J. Viitanen, “Dispersion and reflection properties of artificial media formed by regular lattices of ideally conducting wires,” J. Electromagn. Waves Appl. 16, 1153–1170 (2002).
[CrossRef]

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]

Agranovich, V. M.

V. M. Agranovich and V. L. Ginzburg, Spatial Dispersion in Crystal Optics and the Theory of Excitons (Interscience, 1966).

Alu, A.

M. A. Shapiro, S. Trendafilov, Y. Urzhumov, A. Alu, R. J. Temkin, and G. Shvets, “Active negative-index metamaterial powered by an electron beam,” Phys. Rev. B 86, 085132 (2012).
[CrossRef]

Averkov, Y. O.

Y. O. Averkov, A. V. Kats, and V. M. Yakovenko, “Electron beam excitation of left-handed surface electromagnetic waves at artificial interfaces,” Phys. Rev. B 79, 193402 (2009).
[CrossRef]

Badakov, H.

M. C. Thompson, H. Badakov, A. Cook, J. B. Rosenzweig, R. Tikhoplav, G. Travish, I. Blumenfeld, M. J. Hogan, R. Ischebeck, N. Kirby, R. Siemann, D. Walz, P. Muggli, A. Scott, and R. B. Yoder, “Breakdown limits on gigavolt-per-meter electron-beam-drivenWakefields in dielectric structures,” Phys. Rev. Lett. 100, 214801 (2008).
[CrossRef]

Belonogaya, E. S.

Belov, P. A.

P. A. Belov, R. Marqu’es, S. I. Maslovski, I. S. Nefedov, M. Silveirinha, C. R. Simovski, and S. A. Tretyakov, “Strong spatial dispersion in wire media in the very large wavelength limit,” Phys. Rev. B 67, 113103 (2003).
[CrossRef]

S. I. Maslovski, S. A. Tretyakov, and P. A. Belov, “Wire media with negative effective permittivity: a quasi-static model,” Microw. Opt. Technol. Lett. 35, 47–51 (2002).
[CrossRef]

P. A. Belov, S. Tretyakov, and A. J. Viitanen, “Dispersion and reflection properties of artificial media formed by regular lattices of ideally conducting wires,” J. Electromagn. Waves Appl. 16, 1153–1170 (2002).
[CrossRef]

Blumenfeld, I.

M. C. Thompson, H. Badakov, A. Cook, J. B. Rosenzweig, R. Tikhoplav, G. Travish, I. Blumenfeld, M. J. Hogan, R. Ischebeck, N. Kirby, R. Siemann, D. Walz, P. Muggli, A. Scott, and R. B. Yoder, “Breakdown limits on gigavolt-per-meter electron-beam-drivenWakefields in dielectric structures,” Phys. Rev. Lett. 100, 214801 (2008).
[CrossRef]

Brychkov, Y.

A. P. Prudnikov, Y. Brychkov, and O. I. Marichev, Integrals and Series. Special Functions (Nauka, 1983).

Chen, H. S.

Z. Duan, B.-I. Wu, S. Xi, H. S. Chen, and 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, J. Zhou, J. C. Lu, and M. Chen, “Novel electromagnetic radiation in a semi-infinite space filled with a double-negative metamaterial,” Phys. Plasmas 19, 013112 (2012).
[CrossRef]

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

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

Cook, A.

M. C. Thompson, H. Badakov, A. Cook, J. B. Rosenzweig, R. Tikhoplav, G. Travish, I. Blumenfeld, M. J. Hogan, R. Ischebeck, N. Kirby, R. Siemann, D. Walz, P. Muggli, A. Scott, and R. B. Yoder, “Breakdown limits on gigavolt-per-meter electron-beam-drivenWakefields in dielectric structures,” Phys. Rev. Lett. 100, 214801 (2008).
[CrossRef]

Demetriadou, A.

A. Demetriadou and J. B. Pendry, “Taming spatial dispersion in wire metamaterial,” J. Phys. Condens. Matter 20, 295222 (2008).
[CrossRef]

Dewar, G.

