Abstract

Metallic metamaterials with positive dielectric responses are promising as an alternative to dielectrics for the generation of Cerenkov radiation [J.-K. So et al., Appl. Phys. Lett. 97(15), 151107 (2010)]. We propose here by theoretical analysis a mechanism to couple out Cerenkov radiation from the slab surfaces in the transverse direction. The proposed method based on Brillouin-zone folding is to periodically modify the thickness of the metamaterial slab in the axial direction. Moreover, the intensity of the surface-coupled radiation by this mechanism shows an order-of-magnitude enhancement compared to that of ordinary Smith-Purcell radiation.

©2014 Optical Society of America

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  1. D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, “Metamaterials and negative refractive index,” Science 305(5685), 788–792 (2004).
    [Crossref] [PubMed]
  2. V. M. Shalaev, “Optical negative-index metamaterials,” Nat. Photonics 1(1), 41–48 (2007).
    [Crossref]
  3. C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, Th. Koschny, and C. M. Soukoulis, “Magnetic Metamaterials at telecommunication and visible frequencies,” Phys. Rev. Lett. 95(20), 203901 (2005).
    [Crossref] [PubMed]
  4. G. Dolling, C. Enkrich, M. Wegener, J. F. Zhou, C. M. Soukoulis, and S. Linden, “Cut-wire pairs and plate pairs as magnetic atoms for optical metamaterials,” Opt. Lett. 30(23), 3198–3200 (2005).
    [Crossref] [PubMed]
  5. Y. Liu and X. Zhang, “Metamaterials: a new frontier of science and technology,” Chem. Soc. Rev. 40(5), 2494–2507 (2011).
    [Crossref] [PubMed]
  6. J. Shin, J. T. Shen, P. B. Catrysse, and S. Fan, “Cut-through metal slit array as an anisotropic metamaterial film,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1116–1122 (2006).
    [Crossref]
  7. J. T. Shen, P. B. Catrysse, and S. Fan, “Mechanism for designing metallic metamaterials with a high index of refraction,” Phys. Rev. Lett. 94(19), 197401 (2005).
    [Crossref] [PubMed]
  8. J. Shin, J. T. Shen, and S. Fan, “Three-dimensional metamaterials with an ultrahigh effective refractive index over a broad bandwidth,” Phys. Rev. Lett. 102(9), 093903 (2009).
    [Crossref] [PubMed]
  9. J. K. So, J. H. Won, M. A. Sattorov, S. H. Bak, K. H. Jang, G.-S. Park, D. S. Kim, and F. J. Garcia-Vidal, “Cerenkov radiation in metallic metamaterials,” Appl. Phys. Lett. 97(15), 151107 (2010).
    [Crossref]
  10. J. K. So, K. H. Jang, G.-S. Park, and F. J. Garcia-Vidal, “Bulk and surface electromagnetic response of metallic metamaterials to convection electrons,” Appl. Phys. Lett. 99(7), 071106 (2011).
    [Crossref]
  11. G. Andonian, O. Williams, X. Wei, P. Niknejadi, E. Hemsing, J. B. Rosenzweig, P. Muggli, M. Babzien, M. Fedurin, K. Kusche, R. Malone, and V. Yakimenko, “Resonant excitation of coherent Cerenkov radiation in dielectric lined waveguides,” Appl. Phys. Lett. 98(20), 202901 (2011).
    [Crossref]
  12. A. M. Cook, R. Tikhoplav, S. Y. Tochitsky, G. Travish, O. B. Williams, and J. B. Rosenzweig, “Observation of narrow-band terahertz coherent Cherenkov radiation from a cylindrical dielectric-lined waveguide,” Phys. Rev. Lett. 103(9), 095003 (2009).
    [Crossref] [PubMed]
  13. C. W. Neff, T. Yamashita, and C. J. Summers, “Observation of brillouin zone folding in photonic crystal slab waveguides possessing a superlattice pattern,” Appl. Phys. Lett. 90(2), 021102 (2007).
    [Crossref]
  14. C. W. Neff and C. J. Summers, “A photonic crystal superlattice based on triangular lattice,” Opt. Express 13(8), 3166–3173 (2005).
    [Crossref] [PubMed]
  15. C. S. T. Studio Suite, 2008, http://www.cst.com
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    [Crossref]
  17. T. B. Boykin and G. Klimeck, “Practical application of zone-folding concepts in tight-binding calculations,” Phys. Rev. B 71(11), 115215 (2005).
    [Crossref]
  18. S. Nakashima and H. Harima, “Raman investigation of SiC polytypes,” Phys. Status Solidi 162(1), 39–64 (1997).
    [Crossref]
  19. C. Palmer, Diffraction Grating Handbook, 6th ed. (Newport Corporation, 2005), Chap. 12.
  20. O. A. Tret’yakov, “Theory of Smith-Purcell effect,” Sov. Radio Phys. 2, 219–223 (1966).
  21. H. L. Andrews, C. H. Boulware, C. A. Brau, and J. D. Jarvis, “Gain of a Smith-Purcell free-electron laser,” Phys. Rev. ST Accel. Beams 7(7), 070701 (2004).

