Abstract

We have numerically analyzed, based on a simplified particle-in-cell finite-difference time-domain (PIC-FDTD) method, an electron-beam (e-beam) induced terahertz (THz) radiation from metallic grating structures with graded depths (graded grating). Upon exciting with e-beam, directional THz radiations with wide-band spectrum containing several sharp peaks are obtained only from the one of the edge of the grating, which cannot be expected from the conventional theory of Smith-Purcell radiation. It was clarified that each modes originate from different locations on the graded grating reflecting different dispersion characteristics of spoof surface plasmon polariton (spoof SPP) at each locations, and they can propagate toward only the shallower groove as a surface wave due to the cutoff at each locations, and all of these modes eventually emitted from the one of the edge of the graded grating. These directional radiations can be directed toward either backward or forward by making the groove depth deeper or shallower. The lowest and the highest frequency of the radiation can be chosen by appropriately designing the deepest and the shallowest groove depths, respectively. These unique radiations cannot be obtained from the uniformly grooved grating. Our findings may open the way for a development of novel THz radiation source based on the spoof SPP on the wide variety of metallic grating structures or metasurfaces.

© 2014 Optical Society of America

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  1. M. Tonouchi, “Cutting-edge terahertz technology,” Nat. Photon. 1(2), 97–105 (2007).
    [CrossRef]
  2. S. J. Smith and E. M. Purcell, “Visible light from localized surface charges moving across a grating,” Phys. Rev. 92(4), 1069 (1953).
    [CrossRef]
  3. J. Urata, M. Goldstein, M. F. Kimmitt, A. Naumov, C. Platt, and J. E. Walsh, “Superradiant Smith-Purcell Emission,” Phys. Rev. Lett. 80(3), 516–519 (1998).
    [CrossRef]
  4. H. L. Andrews and C. A. Brau, “Gain of a Smith-Purcell free-electron laser,” Phys. Rev. ST Accel. Beams 7, 070701 (2004).
  5. Y. Zhang, L. Dong, and Y. Zhou, “Enhanced coherent terahertz Smith-Purcell superradiation excited by two electron-beams,” Opt. Express 20(20), 22627–22635 (2012).
    [CrossRef] [PubMed]
  6. V. M. Shalaev, “Optical negative-index metamaterials,” Nat. Photon. 1(1), 41–48 (2007).
    [CrossRef]
  7. N. I. Zheludev and Y. S. Kivshar, “From metamaterials to metadevices,” Nat. Mater. 11(11), 917–924 (2012).
    [CrossRef] [PubMed]
  8. D. Li, M. Hangyo, Z. Yang, M. R. Asakawa, S. Miyamoto, Y. Tsunawaki, K. Takano, and K. Imasaki, “Smith-Purcell radiation from a grating of negative-index material,” Nucl. Instrum. Methods Phys. Res. A 637(1), 135–137 (2011).
    [CrossRef]
  9. J. B. Pendry, L. Martín-Moreno, and F. J. Garcia-Vidal, “Mimicking surface plasmons with structured surfaces,” Science 305(5685), 847–848 (2004).
    [CrossRef] [PubMed]
  10. F. J. Garcia-Vidal, L. Martin-Moreno, and J. B. Pendry, “Surfaces with holes in them: new plasmonic metamaterials,” Pure Appl. Opt. 7(2), S97–S101 (2005).
    [CrossRef]
  11. Q. Gan, Z. Fu, Y. J. Ding, and F. J. Bartoli, “Ultrawide-bandwidth slow-light system based on THz plasmonic graded metallic grating structures,” Phys. Rev. Lett. 100(25), 256803 (2008).
    [CrossRef] [PubMed]
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  14. D. Li, Z. Yang, K. Imasaki, and G. S. Park, “Particle-in-cell simulation of coherent and superradiant Smith-Purcell radiation,” Phys. Rev. ST Accel. Beams 9, 040701 (2006).
  15. S. Taga, K. Inafune, and E. Sano, “Analysis of Smith-Purcell radiation in optical region,” Opt. Express 15(24), 16222–16229 (2007).
    [CrossRef] [PubMed]
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    [CrossRef]
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2014

