Abstract

Radiation of electromagnetic waves by a uniformly moving charge is the subject of extensive research over the last several decades. Fascinating effects such as Vavilov-Cherenkov radiation, transition radiation and the Smith-Purcell effect were discovered and studied in depth. In this letter we study the radiation of a line charge moving with relativistic constant velocity within an average zero index metamaterial consisting of periodically alternating layers with negative and positive refractive index. We observe a strong radiation enhancement, ∼3 orders of magnitude, for specific combinations of velocities and radiation frequencies. This surprising finding is attributed to a gigantic increase in the density of states at the positive/negative index boundary. Furthermore, we shed light on radiation effects of such a line charge propagating within the more “traditional” structure of periodically alternating layers consisting of positive and different refractive index with focus on frequencies satisfying the quarter wave stack and the half wave stack conditions. We show that the quarter-wave-stack case results in emission propagating vertically to the line charge trajectory, while the half-wave-stack results in negligible radiation. All these findings were obtained using a computationally efficient and conceptually intuitive computation method, based on eigenmode expansion of specific frequency components. For validation purposes this method was compared with the finite-difference-time-domain method.

© 2012 OSA

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    [CrossRef]

2012

L.Sh. Khachatryan, S.R. Arzumanyan, and W. Wagner, “Self-amplified Cherenkov radiation from a relativistic electron in a waveguide partially filled with a laminated material,” JJ. Phys.: Conf. Ser.357, 012004 (2012).
[CrossRef]

D. E. Fernandes, S. I. Maslovski, and M. G. Silveirinha, “Cherenkov emission in a nanowire material,” Phys. Rev. B85, 155107 (2012).
[CrossRef]

V. V. Vorobev and A. V. Tyukhtin, “Nondivergent Cherenkov Radiation in a Wire Metamaterial,” Phys. Rev. Lett.108, 184801 (2012).
[CrossRef] [PubMed]

Z. Mohammadi, C. P. Van Vlack, S. Hughes, J. Bornemann, and R. Gordon, “Vortex electron energy loss spectroscopy for near-field mapping of magnetic plasmons,” Opt. Express20, 15024–15034 (2012).
[CrossRef] [PubMed]

A. Yanai, M. Orenstein, and U. Levy, “Giant resonance absorption in ultra-thin metamaterial periodic structures,” Opt. Express20, 3693–3702 (2012).
[CrossRef] [PubMed]

2011

S. Kocaman, M. S. Aras, P. Hsieh, J. F. McMillan, C. G. Biris, N. C. Panoiu, M. B. Yu, D. L. Kwong, A. Stein, and C. W. Wong, “Zero phase delay in negative-refractive-index photonic crystal superlattices,” Nat. Photonics5, 499–505 (2011).
[CrossRef]

2010

F. J. García de Abajo, “Optical excitations in electron microscopy,” Rev. Mod. Phys.82, 209–275 (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. B81, 235134 (2010).
[CrossRef]

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun.181(3), 687–702 (2010).
[CrossRef]

2009

C. Kremers, D. N. Chigrin, and J. Kroha, “Theory of Cherenkov radiation in periodic dielectric media: Emission spectrum,” Phys. Rev. A79, 013829 (2009).
[CrossRef]

C. Kremers and D. N. Chigrin, “Spatial distribution of Cherenkov radiation in periodic dielectric media,” J. Opt. A11, 114008 (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, 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, 194802 (2009).
[CrossRef]

2008

F. J. García de Abajo and M. Kociak, “Probing the photonic local density of states with electron energy loss spectroscopy,” Phys. Rev. Lett.100(10), 106804 (2008).
[CrossRef] [PubMed]

2005

I. Shadrivov, A. Sukhorukov, and Y. Kivshar, “Complete Band Gaps in One-Dimensional Left-Handed Periodic Structures,” Phys. Rev. Lett.95, 193903 (2005).
[CrossRef] [PubMed]

T. Ochiai and K. Ohtaka, “Electron energy loss and Smith-Purcell radiation in two- and three-dimensional photonic crystals,” Opt. Express13, 7683–7698 (2005).
[CrossRef] [PubMed]

2003

J. Lu, T. Grzegorczyk, Y. Zhang, J. Pacheco, B.-I. Wu, J. Kong, and M. Chen, “Cerenkov radiation in materials with negative permittivity and permeability,” Opt. Express11, 723–734 (2003).
[CrossRef] [PubMed]