2011 (3)

Y. Liu and X. Zhang, “Metamaterials: a new frontier of science and technology,” Chem. Soc. Rev. 40(5), 2494–2507 (2011).
[Crossref] [PubMed]

J. K. So, K. H. Jang, G.-S. Park, and F. J. Garcia-Vidal, “Bulk and surface electromagnetic response of metallic metamaterials to convection electrons,” Appl. Phys. Lett. 99(7), 071106 (2011).
[Crossref]

G. Andonian, O. Williams, X. Wei, P. Niknejadi, E. Hemsing, J. B. Rosenzweig, P. Muggli, M. Babzien, M. Fedurin, K. Kusche, R. Malone, and V. Yakimenko, “Resonant excitation of coherent Cerenkov radiation in dielectric lined waveguides,” Appl. Phys. Lett. 98(20), 202901 (2011).
[Crossref]

2010 (1)

J. K. So, J. H. Won, M. A. Sattorov, S. H. Bak, K. H. Jang, G.-S. Park, D. S. Kim, and F. J. Garcia-Vidal, “Cerenkov radiation in metallic metamaterials,” Appl. Phys. Lett. 97(15), 151107 (2010).
[Crossref]

2009 (2)

J. Shin, J. T. Shen, and S. Fan, “Three-dimensional metamaterials with an ultrahigh effective refractive index over a broad bandwidth,” Phys. Rev. Lett. 102(9), 093903 (2009).
[Crossref] [PubMed]

A. M. Cook, R. Tikhoplav, S. Y. Tochitsky, G. Travish, O. B. Williams, and J. B. Rosenzweig, “Observation of narrow-band terahertz coherent Cherenkov radiation from a cylindrical dielectric-lined waveguide,” Phys. Rev. Lett. 103(9), 095003 (2009).
[Crossref] [PubMed]

2007 (2)

C. W. Neff, T. Yamashita, and C. J. Summers, “Observation of brillouin zone folding in photonic crystal slab waveguides possessing a superlattice pattern,” Appl. Phys. Lett. 90(2), 021102 (2007).
[Crossref]

V. M. Shalaev, “Optical negative-index metamaterials,” Nat. Photonics 1(1), 41–48 (2007).
[Crossref]

2006 (1)

J. Shin, J. T. Shen, P. B. Catrysse, and S. Fan, “Cut-through metal slit array as an anisotropic metamaterial film,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1116–1122 (2006).
[Crossref]

2005 (5)

J. T. Shen, P. B. Catrysse, and S. Fan, “Mechanism for designing metallic metamaterials with a high index of refraction,” Phys. Rev. Lett. 94(19), 197401 (2005).
[Crossref] [PubMed]

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, Th. Koschny, and C. M. Soukoulis, “Magnetic Metamaterials at telecommunication and visible frequencies,” Phys. Rev. Lett. 95(20), 203901 (2005).
[Crossref] [PubMed]

G. Dolling, C. Enkrich, M. Wegener, J. F. Zhou, C. M. Soukoulis, and S. Linden, “Cut-wire pairs and plate pairs as magnetic atoms for optical metamaterials,” Opt. Lett. 30(23), 3198–3200 (2005).
[Crossref] [PubMed]

C. W. Neff and C. J. Summers, “A photonic crystal superlattice based on triangular lattice,” Opt. Express 13(8), 3166–3173 (2005).
[Crossref] [PubMed]

T. B. Boykin and G. Klimeck, “Practical application of zone-folding concepts in tight-binding calculations,” Phys. Rev. B 71(11), 115215 (2005).
[Crossref]

2004 (2)

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, “Metamaterials and negative refractive index,” Science 305(5685), 788–792 (2004).
[Crossref] [PubMed]

H. L. Andrews, C. H. Boulware, C. A. Brau, and J. D. Jarvis, “Gain of a Smith-Purcell free-electron laser,” Phys. Rev. ST Accel. Beams 7(7), 070701 (2004).