T. Iwata, A. Okajima, and T. Matsui, “GPGPU-based parallel computing of PIC-FDTD simulation for the development of novel terahertz radiation devices,” Proc. SPIE 8980, 89801V (2014).
[CrossRef]

2012

2011

D. Li, M. Hangyo, Z. Yang, M. R. Asakawa, S. Miyamoto, Y. Tsunawaki, K. Takano, and K. Imasaki, “Smith-Purcell radiation from a grating of negative-index material,” Nucl. Instrum. Methods Phys. Res. A 637(1), 135–137 (2011).
[CrossRef]

2008

Q. Gan, Z. Fu, Y. J. Ding, and F. J. Bartoli, “Ultrawide-bandwidth slow-light system based on THz plasmonic graded metallic grating structures,” Phys. Rev. Lett. 100(25), 256803 (2008).
[CrossRef] [PubMed]

2007

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

S. Taga, K. Inafune, and E. Sano, “Analysis of Smith-Purcell radiation in optical region,” Opt. Express 15(24), 16222–16229 (2007).
[CrossRef] [PubMed]

M. Tonouchi, “Cutting-edge terahertz technology,” Nat. Photon. 1(2), 97–105 (2007).
[CrossRef]

2006

J. T. Donohue and J. Gardelle, “Simulation of Smith-Purcell terahertz radiation using a particle-in-cell code,” Phys. Rev. ST Accel. Beams 9, 060701 (2006).

D. Li, Z. Yang, K. Imasaki, and G. S. Park, “Particle-in-cell simulation of coherent and superradiant Smith-Purcell radiation,” Phys. Rev. ST Accel. Beams 9, 040701 (2006).

2005

J. T. Donohue and J. Gardelle, “Simulation of Smith-Purcell radiation using a particle-in-cell code,” Phys. Rev. ST Accel. Beams 8, 060702 (2005).

F. J. Garcia-Vidal, L. Martin-Moreno, and J. B. Pendry, “Surfaces with holes in them: new plasmonic metamaterials,” Pure Appl. Opt. 7(2), S97–S101 (2005).
[CrossRef]

2004

J. B. Pendry, L. Martín-Moreno, and F. J. Garcia-Vidal, “Mimicking surface plasmons with structured surfaces,” Science 305(5685), 847–848 (2004).
[CrossRef] [PubMed]

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

1998

J. Urata, M. Goldstein, M. F. Kimmitt, A. Naumov, C. Platt, and J. E. Walsh, “Superradiant Smith-Purcell Emission,” Phys. Rev. Lett. 80(3), 516–519 (1998).
[CrossRef]

1983

1953

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

Alexander, R. W.

Andrews, H. L.

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

Asakawa, M. R.

D. Li, M. Hangyo, Z. Yang, M. R. Asakawa, S. Miyamoto, Y. Tsunawaki, K. Takano, and K. Imasaki, “Smith-Purcell radiation from a grating of negative-index material,” Nucl. Instrum. Methods Phys. Res. A 637(1), 135–137 (2011).
[CrossRef]

Bartoli, F. J.

Q. Gan, Z. Fu, Y. J. Ding, and F. J. Bartoli, “Ultrawide-bandwidth slow-light system based on THz plasmonic graded metallic grating structures,” Phys. Rev. Lett. 100(25), 256803 (2008).
[CrossRef] [PubMed]

Bell, R. J.

Bell, R. R.

Bell, S. E.

Brau, C. A.

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

Ding, Y. J.

Q. Gan, Z. Fu, Y. J. Ding, and F. J. Bartoli, “Ultrawide-bandwidth slow-light system based on THz plasmonic graded metallic grating structures,” Phys. Rev. Lett. 100(25), 256803 (2008).
[CrossRef] [PubMed]

Dong, L.

