Surface-coupling of Cerenkov radiation from a modified metallic metamaterial slab via Brillouin-band folding

Anirban Bera; Ranjan Kumar Barik; Matlabjon Sattorov; Ohjoon Kwon; Sun-Hong Min; In-Keun Baek; Seontae Kim; Jin-Kyu So; Gun-Sik Park

doi:10.1364/OE.22.003039

Surface-coupling of Cerenkov radiation from a modified metallic metamaterial slab via Brillouin-band folding

Anirban Bera, Ranjan Kumar Barik, Matlabjon Sattorov, Ohjoon Kwon, Sun-Hong Min, In-Keun Baek, Seontae Kim, Jin-Kyu So, and Gun-Sik Park

Optics Express
Vol. 22,
Issue 3,
pp. 3039-3044
(2014)
•https://doi.org/10.1364/OE.22.003039

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Anirban Bera, Ranjan Kumar Barik, Matlabjon Sattorov, Ohjoon Kwon, Sun-Hong Min, In-Keun Baek, Seontae Kim, Jin-Kyu So, and Gun-Sik Park, "Surface-coupling of Cerenkov radiation from a modified metallic metamaterial slab via Brillouin-band folding," Opt. Express 22, 3039-3044 (2014)

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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.

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Publication

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, “Metamaterials and negative refractive index,” Science 305(5685), 788–792 (2004).
[Crossref] [PubMed]
V. M. Shalaev, “Optical negative-index metamaterials,” Nat. Photonics 1(1), 41–48 (2007).
[Crossref]
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]
Y. Liu and X. Zhang, “Metamaterials: a new frontier of science and technology,” Chem. Soc. Rev. 40(5), 2494–2507 (2011).
[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]
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. 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]
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]
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]
C. S. T. Studio Suite, 2008, http://www.cst.com
S. J. Smith and E. M. Purcell, “Visible light from localized surface charges moving across a grating,” Phys. Rev. 92(4), 1069 (1953).
[Crossref]
T. B. Boykin and G. Klimeck, “Practical application of zone-folding concepts in tight-binding calculations,” Phys. Rev. B 71(11), 115215 (2005).
[Crossref]
S. Nakashima and H. Harima, “Raman investigation of SiC polytypes,” Phys. Status Solidi 162(1), 39–64 (1997).
[Crossref]
C. Palmer, Diffraction Grating Handbook, 6th ed. (Newport Corporation, 2005), Chap. 12.
O. A. Tret’yakov, “Theory of Smith-Purcell effect,” Sov. Radio Phys. 2, 219–223 (1966).
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]

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

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]

2004 (2)

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).

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

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.

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.

Bak, S. H.

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.

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.

Dolling, G.

Enkrich, C.

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.

Garcia-Vidal, F. J.

Harima, H.

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

Hemsing, E.

Jang, K. H.

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.

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.

Kusche, K.

Linden, S.

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.

Muggli, P.

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

Niknejadi, P.

Park, G.-S.

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.

Sattorov, M. A.

Schmidt, F.

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.

Soukoulis, C. M.

Summers, C. J.

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.

Tochitsky, S. Y.

Travish, G.

Tret’yakov, O. A.

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

Wegener, M.

Wei, X.

Williams, O.

Williams, O. B.

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.

Yakimenko, V.

Yamashita, T.

Zhang, X.

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

Zhou, J. F.

Zschiedrich, L.

Appl. Phys. Lett. (4)

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).
[Crossref]

Nat. Photonics (1)

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

Opt. Express (1)

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

Opt. Lett. (1)

Phys. Rev. (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]

Phys. Rev. B (1)

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

Phys. Rev. Lett. (4)

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]

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).

Phys. Status Solidi (1)

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

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)

C. S. T. Studio Suite, 2008, http://www.cst.com

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

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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

(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 E_x field of structure-I. (c) E_x 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

(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 E_x field of structure-II. (c) E_x 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

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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