1997 (1)

S. Nakashima and H. Harima, “Raman investigation of SiC polytypes,” Phys. Status Solidi 162(1), 39–64 (1997).
[Crossref]

1966 (1)

O. A. Tret’yakov, “Theory of Smith-Purcell effect,” Sov. Radio Phys. 2, 219–223 (1966).

1953 (1)

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

Andonian, G.

G. Andonian, O. Williams, X. Wei, P. Niknejadi, E. Hemsing, J. B. Rosenzweig, P. Muggli, M. Babzien, M. Fedurin, K. Kusche, R. Malone, and V. Yakimenko, “Resonant excitation of coherent Cerenkov radiation in dielectric lined waveguides,” Appl. Phys. Lett. 98(20), 202901 (2011).
[Crossref]

Andrews, H. L.

H. L. Andrews, C. H. Boulware, C. A. Brau, and J. D. Jarvis, “Gain of a Smith-Purcell free-electron laser,” Phys. Rev. ST Accel. Beams 7(7), 070701 (2004).

Babzien, M.

G. Andonian, O. Williams, X. Wei, P. Niknejadi, E. Hemsing, J. B. Rosenzweig, P. Muggli, M. Babzien, M. Fedurin, K. Kusche, R. Malone, and V. Yakimenko, “Resonant excitation of coherent Cerenkov radiation in dielectric lined waveguides,” Appl. Phys. Lett. 98(20), 202901 (2011).
[Crossref]

Bak, S. H.

J. K. So, J. H. Won, M. A. Sattorov, S. H. Bak, K. H. Jang, G.-S. Park, D. S. Kim, and F. J. Garcia-Vidal, “Cerenkov radiation in metallic metamaterials,” Appl. Phys. Lett. 97(15), 151107 (2010).
[Crossref]

Boulware, C. H.

H. L. Andrews, C. H. Boulware, C. A. Brau, and J. D. Jarvis, “Gain of a Smith-Purcell free-electron laser,” Phys. Rev. ST Accel. Beams 7(7), 070701 (2004).

Boykin, T. B.

T. B. Boykin and G. Klimeck, “Practical application of zone-folding concepts in tight-binding calculations,” Phys. Rev. B 71(11), 115215 (2005).
[Crossref]

Brau, C. A.

H. L. Andrews, C. H. Boulware, C. A. Brau, and J. D. Jarvis, “Gain of a Smith-Purcell free-electron laser,” Phys. Rev. ST Accel. Beams 7(7), 070701 (2004).

Burger, S.

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, Th. Koschny, and C. M. Soukoulis, “Magnetic Metamaterials at telecommunication and visible frequencies,” Phys. Rev. Lett. 95(20), 203901 (2005).
[Crossref] [PubMed]

Catrysse, P. B.

J. Shin, J. T. Shen, P. B. Catrysse, and S. Fan, “Cut-through metal slit array as an anisotropic metamaterial film,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1116–1122 (2006).
[Crossref]

J. T. Shen, P. B. Catrysse, and S. Fan, “Mechanism for designing metallic metamaterials with a high index of refraction,” Phys. Rev. Lett. 94(19), 197401 (2005).
[Crossref] [PubMed]

Cook, A. M.

A. M. Cook, R. Tikhoplav, S. Y. Tochitsky, G. Travish, O. B. Williams, and J. B. Rosenzweig, “Observation of narrow-band terahertz coherent Cherenkov radiation from a cylindrical dielectric-lined waveguide,” Phys. Rev. Lett. 103(9), 095003 (2009).
[Crossref] [PubMed]

Dolling, G.

Enkrich, C.

G. Dolling, C. Enkrich, M. Wegener, J. F. Zhou, C. M. Soukoulis, and S. Linden, “Cut-wire pairs and plate pairs as magnetic atoms for optical metamaterials,” Opt. Lett. 30(23), 3198–3200 (2005).
[Crossref] [PubMed]

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, Th. Koschny, and C. M. Soukoulis, “Magnetic Metamaterials at telecommunication and visible frequencies,” Phys. Rev. Lett. 95(20), 203901 (2005).
[Crossref] [PubMed]

Fan, S.

J. Shin, J. T. Shen, and S. Fan, “Three-dimensional metamaterials with an ultrahigh effective refractive index over a broad bandwidth,” Phys. Rev. Lett. 102(9), 093903 (2009).
[Crossref] [PubMed]

J. Shin, J. T. Shen, P. B. Catrysse, and S. Fan, “Cut-through metal slit array as an anisotropic metamaterial film,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1116–1122 (2006).
[Crossref]

J. T. Shen, P. B. Catrysse, and S. Fan, “Mechanism for designing metallic metamaterials with a high index of refraction,” Phys. Rev. Lett. 94(19), 197401 (2005).
[Crossref] [PubMed]

Fedurin, M.