G. Dewar, “Complex mediums V: light and complexity,” Proc. SPIE 5508, 158–166 (2004).
[CrossRef]

Doilnitsina, E. G.

A. V. Tyukhtin and E. G. Doilnitsina, “Effective permittivity of a metamaterial from coated wires,” J. Phys. D 44, 265401 (2011).
[CrossRef]

Duan, Z.

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

Duan, Z. Y.

Z. Y. Duan, C. Guo, J. Zhou, J. C. Lu, and M. Chen, “Novel electromagnetic radiation in a semi-infinite space filled with a double-negative metamaterial,” Phys. Plasmas 19, 013112 (2012).
[CrossRef]

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

Fernandes, D. E.

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

Galyamin, S. N.

E. S. Belonogaya, S. N. Galyamin, and A. V. Tyukhtin, “Properties of Vavilov-Cherenkov radiation in an anisotropic medium with a resonant dispersion of permittivity,” J. Opt. Soc. Am. B 28, 2871–2878 (2011).
[CrossRef]

S. N. Galyamin and A. V. Tyukhtin, “Reversed Cherenkov transition radiation of charge entering anisotropic medium,” Phys. Rev. E 84, 056608 (2011).
[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. M. Agranovich and V. L. Ginzburg, Spatial Dispersion in Crystal Optics and the Theory of Excitons (Interscience, 1966).

Grzegorczyk, T. M.

Guo, C.

Z. Y. Duan, C. Guo, J. Zhou, J. C. Lu, and M. Chen, “Novel electromagnetic radiation in a semi-infinite space filled with a double-negative metamaterial,” Phys. Plasmas 19, 013112 (2012).
[CrossRef]

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

Hogan, M. J.

M. C. Thompson, H. Badakov, A. Cook, J. B. Rosenzweig, R. Tikhoplav, G. Travish, I. Blumenfeld, M. J. Hogan, R. Ischebeck, N. Kirby, R. Siemann, D. Walz, P. Muggli, A. Scott, and R. B. Yoder, “Breakdown limits on gigavolt-per-meter electron-beam-drivenWakefields in dielectric structures,” Phys. Rev. Lett. 100, 214801 (2008).
[CrossRef]

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]

Ischebeck, R.

M. C. Thompson, H. Badakov, A. Cook, J. B. Rosenzweig, R. Tikhoplav, G. Travish, I. Blumenfeld, M. J. Hogan, R. Ischebeck, N. Kirby, R. Siemann, D. Walz, P. Muggli, A. Scott, and R. B. Yoder, “Breakdown limits on gigavolt-per-meter electron-beam-drivenWakefields in dielectric structures,” Phys. Rev. Lett. 100, 214801 (2008).
[CrossRef]

Jr, J. P.

Kanareykin, A.

A. Kanareykin, “Cherenkov radiation and dielectric based accelerating structures: Wakefield generation, power extraction and energy transfer efficiency,” J. Phys. Conf. Ser. 236, 012032 (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]

Kats, A. V.

Y. O. Averkov, A. V. Kats, and V. M. Yakovenko, “Electron beam excitation of left-handed surface electromagnetic waves at artificial interfaces,” Phys. Rev. B 79, 193402 (2009).
[CrossRef]

Kirby, N.

M. C. Thompson, H. Badakov, A. Cook, J. B. Rosenzweig, R. Tikhoplav, G. Travish, I. Blumenfeld, M. J. Hogan, R. Ischebeck, N. Kirby, R. Siemann, D. Walz, P. Muggli, A. Scott, and R. B. Yoder, “Breakdown limits on gigavolt-per-meter electron-beam-drivenWakefields in dielectric structures,” Phys. Rev. Lett. 100, 214801 (2008).
[CrossRef]

Kong, J. A.

Lu, J.

Lu, J. C.

Z. Y. Duan, C. Guo, J. Zhou, J. C. Lu, and M. Chen, “Novel electromagnetic radiation in a semi-infinite space filled with a double-negative metamaterial,” Phys. Plasmas 19, 013112 (2012).
[CrossRef]

Marichev, O. I.