Donohue, J. T.

J. T. Donohue and J. Gardelle, “Simulation of Smith-Purcell terahertz radiation using a particle-in-cell code,” Phys. Rev. ST Accel. Beams 9, 060701 (2006).

J. T. Donohue and J. Gardelle, “Simulation of Smith-Purcell radiation using a particle-in-cell code,” Phys. Rev. ST Accel. Beams 8, 060702 (2005).

Fu, Z.

Q. Gan, Z. Fu, Y. J. Ding, and F. J. Bartoli, “Ultrawide-bandwidth slow-light system based on THz plasmonic graded metallic grating structures,” Phys. Rev. Lett. 100(25), 256803 (2008).
[CrossRef] [PubMed]

Gan, Q.

Q. Gan, Z. Fu, Y. J. Ding, and F. J. Bartoli, “Ultrawide-bandwidth slow-light system based on THz plasmonic graded metallic grating structures,” Phys. Rev. Lett. 100(25), 256803 (2008).
[CrossRef] [PubMed]

Garcia-Vidal, F. J.

F. J. Garcia-Vidal, L. Martin-Moreno, and J. B. Pendry, “Surfaces with holes in them: new plasmonic metamaterials,” Pure Appl. Opt. 7(2), S97–S101 (2005).
[CrossRef]

J. B. Pendry, L. Martín-Moreno, and F. J. Garcia-Vidal, “Mimicking surface plasmons with structured surfaces,” Science 305(5685), 847–848 (2004).
[CrossRef] [PubMed]

Gardelle, J.

J. T. Donohue and J. Gardelle, “Simulation of Smith-Purcell terahertz radiation using a particle-in-cell code,” Phys. Rev. ST Accel. Beams 9, 060701 (2006).

J. T. Donohue and J. Gardelle, “Simulation of Smith-Purcell radiation using a particle-in-cell code,” Phys. Rev. ST Accel. Beams 8, 060702 (2005).

Goldstein, M.

J. Urata, M. Goldstein, M. F. Kimmitt, A. Naumov, C. Platt, and J. E. Walsh, “Superradiant Smith-Purcell Emission,” Phys. Rev. Lett. 80(3), 516–519 (1998).
[CrossRef]

Hangyo, M.

D. Li, M. Hangyo, Z. Yang, M. R. Asakawa, S. Miyamoto, Y. Tsunawaki, K. Takano, and K. Imasaki, “Smith-Purcell radiation from a grating of negative-index material,” Nucl. Instrum. Methods Phys. Res. A 637(1), 135–137 (2011).
[CrossRef]

Imasaki, K.

D. Li, M. Hangyo, Z. Yang, M. R. Asakawa, S. Miyamoto, Y. Tsunawaki, K. Takano, and K. Imasaki, “Smith-Purcell radiation from a grating of negative-index material,” Nucl. Instrum. Methods Phys. Res. A 637(1), 135–137 (2011).
[CrossRef]

D. Li, Z. Yang, K. Imasaki, and G. S. Park, “Particle-in-cell simulation of coherent and superradiant Smith-Purcell radiation,” Phys. Rev. ST Accel. Beams 9, 040701 (2006).

Inafune, K.

Iwata, T.

T. Iwata, A. Okajima, and T. Matsui, “GPGPU-based parallel computing of PIC-FDTD simulation for the development of novel terahertz radiation devices,” Proc. SPIE 8980, 89801V (2014).
[CrossRef]

Kimmitt, M. F.

J. Urata, M. Goldstein, M. F. Kimmitt, A. Naumov, C. Platt, and J. E. Walsh, “Superradiant Smith-Purcell Emission,” Phys. Rev. Lett. 80(3), 516–519 (1998).
[CrossRef]

Kivshar, Y. S.

N. I. Zheludev and Y. S. Kivshar, “From metamaterials to metadevices,” Nat. Mater. 11(11), 917–924 (2012).
[CrossRef] [PubMed]

Li, D.