G. Andonian, O. Williams, X. Wei, P. Niknejadi, E. Hemsing, J. B. Rosenzweig, P. Muggli, M. Babzien, M. Fedurin, K. Kusche, R. Malone, and V. Yakimenko, “Resonant excitation of coherent Cerenkov radiation in dielectric lined waveguides,” Appl. Phys. Lett. 98(20), 202901 (2011).
[Crossref]

Garcia-Vidal, F. J.

J. K. So, K. H. Jang, G.-S. Park, and F. J. Garcia-Vidal, “Bulk and surface electromagnetic response of metallic metamaterials to convection electrons,” Appl. Phys. Lett. 99(7), 071106 (2011).
[Crossref]

J. K. So, J. H. Won, M. A. Sattorov, S. H. Bak, K. H. Jang, G.-S. Park, D. S. Kim, and F. J. Garcia-Vidal, “Cerenkov radiation in metallic metamaterials,” Appl. Phys. Lett. 97(15), 151107 (2010).
[Crossref]

Harima, H.

S. Nakashima and H. Harima, “Raman investigation of SiC polytypes,” Phys. Status Solidi 162(1), 39–64 (1997).
[Crossref]

Hemsing, E.

G. Andonian, O. Williams, X. Wei, P. Niknejadi, E. Hemsing, J. B. Rosenzweig, P. Muggli, M. Babzien, M. Fedurin, K. Kusche, R. Malone, and V. Yakimenko, “Resonant excitation of coherent Cerenkov radiation in dielectric lined waveguides,” Appl. Phys. Lett. 98(20), 202901 (2011).
[Crossref]

Jang, K. H.

J. K. So, K. H. Jang, G.-S. Park, and F. J. Garcia-Vidal, “Bulk and surface electromagnetic response of metallic metamaterials to convection electrons,” Appl. Phys. Lett. 99(7), 071106 (2011).
[Crossref]

J. K. So, J. H. Won, M. A. Sattorov, S. H. Bak, K. H. Jang, G.-S. Park, D. S. Kim, and F. J. Garcia-Vidal, “Cerenkov radiation in metallic metamaterials,” Appl. Phys. Lett. 97(15), 151107 (2010).
[Crossref]

Jarvis, J. D.

H. L. Andrews, C. H. Boulware, C. A. Brau, and J. D. Jarvis, “Gain of a Smith-Purcell free-electron laser,” Phys. Rev. ST Accel. Beams 7(7), 070701 (2004).

Kim, D. S.

J. K. So, J. H. Won, M. A. Sattorov, S. H. Bak, K. H. Jang, G.-S. Park, D. S. Kim, and F. J. Garcia-Vidal, “Cerenkov radiation in metallic metamaterials,” Appl. Phys. Lett. 97(15), 151107 (2010).
[Crossref]

Klimeck, G.

T. B. Boykin and G. Klimeck, “Practical application of zone-folding concepts in tight-binding calculations,” Phys. Rev. B 71(11), 115215 (2005).
[Crossref]

Koschny, Th.

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, Th. Koschny, and C. M. Soukoulis, “Magnetic Metamaterials at telecommunication and visible frequencies,” Phys. Rev. Lett. 95(20), 203901 (2005).
[Crossref] [PubMed]

Kusche, K.

G. Andonian, O. Williams, X. Wei, P. Niknejadi, E. Hemsing, J. B. Rosenzweig, P. Muggli, M. Babzien, M. Fedurin, K. Kusche, R. Malone, and V. Yakimenko, “Resonant excitation of coherent Cerenkov radiation in dielectric lined waveguides,” Appl. Phys. Lett. 98(20), 202901 (2011).
[Crossref]

Linden, S.

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, Th. Koschny, and C. M. Soukoulis, “Magnetic Metamaterials at telecommunication and visible frequencies,” Phys. Rev. Lett. 95(20), 203901 (2005).
[Crossref] [PubMed]

G. Dolling, C. Enkrich, M. Wegener, J. F. Zhou, C. M. Soukoulis, and S. Linden, “Cut-wire pairs and plate pairs as magnetic atoms for optical metamaterials,” Opt. Lett. 30(23), 3198–3200 (2005).
[Crossref] [PubMed]

Liu, Y.

Y. Liu and X. Zhang, “Metamaterials: a new frontier of science and technology,” Chem. Soc. Rev. 40(5), 2494–2507 (2011).
[Crossref] [PubMed]

Malone, R.