A. P. Prudnikov, Y. Brychkov, and O. I. Marichev, Integrals and Series. Special Functions (Nauka, 1983).

Marqu’es, R.

P. A. Belov, R. Marqu’es, S. I. Maslovski, I. S. Nefedov, M. Silveirinha, C. R. Simovski, and S. A. Tretyakov, “Strong spatial dispersion in wire media in the very large wavelength limit,” Phys. Rev. B 67, 113103 (2003).
[CrossRef]

Maslovski, S. I.

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

M. G. Silveirinha and S. I. Maslovski, “Radiation from elementary sources in a uniaxial wire medium,” Phys. Rev. B 85, 155125 (2012).
[CrossRef]

P. A. Belov, R. Marqu’es, S. I. Maslovski, I. S. Nefedov, M. Silveirinha, C. R. Simovski, and S. A. Tretyakov, “Strong spatial dispersion in wire media in the very large wavelength limit,” Phys. Rev. B 67, 113103 (2003).
[CrossRef]

S. I. Maslovski, S. A. Tretyakov, and P. A. Belov, “Wire media with negative effective permittivity: a quasi-static model,” Microw. Opt. Technol. Lett. 35, 47–51 (2002).
[CrossRef]

Muggli, P.

M. C. Thompson, H. Badakov, A. Cook, J. B. Rosenzweig, R. Tikhoplav, G. Travish, I. Blumenfeld, M. J. Hogan, R. Ischebeck, N. Kirby, R. Siemann, D. Walz, P. Muggli, A. Scott, and R. B. Yoder, “Breakdown limits on gigavolt-per-meter electron-beam-drivenWakefields in dielectric structures,” Phys. Rev. Lett. 100, 214801 (2008).
[CrossRef]

Nefedov, I. S.

P. A. Belov, R. Marqu’es, S. I. Maslovski, I. S. Nefedov, M. Silveirinha, C. R. Simovski, and S. A. Tretyakov, “Strong spatial dispersion in wire media in the very large wavelength limit,” Phys. Rev. B 67, 113103 (2003).
[CrossRef]

Pendry, J. B.

A. Demetriadou and J. B. Pendry, “Taming spatial dispersion in wire metamaterial,” J. Phys. Condens. Matter 20, 295222 (2008).
[CrossRef]

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]

Prudnikov, A. P.

A. P. Prudnikov, Y. Brychkov, and O. I. Marichev, Integrals and Series. Special Functions (Nauka, 1983).

Rosenzweig, J. B.

M. C. Thompson, H. Badakov, A. Cook, J. B. Rosenzweig, R. Tikhoplav, G. Travish, I. Blumenfeld, M. J. Hogan, R. Ischebeck, N. Kirby, R. Siemann, D. Walz, P. Muggli, A. Scott, and R. B. Yoder, “Breakdown limits on gigavolt-per-meter electron-beam-drivenWakefields in dielectric structures,” Phys. Rev. Lett. 100, 214801 (2008).
[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]

Scott, A.

M. C. Thompson, H. Badakov, A. Cook, J. B. Rosenzweig, R. Tikhoplav, G. Travish, I. Blumenfeld, M. J. Hogan, R. Ischebeck, N. Kirby, R. Siemann, D. Walz, P. Muggli, A. Scott, and R. B. Yoder, “Breakdown limits on gigavolt-per-meter electron-beam-drivenWakefields in dielectric structures,” Phys. Rev. Lett. 100, 214801 (2008).
[CrossRef]

Shapiro, M. A.

M. A. Shapiro, S. Trendafilov, Y. Urzhumov, A. Alu, R. J. Temkin, and G. Shvets, “Active negative-index metamaterial powered by an electron beam,” Phys. Rev. B 86, 085132 (2012).
[CrossRef]

Shvets, G.

M. A. Shapiro, S. Trendafilov, Y. Urzhumov, A. Alu, R. J. Temkin, and G. Shvets, “Active negative-index metamaterial powered by an electron beam,” Phys. Rev. B 86, 085132 (2012).
[CrossRef]

Siemann, R.