C. Luo, M. Ibanescu, S. G. Johnson, and J. D. Joannopoulos, “Cherenkov radiation in photonic crystals,” Science299(5605), 368–371 (2003).
[CrossRef] [PubMed]

L. Wu, S. He, and L. F. Shen, “Band structure for a one-dimensional photonic crystal containing left-handed materials,” Phys. Rev. B67, 235103 (2003).
[CrossRef]

2002

S. Nefedov and S. A. Tretyakov, “Photonic band gap structure containing metamaterial with negative permittivity and permeability,” Phys. Rev. E66, 036611 (2002).
[CrossRef]

1996

1995

1984

1973

1970

K. F. Casey and C. Yeh, “Transition Radiation in a Periodically Stratified Plasma,” Phys. Rev. A2, 810–818 (1970).
[CrossRef]

1968

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

1962

B. M. Bolotovskii, “Theory of Cerenkov radiation (III),” Sov. Phys. Usp.4, 781–811 (1962).
[CrossRef]

1957

I. A. Fainberg and N. A. Khizhniak, “Energy Loss of a Charged Particle Passing Through a Laminar Dielectric,” Sov. Phys. JETP5720–729 (1957).

1953

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

Aras, M. S.

S. Kocaman, M. S. Aras, P. Hsieh, J. F. McMillan, C. G. Biris, N. C. Panoiu, M. B. Yu, D. L. Kwong, A. Stein, and C. W. Wong, “Zero phase delay in negative-refractive-index photonic crystal superlattices,” Nat. Photonics5, 499–505 (2011).
[CrossRef]

Arzumanyan, S.R.

L.Sh. Khachatryan, S.R. Arzumanyan, and W. Wagner, “Self-amplified Cherenkov radiation from a relativistic electron in a waveguide partially filled with a laminated material,” JJ. Phys.: Conf. Ser.357, 012004 (2012).
[CrossRef]

Bermel, P.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun.181(3), 687–702 (2010).
[CrossRef]

Biris, C. G.

S. Kocaman, M. S. Aras, P. Hsieh, J. F. McMillan, C. G. Biris, N. C. Panoiu, M. B. Yu, D. L. Kwong, A. Stein, and C. W. Wong, “Zero phase delay in negative-refractive-index photonic crystal superlattices,” Nat. Photonics5, 499–505 (2011).
[CrossRef]

Bolotovskii, B. M.

B. M. Bolotovskii, “Theory of Cerenkov radiation (III),” Sov. Phys. Usp.4, 781–811 (1962).
[CrossRef]

Bornemann, J.

Casey, K. F.

K. F. Casey and C. Yeh, “Transition Radiation in a Periodically Stratified Plasma,” Phys. Rev. A2, 810–818 (1970).
[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, 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, 194801 (2009).
[CrossRef]

J. Lu, T. Grzegorczyk, Y. Zhang, J. Pacheco, B.-I. Wu, J. Kong, and M. Chen, “Cerenkov radiation in materials with negative permittivity and permeability,” Opt. Express11, 723–734 (2003).
[CrossRef] [PubMed]

Chigrin, D. N.

C. Kremers, D. N. Chigrin, and J. Kroha, “Theory of Cherenkov radiation in periodic dielectric media: Emission spectrum,” Phys. Rev. A79, 013829 (2009).
[CrossRef]

C. Kremers and D. N. Chigrin, “Spatial distribution of Cherenkov radiation in periodic dielectric media,” J. Opt. A11, 114008 (2009).
[CrossRef]

Chuang, S. L.

Fainberg, I. A.

I. A. Fainberg and N. A. Khizhniak, “Energy Loss of a Charged Particle Passing Through a Laminar Dielectric,” Sov. Phys. JETP5720–729 (1957).

Fernandes, D. E.

D. E. Fernandes, S. I. Maslovski, and M. G. Silveirinha, “Cherenkov emission in a nanowire material,” Phys. Rev. B85, 155107 (2012).
[CrossRef]

Galyamin, S. N.

S. N. Galyamin and A. V. Tyukhtin, “Electromagnetic field of a moving charge in the presence of a left-handed medium,” Phys. Rev. B81, 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]

García de Abajo, F. J.