G. Andonian, O. Williams, X. Wei, P. Niknejadi, E. Hemsing, J. B. Rosenzweig, P. Muggli, M. Babzien, M. Fedurin, K. Kusche, R. Malone, and V. Yakimenko, “Resonant excitation of coherent Cerenkov radiation in dielectric lined waveguides,” Appl. Phys. Lett. 98(20), 202901 (2011).
[Crossref]

Muggli, P.

G. Andonian, O. Williams, X. Wei, P. Niknejadi, E. Hemsing, J. B. Rosenzweig, P. Muggli, M. Babzien, M. Fedurin, K. Kusche, R. Malone, and V. Yakimenko, “Resonant excitation of coherent Cerenkov radiation in dielectric lined waveguides,” Appl. Phys. Lett. 98(20), 202901 (2011).
[Crossref]

Nakashima, S.

S. Nakashima and H. Harima, “Raman investigation of SiC polytypes,” Phys. Status Solidi 162(1), 39–64 (1997).
[Crossref]

Neff, C. W.

C. W. Neff, T. Yamashita, and C. J. Summers, “Observation of brillouin zone folding in photonic crystal slab waveguides possessing a superlattice pattern,” Appl. Phys. Lett. 90(2), 021102 (2007).
[Crossref]

C. W. Neff and C. J. Summers, “A photonic crystal superlattice based on triangular lattice,” Opt. Express 13(8), 3166–3173 (2005).
[Crossref] [PubMed]

Niknejadi, P.

G. Andonian, O. Williams, X. Wei, P. Niknejadi, E. Hemsing, J. B. Rosenzweig, P. Muggli, M. Babzien, M. Fedurin, K. Kusche, R. Malone, and V. Yakimenko, “Resonant excitation of coherent Cerenkov radiation in dielectric lined waveguides,” Appl. Phys. Lett. 98(20), 202901 (2011).
[Crossref]

Park, G.-S.

J. K. So, K. H. Jang, G.-S. Park, and F. J. Garcia-Vidal, “Bulk and surface electromagnetic response of metallic metamaterials to convection electrons,” Appl. Phys. Lett. 99(7), 071106 (2011).
[Crossref]

J. K. So, J. H. Won, M. A. Sattorov, S. H. Bak, K. H. Jang, G.-S. Park, D. S. Kim, and F. J. Garcia-Vidal, “Cerenkov radiation in metallic metamaterials,” Appl. Phys. Lett. 97(15), 151107 (2010).
[Crossref]

Pendry, J. B.

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, “Metamaterials and negative refractive index,” Science 305(5685), 788–792 (2004).
[Crossref] [PubMed]

Purcell, E. M.

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

Rosenzweig, J. B.

G. Andonian, O. Williams, X. Wei, P. Niknejadi, E. Hemsing, J. B. Rosenzweig, P. Muggli, M. Babzien, M. Fedurin, K. Kusche, R. Malone, and V. Yakimenko, “Resonant excitation of coherent Cerenkov radiation in dielectric lined waveguides,” Appl. Phys. Lett. 98(20), 202901 (2011).
[Crossref]

A. M. Cook, R. Tikhoplav, S. Y. Tochitsky, G. Travish, O. B. Williams, and J. B. Rosenzweig, “Observation of narrow-band terahertz coherent Cherenkov radiation from a cylindrical dielectric-lined waveguide,” Phys. Rev. Lett. 103(9), 095003 (2009).
[Crossref] [PubMed]

Sattorov, M. A.

J. K. So, J. H. Won, M. A. Sattorov, S. H. Bak, K. H. Jang, G.-S. Park, D. S. Kim, and F. J. Garcia-Vidal, “Cerenkov radiation in metallic metamaterials,” Appl. Phys. Lett. 97(15), 151107 (2010).
[Crossref]

Schmidt, F.

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, Th. Koschny, and C. M. Soukoulis, “Magnetic Metamaterials at telecommunication and visible frequencies,” Phys. Rev. Lett. 95(20), 203901 (2005).
[Crossref] [PubMed]

Shalaev, V. M.

V. M. Shalaev, “Optical negative-index metamaterials,” Nat. Photonics 1(1), 41–48 (2007).
[Crossref]

Shen, J. T.

J. Shin, J. T. Shen, and S. Fan, “Three-dimensional metamaterials with an ultrahigh effective refractive index over a broad bandwidth,” Phys. Rev. Lett. 102(9), 093903 (2009).
[Crossref] [PubMed]

J. Shin, J. T. Shen, P. B. Catrysse, and S. Fan, “Cut-through metal slit array as an anisotropic metamaterial film,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1116–1122 (2006).
[Crossref]

J. T. Shen, P. B. Catrysse, and S. Fan, “Mechanism for designing metallic metamaterials with a high index of refraction,” Phys. Rev. Lett. 94(19), 197401 (2005).
[Crossref] [PubMed]

Shin, J.