M. C. Thompson, H. Badakov, A. Cook, J. B. Rosenzweig, R. Tikhoplav, G. Travish, I. Blumenfeld, M. J. Hogan, R. Ischebeck, N. Kirby, R. Siemann, D. Walz, P. Muggli, A. Scott, and R. B. Yoder, “Breakdown limits on gigavolt-per-meter electron-beam-drivenWakefields in dielectric structures,” Phys. Rev. Lett. 100, 214801 (2008).
[CrossRef]

Silveirinha, M.

P. A. Belov, R. Marqu’es, S. I. Maslovski, I. S. Nefedov, M. Silveirinha, C. R. Simovski, and S. A. Tretyakov, “Strong spatial dispersion in wire media in the very large wavelength limit,” Phys. Rev. B 67, 113103 (2003).
[CrossRef]

Silveirinha, M. G.

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

M. G. Silveirinha and S. I. Maslovski, “Radiation from elementary sources in a uniaxial wire medium,” Phys. Rev. B 85, 155125 (2012).
[CrossRef]

M. G. Silveirinha, “Poynting vector, heating rate, and stored energy in structured materials: a first-principles derivation,” Phys. Rev. B 80, 235120 (2009).
[CrossRef]

Simovski, C. R.

P. A. Belov, R. Marqu’es, S. I. Maslovski, I. S. Nefedov, M. Silveirinha, C. R. Simovski, and S. A. Tretyakov, “Strong spatial dispersion in wire media in the very large wavelength limit,” Phys. Rev. B 67, 113103 (2003).
[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]

Temkin, R. J.

M. A. Shapiro, S. Trendafilov, Y. Urzhumov, A. Alu, R. J. Temkin, and G. Shvets, “Active negative-index metamaterial powered by an electron beam,” Phys. Rev. B 86, 085132 (2012).
[CrossRef]

Thompson, M. C.

M. C. Thompson, H. Badakov, A. Cook, J. B. Rosenzweig, R. Tikhoplav, G. Travish, I. Blumenfeld, M. J. Hogan, R. Ischebeck, N. Kirby, R. Siemann, D. Walz, P. Muggli, A. Scott, and R. B. Yoder, “Breakdown limits on gigavolt-per-meter electron-beam-drivenWakefields in dielectric structures,” Phys. Rev. Lett. 100, 214801 (2008).
[CrossRef]

Tikhoplav, R.

M. C. Thompson, H. Badakov, A. Cook, J. B. Rosenzweig, R. Tikhoplav, G. Travish, I. Blumenfeld, M. J. Hogan, R. Ischebeck, N. Kirby, R. Siemann, D. Walz, P. Muggli, A. Scott, and R. B. Yoder, “Breakdown limits on gigavolt-per-meter electron-beam-drivenWakefields in dielectric structures,” Phys. Rev. Lett. 100, 214801 (2008).
[CrossRef]

Travish, G.

M. C. Thompson, H. Badakov, A. Cook, J. B. Rosenzweig, R. Tikhoplav, G. Travish, I. Blumenfeld, M. J. Hogan, R. Ischebeck, N. Kirby, R. Siemann, D. Walz, P. Muggli, A. Scott, and R. B. Yoder, “Breakdown limits on gigavolt-per-meter electron-beam-drivenWakefields in dielectric structures,” Phys. Rev. Lett. 100, 214801 (2008).
[CrossRef]

Trendafilov, S.

M. A. Shapiro, S. Trendafilov, Y. Urzhumov, A. Alu, R. J. Temkin, and G. Shvets, “Active negative-index metamaterial powered by an electron beam,” Phys. Rev. B 86, 085132 (2012).
[CrossRef]

Tretyakov, S.

P. A. Belov, S. Tretyakov, and A. J. Viitanen, “Dispersion and reflection properties of artificial media formed by regular lattices of ideally conducting wires,” J. Electromagn. Waves Appl. 16, 1153–1170 (2002).
[CrossRef]

Tretyakov, S. A.