F. J. García de Abajo, “Optical excitations in electron microscopy,” Rev. Mod. Phys.82, 209–275 (2010).
[CrossRef]

F. J. García de Abajo and M. Kociak, “Probing the photonic local density of states with electron energy loss spectroscopy,” Phys. Rev. Lett.100(10), 106804 (2008).
[CrossRef] [PubMed]

Gaylord, T. K.

Ginzburg, V. L.

V. L. Ginzburg, “Radiation by uniformly moving sources (Vavilov - Cherenkov effect, transition radiation,and other phenomena),” Usp. Fiz. Nauk166, 1033–1042 (1996).
[CrossRef]

Gordon, R.

Grann, E. B.

Grzegorczyk, T.

He, S.

L. Wu, S. He, and L. F. Shen, “Band structure for a one-dimensional photonic crystal containing left-handed materials,” Phys. Rev. B67, 235103 (2003).
[CrossRef]

Hsieh, P.

S. Kocaman, M. S. Aras, P. Hsieh, J. F. McMillan, C. G. Biris, N. C. Panoiu, M. B. Yu, D. L. Kwong, A. Stein, and C. W. Wong, “Zero phase delay in negative-refractive-index photonic crystal superlattices,” Nat. Photonics5, 499–505 (2011).
[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, 194801 (2009).
[CrossRef]

Hughes, S.

Ibanescu, M.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun.181(3), 687–702 (2010).
[CrossRef]

C. Luo, M. Ibanescu, S. G. Johnson, and J. D. Joannopoulos, “Cherenkov radiation in photonic crystals,” Science299(5605), 368–371 (2003).
[CrossRef] [PubMed]

Jackson, J. D.

J. D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, 1999).

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, 194801 (2009).
[CrossRef]

Joannopoulos, J. D.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun.181(3), 687–702 (2010).
[CrossRef]

C. Luo, M. Ibanescu, S. G. Johnson, and J. D. Joannopoulos, “Cherenkov radiation in photonic crystals,” Science299(5605), 368–371 (2003).
[CrossRef] [PubMed]

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light, 2nd ed. (Princeton University Press, 2008).

Johnson, S. G.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun.181(3), 687–702 (2010).
[CrossRef]

C. Luo, M. Ibanescu, S. G. Johnson, and J. D. Joannopoulos, “Cherenkov radiation in photonic crystals,” Science299(5605), 368–371 (2003).
[CrossRef] [PubMed]

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light, 2nd ed. (Princeton University Press, 2008).

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]

Khachatryan, L.Sh.

L.Sh. Khachatryan, S.R. Arzumanyan, and W. Wagner, “Self-amplified Cherenkov radiation from a relativistic electron in a waveguide partially filled with a laminated material,” JJ. Phys.: Conf. Ser.357, 012004 (2012).
[CrossRef]

Khizhniak, N. A.

I. A. Fainberg and N. A. Khizhniak, “Energy Loss of a Charged Particle Passing Through a Laminar Dielectric,” Sov. Phys. JETP5720–729 (1957).

Kivshar, Y.

I. Shadrivov, A. Sukhorukov, and Y. Kivshar, “Complete Band Gaps in One-Dimensional Left-Handed Periodic Structures,” Phys. Rev. Lett.95, 193903 (2005).
[CrossRef] [PubMed]

Kocaman, S.

S. Kocaman, M. S. Aras, P. Hsieh, J. F. McMillan, C. G. Biris, N. C. Panoiu, M. B. Yu, D. L. Kwong, A. Stein, and C. W. Wong, “Zero phase delay in negative-refractive-index photonic crystal superlattices,” Nat. Photonics5, 499–505 (2011).
[CrossRef]

Kociak, M.

F. J. García de Abajo and M. Kociak, “Probing the photonic local density of states with electron energy loss spectroscopy,” Phys. Rev. Lett.100(10), 106804 (2008).
[CrossRef] [PubMed]

Kong, J.

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, 194801 (2009).
[CrossRef]

S. L. Chuang and J. A. Kong, “Enhancement of Smith-Purcell radiation from a grating with surface-plasmon excitation,” J. Opt. Soc. Am. A1, 672–676 (1984).
[CrossRef]

Kremers, C.