J. Shin, J. T. Shen, and S. Fan, “Three-dimensional metamaterials with an ultrahigh effective refractive index over a broad bandwidth,” Phys. Rev. Lett. 102(9), 093903 (2009).
[Crossref] [PubMed]

J. Shin, J. T. Shen, P. B. Catrysse, and S. Fan, “Cut-through metal slit array as an anisotropic metamaterial film,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1116–1122 (2006).
[Crossref]

Smith, D. R.

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, “Metamaterials and negative refractive index,” Science 305(5685), 788–792 (2004).
[Crossref] [PubMed]

Smith, S. J.

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

So, J. K.

J. K. So, K. H. Jang, G.-S. Park, and F. J. Garcia-Vidal, “Bulk and surface electromagnetic response of metallic metamaterials to convection electrons,” Appl. Phys. Lett. 99(7), 071106 (2011).
[Crossref]

J. K. So, J. H. Won, M. A. Sattorov, S. H. Bak, K. H. Jang, G.-S. Park, D. S. Kim, and F. J. Garcia-Vidal, “Cerenkov radiation in metallic metamaterials,” Appl. Phys. Lett. 97(15), 151107 (2010).
[Crossref]

Soukoulis, C. M.

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, Th. Koschny, and C. M. Soukoulis, “Magnetic Metamaterials at telecommunication and visible frequencies,” Phys. Rev. Lett. 95(20), 203901 (2005).
[Crossref] [PubMed]

G. Dolling, C. Enkrich, M. Wegener, J. F. Zhou, C. M. Soukoulis, and S. Linden, “Cut-wire pairs and plate pairs as magnetic atoms for optical metamaterials,” Opt. Lett. 30(23), 3198–3200 (2005).
[Crossref] [PubMed]

Summers, C. J.

C. W. Neff, T. Yamashita, and C. J. Summers, “Observation of brillouin zone folding in photonic crystal slab waveguides possessing a superlattice pattern,” Appl. Phys. Lett. 90(2), 021102 (2007).
[Crossref]

C. W. Neff and C. J. Summers, “A photonic crystal superlattice based on triangular lattice,” Opt. Express 13(8), 3166–3173 (2005).
[Crossref] [PubMed]

Tikhoplav, R.

A. M. Cook, R. Tikhoplav, S. Y. Tochitsky, G. Travish, O. B. Williams, and J. B. Rosenzweig, “Observation of narrow-band terahertz coherent Cherenkov radiation from a cylindrical dielectric-lined waveguide,” Phys. Rev. Lett. 103(9), 095003 (2009).
[Crossref] [PubMed]

Tochitsky, S. Y.

A. M. Cook, R. Tikhoplav, S. Y. Tochitsky, G. Travish, O. B. Williams, and J. B. Rosenzweig, “Observation of narrow-band terahertz coherent Cherenkov radiation from a cylindrical dielectric-lined waveguide,” Phys. Rev. Lett. 103(9), 095003 (2009).
[Crossref] [PubMed]

Travish, G.

A. M. Cook, R. Tikhoplav, S. Y. Tochitsky, G. Travish, O. B. Williams, and J. B. Rosenzweig, “Observation of narrow-band terahertz coherent Cherenkov radiation from a cylindrical dielectric-lined waveguide,” Phys. Rev. Lett. 103(9), 095003 (2009).
[Crossref] [PubMed]

Tret’yakov, O. A.

O. A. Tret’yakov, “Theory of Smith-Purcell effect,” Sov. Radio Phys. 2, 219–223 (1966).

Wegener, M.

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, Th. Koschny, and C. M. Soukoulis, “Magnetic Metamaterials at telecommunication and visible frequencies,” Phys. Rev. Lett. 95(20), 203901 (2005).
[Crossref] [PubMed]

G. Dolling, C. Enkrich, M. Wegener, J. F. Zhou, C. M. Soukoulis, and S. Linden, “Cut-wire pairs and plate pairs as magnetic atoms for optical metamaterials,” Opt. Lett. 30(23), 3198–3200 (2005).
[Crossref] [PubMed]

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G. Andonian, O. Williams, X. Wei, P. Niknejadi, E. Hemsing, J. B. Rosenzweig, P. Muggli, M. Babzien, M. Fedurin, K. Kusche, R. Malone, and V. Yakimenko, “Resonant excitation of coherent Cerenkov radiation in dielectric lined waveguides,” Appl. Phys. Lett. 98(20), 202901 (2011).
[Crossref]

Williams, O.