P. A. Belov, R. Marqu’es, S. I. Maslovski, I. S. Nefedov, M. Silveirinha, C. R. Simovski, and S. A. Tretyakov, “Strong spatial dispersion in wire media in the very large wavelength limit,” Phys. Rev. B 67, 113103 (2003).
[CrossRef]

S. I. Maslovski, S. A. Tretyakov, and P. A. Belov, “Wire media with negative effective permittivity: a quasi-static model,” Microw. Opt. Technol. Lett. 35, 47–51 (2002).
[CrossRef]

Tyukhtin, A. V.

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

A. V. Tyukhtin and E. G. Doilnitsina, “Effective permittivity of a metamaterial from coated wires,” J. Phys. D 44, 265401 (2011).
[CrossRef]

S. N. Galyamin and A. V. Tyukhtin, “Reversed Cherenkov transition radiation of charge entering anisotropic medium,” Phys. Rev. E 84, 056608 (2011).
[CrossRef]

E. S. Belonogaya, S. N. Galyamin, and A. V. Tyukhtin, “Properties of Vavilov-Cherenkov radiation in an anisotropic medium with a resonant dispersion of permittivity,” J. Opt. Soc. Am. B 28, 2871–2878 (2011).
[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]

Urzhumov, Y.

M. A. Shapiro, S. Trendafilov, Y. Urzhumov, A. Alu, R. J. Temkin, and G. Shvets, “Active negative-index metamaterial powered by an electron beam,” Phys. Rev. B 86, 085132 (2012).
[CrossRef]

Viitanen, A. J.

P. A. Belov, S. Tretyakov, and A. J. Viitanen, “Dispersion and reflection properties of artificial media formed by regular lattices of ideally conducting wires,” J. Electromagn. Waves Appl. 16, 1153–1170 (2002).
[CrossRef]

Vorobev, V. V.

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

Walz, D.

M. C. Thompson, H. Badakov, A. Cook, J. B. Rosenzweig, R. Tikhoplav, G. Travish, I. Blumenfeld, M. J. Hogan, R. Ischebeck, N. Kirby, R. Siemann, D. Walz, P. Muggli, A. Scott, and R. B. Yoder, “Breakdown limits on gigavolt-per-meter electron-beam-drivenWakefields in dielectric structures,” Phys. Rev. Lett. 100, 214801 (2008).
[CrossRef]

Wu, B.-I.

Z. Duan, B.-I. Wu, S. Xi, H. S. Chen, and 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. P. Jr, B.-I. Wu, and J. A. Kong, “Cerenkov radiation in materials with negative permittivity and permeability,” Opt. Express 11, 723–734 (2003).
[CrossRef]

Xi, S.

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

Yakovenko, V. M.

Y. O. Averkov, A. V. Kats, and V. M. Yakovenko, “Electron beam excitation of left-handed surface electromagnetic waves at artificial interfaces,” Phys. Rev. B 79, 193402 (2009).
[CrossRef]

Yoder, R. B.

M. C. Thompson, H. Badakov, A. Cook, J. B. Rosenzweig, R. Tikhoplav, G. Travish, I. Blumenfeld, M. J. Hogan, R. Ischebeck, N. Kirby, R. Siemann, D. Walz, P. Muggli, A. Scott, and R. B. Yoder, “Breakdown limits on gigavolt-per-meter electron-beam-drivenWakefields in dielectric structures,” Phys. Rev. Lett. 100, 214801 (2008).
[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]

Zhang, Y.

Zhou, J.

Z. Y. Duan, C. Guo, J. Zhou, J. C. Lu, and M. Chen, “Novel electromagnetic radiation in a semi-infinite space filled with a double-negative metamaterial,” Phys. Plasmas 19, 013112 (2012).
[CrossRef]

Zrelov, V. P.