C. Kremers, D. N. Chigrin, and J. Kroha, “Theory of Cherenkov radiation in periodic dielectric media: Emission spectrum,” Phys. Rev. A79, 013829 (2009).
[CrossRef]

C. Kremers and D. N. Chigrin, “Spatial distribution of Cherenkov radiation in periodic dielectric media,” J. Opt. A11, 114008 (2009).
[CrossRef]

Kroha, J.

C. Kremers, D. N. Chigrin, and J. Kroha, “Theory of Cherenkov radiation in periodic dielectric media: Emission spectrum,” Phys. Rev. A79, 013829 (2009).
[CrossRef]

Kwong, D. L.

S. Kocaman, M. S. Aras, P. Hsieh, J. F. McMillan, C. G. Biris, N. C. Panoiu, M. B. Yu, D. L. Kwong, A. Stein, and C. W. Wong, “Zero phase delay in negative-refractive-index photonic crystal superlattices,” Nat. Photonics5, 499–505 (2011).
[CrossRef]

Lalanne, P.

Levy, U.

Li, L.

Lu, J.

Luo, C.

C. Luo, M. Ibanescu, S. G. Johnson, and J. D. Joannopoulos, “Cherenkov radiation in photonic crystals,” Science299(5605), 368–371 (2003).
[CrossRef] [PubMed]

Maslovski, S. I.

D. E. Fernandes, S. I. Maslovski, and M. G. Silveirinha, “Cherenkov emission in a nanowire material,” Phys. Rev. B85, 155107 (2012).
[CrossRef]

McMillan, J. F.

S. Kocaman, M. S. Aras, P. Hsieh, J. F. McMillan, C. G. Biris, N. C. Panoiu, M. B. Yu, D. L. Kwong, A. Stein, and C. W. Wong, “Zero phase delay in negative-refractive-index photonic crystal superlattices,” Nat. Photonics5, 499–505 (2011).
[CrossRef]

Meade, R. D.

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light, 2nd ed. (Princeton University Press, 2008).

Mohammadi, Z.

Moharam, M. G.

Morris, G.

Nefedov, S.

S. Nefedov and S. A. Tretyakov, “Photonic band gap structure containing metamaterial with negative permittivity and permeability,” Phys. Rev. E66, 036611 (2002).
[CrossRef]

Ochiai, T.

Ohtaka, K.

Orenstein, M.

Oskooi, A. F.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun.181(3), 687–702 (2010).
[CrossRef]

Pacheco, J.

Panoiu, N. C.

S. Kocaman, M. S. Aras, P. Hsieh, J. F. McMillan, C. G. Biris, N. C. Panoiu, M. B. Yu, D. L. Kwong, A. Stein, and C. W. Wong, “Zero phase delay in negative-refractive-index photonic crystal superlattices,” Nat. Photonics5, 499–505 (2011).
[CrossRef]

Petit, R.

R. Petit, Electromagnetic Theory of Gratings (Topics in Applied Physics) (Springer, 1980).
[CrossRef]

Pommet, D. A.

Purcell, E. M.

S. J. Smith and E. M. Purcell, “Visible light from localized surface charges moving across a grating,” Phys. Rev.92, 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, 194801 (2009).
[CrossRef]

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A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun.181(3), 687–702 (2010).
[CrossRef]

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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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I. Shadrivov, A. Sukhorukov, and Y. Kivshar, “Complete Band Gaps in One-Dimensional Left-Handed Periodic Structures,” Phys. Rev. Lett.95, 193903 (2005).
[CrossRef] [PubMed]

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L. Wu, S. He, and L. F. Shen, “Band structure for a one-dimensional photonic crystal containing left-handed materials,” Phys. Rev. B67, 235103 (2003).
[CrossRef]

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D. E. Fernandes, S. I. Maslovski, and M. G. Silveirinha, “Cherenkov emission in a nanowire material,” Phys. Rev. B85, 155107 (2012).
[CrossRef]

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

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S. Kocaman, M. S. Aras, P. Hsieh, J. F. McMillan, C. G. Biris, N. C. Panoiu, M. B. Yu, D. L. Kwong, A. Stein, and C. W. Wong, “Zero phase delay in negative-refractive-index photonic crystal superlattices,” Nat. Photonics5, 499–505 (2011).
[CrossRef]

Sukhorukov, A.