G. Andonian, O. Williams, X. Wei, P. Niknejadi, E. Hemsing, J. B. Rosenzweig, P. Muggli, M. Babzien, M. Fedurin, K. Kusche, R. Malone, and V. Yakimenko, “Resonant excitation of coherent Cerenkov radiation in dielectric lined waveguides,” Appl. Phys. Lett. 98(20), 202901 (2011).
[Crossref]

Williams, O. B.

A. M. Cook, R. Tikhoplav, S. Y. Tochitsky, G. Travish, O. B. Williams, and J. B. Rosenzweig, “Observation of narrow-band terahertz coherent Cherenkov radiation from a cylindrical dielectric-lined waveguide,” Phys. Rev. Lett. 103(9), 095003 (2009).
[Crossref] [PubMed]

Wiltshire, M. C. K.

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, “Metamaterials and negative refractive index,” Science 305(5685), 788–792 (2004).
[Crossref] [PubMed]

Won, J. H.

J. K. So, J. H. Won, M. A. Sattorov, S. H. Bak, K. H. Jang, G.-S. Park, D. S. Kim, and F. J. Garcia-Vidal, “Cerenkov radiation in metallic metamaterials,” Appl. Phys. Lett. 97(15), 151107 (2010).
[Crossref]

Yakimenko, V.

G. Andonian, O. Williams, X. Wei, P. Niknejadi, E. Hemsing, J. B. Rosenzweig, P. Muggli, M. Babzien, M. Fedurin, K. Kusche, R. Malone, and V. Yakimenko, “Resonant excitation of coherent Cerenkov radiation in dielectric lined waveguides,” Appl. Phys. Lett. 98(20), 202901 (2011).
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Yamashita, T.

C. W. Neff, T. Yamashita, and C. J. Summers, “Observation of brillouin zone folding in photonic crystal slab waveguides possessing a superlattice pattern,” Appl. Phys. Lett. 90(2), 021102 (2007).
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Zhang, X.

Y. Liu and X. Zhang, “Metamaterials: a new frontier of science and technology,” Chem. Soc. Rev. 40(5), 2494–2507 (2011).
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C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, Th. Koschny, and C. M. Soukoulis, “Magnetic Metamaterials at telecommunication and visible frequencies,” Phys. Rev. Lett. 95(20), 203901 (2005).
[Crossref] [PubMed]

G. Dolling, C. Enkrich, M. Wegener, J. F. Zhou, C. M. Soukoulis, and S. Linden, “Cut-wire pairs and plate pairs as magnetic atoms for optical metamaterials,” Opt. Lett. 30(23), 3198–3200 (2005).
[Crossref] [PubMed]

Zschiedrich, L.

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, Th. Koschny, and C. M. Soukoulis, “Magnetic Metamaterials at telecommunication and visible frequencies,” Phys. Rev. Lett. 95(20), 203901 (2005).
[Crossref] [PubMed]

Appl. Phys. Lett. (4)

J. K. So, J. H. Won, M. A. Sattorov, S. H. Bak, K. H. Jang, G.-S. Park, D. S. Kim, and F. J. Garcia-Vidal, “Cerenkov radiation in metallic metamaterials,” Appl. Phys. Lett. 97(15), 151107 (2010).
[Crossref]

J. K. So, K. H. Jang, G.-S. Park, and F. J. Garcia-Vidal, “Bulk and surface electromagnetic response of metallic metamaterials to convection electrons,” Appl. Phys. Lett. 99(7), 071106 (2011).
[Crossref]

G. Andonian, O. Williams, X. Wei, P. Niknejadi, E. Hemsing, J. B. Rosenzweig, P. Muggli, M. Babzien, M. Fedurin, K. Kusche, R. Malone, and V. Yakimenko, “Resonant excitation of coherent Cerenkov radiation in dielectric lined waveguides,” Appl. Phys. Lett. 98(20), 202901 (2011).
[Crossref]

C. W. Neff, T. Yamashita, and C. J. Summers, “Observation of brillouin zone folding in photonic crystal slab waveguides possessing a superlattice pattern,” Appl. Phys. Lett. 90(2), 021102 (2007).
[Crossref]

Chem. Soc. Rev. (1)

Y. Liu and X. Zhang, “Metamaterials: a new frontier of science and technology,” Chem. Soc. Rev. 40(5), 2494–2507 (2011).
[Crossref] [PubMed]