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

J. Electromagn. Waves Appl.

P. A. Belov, S. Tretyakov, and A. J. Viitanen, “Dispersion and reflection properties of artificial media formed by regular lattices of ideally conducting wires,” J. Electromagn. Waves Appl. 16, 1153–1170 (2002).
[CrossRef]

J. Opt. Soc. Am. B

J. Phys. Condens. Matter

A. Demetriadou and J. B. Pendry, “Taming spatial dispersion in wire metamaterial,” J. Phys. Condens. Matter 20, 295222 (2008).
[CrossRef]

J. Phys. Conf. Ser.

A. Kanareykin, “Cherenkov radiation and dielectric based accelerating structures: Wakefield generation, power extraction and energy transfer efficiency,” J. Phys. Conf. Ser. 236, 012032 (2010).
[CrossRef]

J. Phys. D

A. V. Tyukhtin and E. G. Doilnitsina, “Effective permittivity of a metamaterial from coated wires,” J. Phys. D 44, 265401 (2011).
[CrossRef]

Microw. Opt. Technol. Lett.

S. I. Maslovski, S. A. Tretyakov, and P. A. Belov, “Wire media with negative effective permittivity: a quasi-static model,” Microw. Opt. Technol. Lett. 35, 47–51 (2002).
[CrossRef]

Opt. Express

Phys. Plasmas

Z. Y. Duan, C. Guo, J. Zhou, J. C. Lu, and M. Chen, “Novel electromagnetic radiation in a semi-infinite space filled with a double-negative metamaterial,” Phys. Plasmas 19, 013112 (2012).
[CrossRef]

Phys. Rev. B

P. A. Belov, R. Marqu’es, S. I. Maslovski, I. S. Nefedov, M. Silveirinha, C. R. Simovski, and S. A. Tretyakov, “Strong spatial dispersion in wire media in the very large wavelength limit,” Phys. Rev. B 67, 113103 (2003).
[CrossRef]

M. A. Shapiro, S. Trendafilov, Y. Urzhumov, A. Alu, R. J. Temkin, and G. Shvets, “Active negative-index metamaterial powered by an electron beam,” Phys. Rev. B 86, 085132 (2012).
[CrossRef]

Y. O. Averkov, A. V. Kats, and V. M. Yakovenko, “Electron beam excitation of left-handed surface electromagnetic waves at artificial interfaces,” Phys. Rev. B 79, 193402 (2009).
[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]

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

M. G. Silveirinha, “Poynting vector, heating rate, and stored energy in structured materials: a first-principles derivation,” Phys. Rev. B 80, 235120 (2009).
[CrossRef]

M. G. Silveirinha and S. I. Maslovski, “Radiation from elementary sources in a uniaxial wire medium,” Phys. Rev. B 85, 155125 (2012).
[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]

S. N. Galyamin and A. V. Tyukhtin, “Reversed Cherenkov transition radiation of charge entering anisotropic medium,” Phys. Rev. E 84, 056608 (2011).
[CrossRef]

Phys. Rev. Lett.

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

M. C. Thompson, H. Badakov, A. Cook, J. B. Rosenzweig, R. Tikhoplav, G. Travish, I. Blumenfeld, M. J. Hogan, R. Ischebeck, N. Kirby, R. Siemann, D. Walz, P. Muggli, A. Scott, and R. B. Yoder, “Breakdown limits on gigavolt-per-meter electron-beam-drivenWakefields in dielectric structures,” Phys. Rev. Lett. 100, 214801 (2008).
[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]

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]

Proc. SPIE

G. Dewar, “Complex mediums V: light and complexity,” Proc. SPIE 5508, 158–166 (2004).
[CrossRef]

Prog. Electromagn. Res.

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

Other

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

A. P. Prudnikov, Y. Brychkov, and O. I. Marichev, Integrals and Series. Special Functions (Nauka, 1983).

V. M. Agranovich and V. L. Ginzburg, Spatial Dispersion in Crystal Optics and the Theory of Excitons (Interscience, 1966).

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Figures (7)

Fig. 1.
Fig. 1.

Metamaterial cross section in the plane perpendicular to the z axis.

Fig. 2.
Fig. 2.

Cuts on the Riemann plane for ωd0 (a) and for ωd0 (b) when β<χ.

Fig. 3.
Fig. 3.

Cuts on the Riemann plane for ωd0 (a) and for ωd0 (b) when β>χ.

Fig. 4.
Fig. 4.