D. Li, M. Hangyo, Z. Yang, M. R. Asakawa, S. Miyamoto, Y. Tsunawaki, K. Takano, and K. Imasaki, “Smith-Purcell radiation from a grating of negative-index material,” Nucl. Instrum. Methods Phys. Res. A 637(1), 135–137 (2011).
[CrossRef]

D. Li, Z. Yang, K. Imasaki, and G. S. Park, “Particle-in-cell simulation of coherent and superradiant Smith-Purcell radiation,” Phys. Rev. ST Accel. Beams 9, 040701 (2006).

Long, L. L.

Martin-Moreno, L.

F. J. Garcia-Vidal, L. Martin-Moreno, and J. B. Pendry, “Surfaces with holes in them: new plasmonic metamaterials,” Pure Appl. Opt. 7(2), S97–S101 (2005).
[CrossRef]

Martín-Moreno, L.

J. B. Pendry, L. Martín-Moreno, and F. J. Garcia-Vidal, “Mimicking surface plasmons with structured surfaces,” Science 305(5685), 847–848 (2004).
[CrossRef] [PubMed]

Matsui, T.

T. Iwata, A. Okajima, and T. Matsui, “GPGPU-based parallel computing of PIC-FDTD simulation for the development of novel terahertz radiation devices,” Proc. SPIE 8980, 89801V (2014).
[CrossRef]

Miyamoto, S.

D. Li, M. Hangyo, Z. Yang, M. R. Asakawa, S. Miyamoto, Y. Tsunawaki, K. Takano, and K. Imasaki, “Smith-Purcell radiation from a grating of negative-index material,” Nucl. Instrum. Methods Phys. Res. A 637(1), 135–137 (2011).
[CrossRef]

Naumov, A.

J. Urata, M. Goldstein, M. F. Kimmitt, A. Naumov, C. Platt, and J. E. Walsh, “Superradiant Smith-Purcell Emission,” Phys. Rev. Lett. 80(3), 516–519 (1998).
[CrossRef]

Okajima, A.

T. Iwata, A. Okajima, and T. Matsui, “GPGPU-based parallel computing of PIC-FDTD simulation for the development of novel terahertz radiation devices,” Proc. SPIE 8980, 89801V (2014).
[CrossRef]

Ordal, M. A.

Park, G. S.

D. Li, Z. Yang, K. Imasaki, and G. S. Park, “Particle-in-cell simulation of coherent and superradiant Smith-Purcell radiation,” Phys. Rev. ST Accel. Beams 9, 040701 (2006).

Pendry, J. B.

F. J. Garcia-Vidal, L. Martin-Moreno, and J. B. Pendry, “Surfaces with holes in them: new plasmonic metamaterials,” Pure Appl. Opt. 7(2), S97–S101 (2005).
[CrossRef]

J. B. Pendry, L. Martín-Moreno, and F. J. Garcia-Vidal, “Mimicking surface plasmons with structured surfaces,” Science 305(5685), 847–848 (2004).
[CrossRef] [PubMed]

Platt, C.

J. Urata, M. Goldstein, M. F. Kimmitt, A. Naumov, C. Platt, and J. E. Walsh, “Superradiant Smith-Purcell Emission,” Phys. Rev. Lett. 80(3), 516–519 (1998).
[CrossRef]

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]

Sano, E.

Shalaev, V. M.

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

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]

Taga, S.

Takano, K.

D. Li, M. Hangyo, Z. Yang, M. R. Asakawa, S. Miyamoto, Y. Tsunawaki, K. Takano, and K. Imasaki, “Smith-Purcell radiation from a grating of negative-index material,” Nucl. Instrum. Methods Phys. Res. A 637(1), 135–137 (2011).
[CrossRef]

Tonouchi, M.

M. Tonouchi, “Cutting-edge terahertz technology,” Nat. Photon. 1(2), 97–105 (2007).
[CrossRef]

Tsunawaki, Y.