IEEE J. Sel. Top. Quantum Electron. (1)

J. Shin, J. T. Shen, P. B. Catrysse, and S. Fan, “Cut-through metal slit array as an anisotropic metamaterial film,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1116–1122 (2006).
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V. M. Shalaev, “Optical negative-index metamaterials,” Nat. Photonics 1(1), 41–48 (2007).
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T. B. Boykin and G. Klimeck, “Practical application of zone-folding concepts in tight-binding calculations,” Phys. Rev. B 71(11), 115215 (2005).
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Phys. Rev. Lett. (4)

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, Th. Koschny, and C. M. Soukoulis, “Magnetic Metamaterials at telecommunication and visible frequencies,” Phys. Rev. Lett. 95(20), 203901 (2005).
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J. T. Shen, P. B. Catrysse, and S. Fan, “Mechanism for designing metallic metamaterials with a high index of refraction,” Phys. Rev. Lett. 94(19), 197401 (2005).
[Crossref] [PubMed]

J. Shin, J. T. Shen, and S. Fan, “Three-dimensional metamaterials with an ultrahigh effective refractive index over a broad bandwidth,” Phys. Rev. Lett. 102(9), 093903 (2009).
[Crossref] [PubMed]

A. M. Cook, R. Tikhoplav, S. Y. Tochitsky, G. Travish, O. B. Williams, and J. B. Rosenzweig, “Observation of narrow-band terahertz coherent Cherenkov radiation from a cylindrical dielectric-lined waveguide,” Phys. Rev. Lett. 103(9), 095003 (2009).
[Crossref] [PubMed]

Phys. Rev. ST Accel. Beams (1)

H. L. Andrews, C. H. Boulware, C. A. Brau, and J. D. Jarvis, “Gain of a Smith-Purcell free-electron laser,” Phys. Rev. ST Accel. Beams 7(7), 070701 (2004).

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S. Nakashima and H. Harima, “Raman investigation of SiC polytypes,” Phys. Status Solidi 162(1), 39–64 (1997).
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Science (1)

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, “Metamaterials and negative refractive index,” Science 305(5685), 788–792 (2004).
[Crossref] [PubMed]

Sov. Radio Phys. (1)

O. A. Tret’yakov, “Theory of Smith-Purcell effect,” Sov. Radio Phys. 2, 219–223 (1966).

Other (2)

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C. Palmer, Diffraction Grating Handbook, 6th ed. (Newport Corporation, 2005), Chap. 12.

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Figures (4)

Fig. 1
Fig. 1 (a) Metallic metamaterial structure consisting of a one-dimensional array of periodic cut-through silts perforated on a metallic slab (structure-I) in proximity to a moving electron bunch and, (b) the proposed metamaterial structure obtained by periodically modifying the thickness of structure-I so as to provide additional periodicity (structure-II).

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Fig. 2
Fig. 2 (a) Guided-mode dispersion characteristics of structure-I along with a typical beam-mode dispersion line β( = v/c) = 0.5, the shaded and non-shaded regions indicating the non-radiating and radiating regimes and (b) Inside-slit and far-field (magnified 25 times) FFT spectrum of the Ex field of structure-I. (c) Ex field pattern at the typical angular frequency ω ( = 2πc/p) of 0.12 for structure-I showing fields confined to the top and bottom surfaces.

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Fig. 3
Fig. 3 (a) Guided-mode dispersion characteristics of structure-II, along with a typical beam-mode dispersion line β( = v/c) = 0.5, the shaded and non-shaded regions indicating the non-radiating and radiating regimes, respectively. The first four lower dispersion intersecting points are represented by 1, 2, 3 and 4, respectively. The folded bands are shown in solid lines, with the vertical dotted line indicating band-folding symmetry and with the points indicated by the arrows on the folded dispersion curve representing the points at which the momentums corresponding to points 2, 3 and 4, respectively, are shifted due to band folding. (b) Inside-slit and far-field (magnified 25 times) FFT spectrum of the Ex field of structure-II. (c) Ex field pattern at the typical angular frequency (ω = 2πc/p) of 0.12 for structure-II showing fields radiated from the top and bottom surfaces.

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Fig. 4
Fig. 4 Angular dependence of the far-field radiation of structure-II compared to that of the reflection grating (magnified 5 times) at an angular frequency ω( = 2πc/p) of 0.12, the measurement angle being the angle between the direction of the moving electron bunch and that of the radiation, with the inset showing the variation of the radiation intensity of the reflection grating with the grating groove depth having a moving electron bunch energy level corresponding to β( = v/c) = 0.5.

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