Solutions of the dispersion Eq. (28) for χ=1 (a) and χ<1 (b) in unity ω/c. The dashed–dotted line shows an “ordinary” wave (marked “o”), the dashed line represents an “extraordinary anisotropic” wave (marked “ea”), and the dashed-double-dotted line represents an “extraordinary isotropic” wave (marked “ei”). The long arrows represent the wave vectors and their z projection. The short bold arrows represent the group velocities.

Fig. 5.
Fig. 5.

Cuts and poles for the case of a cold plasma.

Fig. 6.
Fig. 6.

Polar diagrams for 2πρ·w (in J×s/m2) in the setting of the charge velocity and the coating radius: r0=0.05mm, a=1mm, ε1=5, μ1=1, q=1nC, ρ=20c/ωp. For the first row ωd=0, for the second row ωd=0.001ωp, for the third row ωd=0.01ωp.

Fig. 7.
Fig. 7.

Emitted electromagnetic energy 2πρ·w (in J×s/m2) in a metamaterial (solid line) and an ordinary dielectric with a permittivity ε1 (dotted line) depending on frequency f=ω/(2π)(inHz); in the setting of the permittivity and the charge velocity: r0=0.05mm, rd=0.15mm, a=1mm, μ1=1, q=1nC, ωd=0.

Equations (50)