I. Shadrivov, A. Sukhorukov, and Y. Kivshar, “Complete Band Gaps in One-Dimensional Left-Handed Periodic Structures,” Phys. Rev. Lett.95, 193903 (2005).
[CrossRef] [PubMed]

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S. Nefedov and S. A. Tretyakov, “Photonic band gap structure containing metamaterial with negative permittivity and permeability,” Phys. Rev. E66, 036611 (2002).
[CrossRef]

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V. V. Vorobev and A. V. Tyukhtin, “Nondivergent Cherenkov Radiation in a Wire Metamaterial,” Phys. Rev. Lett.108, 184801 (2012).
[CrossRef] [PubMed]

S. N. Galyamin and A. V. Tyukhtin, “Electromagnetic field of a moving charge in the presence of a left-handed medium,” Phys. Rev. B81, 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]

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[CrossRef]

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V. V. Vorobev and A. V. Tyukhtin, “Nondivergent Cherenkov Radiation in a Wire Metamaterial,” Phys. Rev. Lett.108, 184801 (2012).
[CrossRef] [PubMed]

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[CrossRef]

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J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light, 2nd ed. (Princeton University Press, 2008).

Wong, C. W.

S. Kocaman, M. S. Aras, P. Hsieh, J. F. McMillan, C. G. Biris, N. C. Panoiu, M. B. Yu, D. L. Kwong, A. Stein, and C. W. Wong, “Zero phase delay in negative-refractive-index photonic crystal superlattices,” Nat. Photonics5, 499–505 (2011).
[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, 194801 (2009).
[CrossRef]

Wu, B.-I.

Wu, L.

L. Wu, S. He, and L. F. Shen, “Band structure for a one-dimensional photonic crystal containing left-handed materials,” Phys. Rev. B67, 235103 (2003).
[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, 194801 (2009).
[CrossRef]

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Yeh, C.

K. F. Casey and C. Yeh, “Transition Radiation in a Periodically Stratified Plasma,” Phys. Rev. A2, 810–818 (1970).
[CrossRef]

Yu, M. B.

S. Kocaman, M. S. Aras, P. Hsieh, J. F. McMillan, C. G. Biris, N. C. Panoiu, M. B. Yu, D. L. Kwong, A. Stein, and C. W. Wong, “Zero phase delay in negative-refractive-index photonic crystal superlattices,” Nat. Photonics5, 499–505 (2011).
[CrossRef]

Zhang, Y.

Comput. Phys. Commun.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun.181(3), 687–702 (2010).
[CrossRef]

J. Opt. A

C. Kremers and D. N. Chigrin, “Spatial distribution of Cherenkov radiation in periodic dielectric media,” J. Opt. A11, 114008 (2009).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

JJ. Phys.: Conf. Ser.

L.Sh. Khachatryan, S.R. Arzumanyan, and W. Wagner, “Self-amplified Cherenkov radiation from a relativistic electron in a waveguide partially filled with a laminated material,” JJ. Phys.: Conf. Ser.357, 012004 (2012).
[CrossRef]

Nat. Photonics

S. Kocaman, M. S. Aras, P. Hsieh, J. F. McMillan, C. G. Biris, N. C. Panoiu, M. B. Yu, D. L. Kwong, A. Stein, and C. W. Wong, “Zero phase delay in negative-refractive-index photonic crystal superlattices,” Nat. Photonics5, 499–505 (2011).
[CrossRef]

Opt. Express

Phys. Rev.

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

Phys. Rev. A

K. F. Casey and C. Yeh, “Transition Radiation in a Periodically Stratified Plasma,” Phys. Rev. A2, 810–818 (1970).
[CrossRef]

C. Kremers, D. N. Chigrin, and J. Kroha, “Theory of Cherenkov radiation in periodic dielectric media: Emission spectrum,” Phys. Rev. A79, 013829 (2009).
[CrossRef]

Phys. Rev. B

L. Wu, S. He, and L. F. Shen, “Band structure for a one-dimensional photonic crystal containing left-handed materials,” Phys. Rev. B67, 235103 (2003).
[CrossRef]

S. N. Galyamin and A. V. Tyukhtin, “Electromagnetic field of a moving charge in the presence of a left-handed medium,” Phys. Rev. B81, 235134 (2010).
[CrossRef]

D. E. Fernandes, S. I. Maslovski, and M. G. Silveirinha, “Cherenkov emission in a nanowire material,” Phys. Rev. B85, 155107 (2012).
[CrossRef]

Phys. Rev. E

S. Nefedov and S. A. Tretyakov, “Photonic band gap structure containing metamaterial with negative permittivity and permeability,” Phys. Rev. E66, 036611 (2002).
[CrossRef]

Phys. Rev. Lett.