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

ε^=(10001000ε),μ=1,
ε(ω,kz)=1ωp2ω2c2χ2kz2+2iωdω.
ωp2=2πc2a2[ln(a/rd)+μ1ln(rd/r0)C],
χ2=1+(ε11μ1)ln(rd/r0)ln(a/rd)+μ1ln(rd/r0)C,
j⃗=Vqδ(x)δ(y)δ(zVt)e⃗z.
H⃗=rotA⃗,E⃗=ϕ1cdA⃗dt,
H⃗ωk⃗=[ik⃗,A⃗ωk⃗],E⃗ωk⃗=ik⃗ϕωk⃗+iωcA⃗ωk⃗,
[ik⃗,E⃗ωk⃗]=iωcB⃗ωk⃗,[ik⃗,H⃗ωk⃗]=iωcD⃗ωk⃗+4πcj⃗ωk⃗,
{Azϕ}=q2π2+dωR3dkρdkzdφk{ω/(ckz)1}×kρδ(ωkzV)kρ2+(kz2ω2/c2)ε(ω,kz)×exp{ikρρcos(φφk)+ikzziωt},
{Azϕ}=q2πV{β1}+dω+dkρkρH0(1)(kρρ)kρ2s2eiωVζ,
ζ=zVt,
s2=ε(ω,ωV)·ω2V2(1β2).
{Azϕ}=iq2V{β1}+H0(1)(sρ)eiωVζdω.
{EρEzHφ}=q2c+{eρ(ω)ez(ω)hφ(ω)}eiωVζdω,
{eρ(ω)ez(ω)hφ(ω)}={iβs(ω)H1(1)(s(ω)ρ)1β2cβ2ωH0(1)(s(ω)ρ)is(ω)H1(1)(s(ω)ρ)}.
s2(ω)=1β2c2β2·ω·(ωΩ1)(ωΩ2)ω2iωdκ,
Ω1,2=iωdκ±iωd2κ2+ωp2κ,
κ=β2/(χ2β2).
s2=1β2c2β2(ω2+Ω2),Ω2=ωp2β2χ2β2,
Eρ=qcβΩ+|s(iω)|J1(|s(iω)|ρ)eωV|ζ|dω,Ez=q1β2c2β2signζΩ+J0(|s(iω)|ρ)ωeωV|ζ|dω,Hφ=qcΩ+|s(iω)|J1(|s(iω)|ρ)eωV|ζ|dω.
{EρEzHφ}=qγ2{ρζρβ}1+ωpκβcζ2+ρ2γ2[ζ2+ρ2γ2]3/2×exp(ωpκβcζ2+ρ2γ2),
{ERHφ}=qγ2{1sinθ}1+ωpRcχ2β2cos2θ+sin2θγ2R2[cos2θ+sin2θγ2]3/2×exp(ωpRcχ2β2cos2θ+sin2θγ2).
{ω=0,ω(;2ωdκ)(0;+)
{w34w2ωdκ+ω2ωωdκ(ReΩ1)2=0,ω>ωdκ.
s2=1β2c2β2(ω2Ω2),
Eρ=EρC+EρW,Ez=EzC+EzW,Hφ=HφC+HφW,
EρC=qc2β2γ0+Ω2+ω2J1(ξC)eω|ζ|/Vdω,EzC=qsignζc2β2γ20+J0(ξC)ωeω|ζ|/Vdω,HφC=qc2βγ0+Ω2+ω2J1(ξC)eω|ζ|/Vdω,
EρW=2qΘ(ζ)c2β2γ0ΩΩ2ω2J1(ξW)sin(ωVζ)dω,EzW=2qΘ(ζ)c2β2γ20ΩJ0(ξW)ωcos(ωVζ)dω,HφW=2qΘ(ζ)c2βγ0ΩΩ2ω2J1(ξW)sin(ωVζ)dω,
ξC=ρΩ2+ω2cβγ,ξW=ρΩ2ω2cβγ.
(kx2+ky2+εkz2εω2c2)(k2ω2c2)=0,
kzo2=ω2c2kx2ky2,
kzea,ei2=12χ2{ω2c2(1+χ2)χ2(kx2+ky2)ωp2c2±A(1χ2)+(χ2(kx2+ky2)+ωp2c2)2},A=ω2c2(ω2c2(1χ2)2ωp2c2+2χ2(kx2+ky2)),
kzei2=ω2ωp2c2kx2ky2,kzea2=ω2c2,
ε=1ωp2ω2+2iωωd.
Eρ=q2c+is(ω)βε(ω)H1(1)(s(ω)ρ)eiωVζdω,Ez=q2c+1ε(ω)β2cβ2ε(ω)H0(1)(s(ω)ρ)ωeiωVζdω,Hφ=q2c+is(ω)H1(1)(s(ω)ρ)eiωVζdω,
s(ω)=ω2V2(ε(ω)β21),Ims>0.
s2=1β2c2β2(ω2+Ω2),Ω2=ωp2β21β2.
E⃗=E⃗C+E⃗P,H⃗=H⃗C,EρC=qcΩ+s(iω)βε(iω)J1(s(iω)ρ)eωV|ζ|dω,EzC=qcsignζΩ+1ε(iω)β2cβ2ε(iω)J0(s(iω)ρ)ωeωV|ζ|dω,HφC=qcΩ+s(iω)J1(s(iω)ρ)eωV|ζ|dω,
EρP=2qωp2c2β2K1(ωpVρ)sin(ωpVζ)Θ(ζ),EzP=2qωp2c2β2K0(ωpVρ)cos(ωpVζ)Θ(ζ),
R2exp(Rc1ωpγcos2θ+γ2sin2θ).
{WzWρ}=q216πc+dωdω˜dt{eρ(ω)hφ(ω˜)ez(ω)hφ(ω˜)}eiω+ω˜V(zcβt).
Wz=q28c+eρ(ω)hφ(ω)dω,Wρ=q28c+ez(ω)hφ(ω)dω.
Wz=0+wz(ω)dω,Wρ=0+wρ(ω)dω,
wz=q24cRe[eρ(ω)hφ*(ω)],wρ=q24cRe[ez(ω)hφ*(ω)].
{wz(ω)wρ(ω)}=q22πρcβ{|s(ω)|e2ρIm(s(ω))1cβγ2ωRes(ω)|s(ω)|e2ρIm(s(ω))}.
{wz(ω)wρ(ω)}=q22πρcβ{1cβγωp2β2β2χ2ω2ωcβγ2}.
w(ω)=q22πρc2βγωp2β2χ2ω2,sinθw=wρ(ω)w(ω)=ωβγωp2(β2χ2)1ω2.
w0=w0ρ2+w0z2=q2ω2πρc2βεεβ21.
d2Edzdω=2πρwρ(ω)=q2(1β2)c2β2ω.
d2E0dzdω=2πρw0ρ=q2c2(11εβ2)ω.

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