I. Shadrivov, A. Sukhorukov, and Y. Kivshar, “Complete Band Gaps in One-Dimensional Left-Handed Periodic Structures,” Phys. Rev. Lett.95, 193903 (2005).
[CrossRef] [PubMed]

F. J. García de Abajo and M. Kociak, “Probing the photonic local density of states with electron energy loss spectroscopy,” Phys. Rev. Lett.100(10), 106804 (2008).
[CrossRef] [PubMed]

V. V. Vorobev and A. V. Tyukhtin, “Nondivergent Cherenkov Radiation in a Wire Metamaterial,” Phys. Rev. Lett.108, 184801 (2012).
[CrossRef] [PubMed]

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, 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, 194802 (2009).
[CrossRef]

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F. J. García de Abajo, “Optical excitations in electron microscopy,” Rev. Mod. Phys.82, 209–275 (2010).
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[CrossRef]

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L. Schächter, Beam-Wave Interaction in Periodic and Quasi-Periodic Structures (Springer, 1997).

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[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

Schematic drawing of the structure, extending infinitely in the x and y directions, with periodicity in the z direction. Two unit cells of the structure are shown. The thick blue arrow denotes the propagation direction of the line charge. x = 0 is defined as the x position of the line source.

Fig. 2
Fig. 2

Radiated power P(ω) from one unit cell, normalized by ρ2/(0) as a function of ε2 calculated for ε1 = 1, μ1 = 1, μ2 = 2, v = 0.85c, L = 0.4536λ = 2L1 = 2L2. The blue line and the red circles correspond to FMM and FDTD results respectively.

Fig. 3
Fig. 3

(a) Re(Sx) normalized by of ρ2/(0) (b,c) Field distribution of Re(Hy) and Im(Hy) (corresponding to an exp(jωt) time dependence) normalized by ρ. (d) Magnitude of the Fourier orders of Hy.

Fig. 4
Fig. 4

(a,b) Field distribution of Re(Hy) and Im(Hy) (corresponding to an exp(jωt) time dependence), normalized by ρ. (c,d) Field distribution of Re(Ez) and Im(Ez) normalized by ρ/(0).

Fig. 5
Fig. 5

(a) Work done by the line charge normalized by ρ2/(0) as a function of λ/L and v/c. (b) Work done by the line charge normalized by ρ2/(0) as a function of (λ/L)*(v/c) and λ/L. (c) Same as (b) but with saturated color scale for visualization purposes.

Equations (12)

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J z ( x , z , t ) = ρ v δ ( x ) δ ( z v t )
F ( x , z ) = m = n = 1 W m n C n exp ( j k x , n x ) exp ( j k z , m z )
J ˜ z ( x , z , ω ) = ρ δ ( x ) exp ( j ω v z )
J ˜ z ( x , z , ω ) = ρ δ ( x ) exp ( j k z , c z )
2 H y | σ = ρ exp ( j k z , c z )
n = 1 2 N + 1 C n W m n exp ( j k z , m z ) exp ( j k x , n σ ) = 1 2 ρ exp ( j k z , c z )
C _ = 1 2 ρ W = 1 δ m , 0 _
P ( ω ) = 1 2 Re ( σ , L J ˜ z E z * d x d z )
E z _ = E = 1 W = K x = X = C _ = V = X = C _
P ( ω ) = 1 2 Re σ , L ρ δ ( x ) exp ( j k z , c z ) ( m = n = 1 V m n C n exp ( j k z , m z ) ) * d x d z
P ( ω ) = 1 2 ρ L Re ( V _ m = 0 , n C _ )
S z , tot = Re ( E x H y * ) = Re ( ( V = C _ ) ( W = C _ ) T ) = 1 2 ρ Re ( ( V = C _ ) ( W = W = 1 δ m , 0 _ ) T ) = 1 2 ρ Re ( ( V _ m = 0 , n C _ ) )

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