D. Li, M. Hangyo, Z. Yang, M. R. Asakawa, S. Miyamoto, Y. Tsunawaki, K. Takano, and K. Imasaki, “Smith-Purcell radiation from a grating of negative-index material,” Nucl. Instrum. Methods Phys. Res. A 637(1), 135–137 (2011).
[CrossRef]

Urata, J.

J. Urata, M. Goldstein, M. F. Kimmitt, A. Naumov, C. Platt, and J. E. Walsh, “Superradiant Smith-Purcell Emission,” Phys. Rev. Lett. 80(3), 516–519 (1998).
[CrossRef]

Walsh, J. E.

J. Urata, M. Goldstein, M. F. Kimmitt, A. Naumov, C. Platt, and J. E. Walsh, “Superradiant Smith-Purcell Emission,” Phys. Rev. Lett. 80(3), 516–519 (1998).
[CrossRef]

Ward, C. A.

Yang, Z.

D. Li, M. Hangyo, Z. Yang, M. R. Asakawa, S. Miyamoto, Y. Tsunawaki, K. Takano, and K. Imasaki, “Smith-Purcell radiation from a grating of negative-index material,” Nucl. Instrum. Methods Phys. Res. A 637(1), 135–137 (2011).
[CrossRef]

D. Li, Z. Yang, K. Imasaki, and G. S. Park, “Particle-in-cell simulation of coherent and superradiant Smith-Purcell radiation,” Phys. Rev. ST Accel. Beams 9, 040701 (2006).

Zhang, Y.

Zheludev, N. I.

N. I. Zheludev and Y. S. Kivshar, “From metamaterials to metadevices,” Nat. Mater. 11(11), 917–924 (2012).
[CrossRef] [PubMed]

Zhou, Y.

Appl. Opt.

Nat. Mater.

N. I. Zheludev and Y. S. Kivshar, “From metamaterials to metadevices,” Nat. Mater. 11(11), 917–924 (2012).
[CrossRef] [PubMed]

Nat. Photon.

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

M. Tonouchi, “Cutting-edge terahertz technology,” Nat. Photon. 1(2), 97–105 (2007).
[CrossRef]

Nucl. Instrum. Methods Phys. Res. A

D. Li, M. Hangyo, Z. Yang, M. R. Asakawa, S. Miyamoto, Y. Tsunawaki, K. Takano, and K. Imasaki, “Smith-Purcell radiation from a grating of negative-index material,” Nucl. Instrum. Methods Phys. Res. A 637(1), 135–137 (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(4), 1069 (1953).
[CrossRef]

Phys. Rev. Lett.

J. Urata, M. Goldstein, M. F. Kimmitt, A. Naumov, C. Platt, and J. E. Walsh, “Superradiant Smith-Purcell Emission,” Phys. Rev. Lett. 80(3), 516–519 (1998).
[CrossRef]

Q. Gan, Z. Fu, Y. J. Ding, and F. J. Bartoli, “Ultrawide-bandwidth slow-light system based on THz plasmonic graded metallic grating structures,” Phys. Rev. Lett. 100(25), 256803 (2008).
[CrossRef] [PubMed]

Phys. Rev. ST Accel. Beams

J. T. Donohue and J. Gardelle, “Simulation of Smith-Purcell radiation using a particle-in-cell code,” Phys. Rev. ST Accel. Beams 8, 060702 (2005).

J. T. Donohue and J. Gardelle, “Simulation of Smith-Purcell terahertz radiation using a particle-in-cell code,” Phys. Rev. ST Accel. Beams 9, 060701 (2006).

D. Li, Z. Yang, K. Imasaki, and G. S. Park, “Particle-in-cell simulation of coherent and superradiant Smith-Purcell radiation,” Phys. Rev. ST Accel. Beams 9, 040701 (2006).

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

Proc. SPIE

T. Iwata, A. Okajima, and T. Matsui, “GPGPU-based parallel computing of PIC-FDTD simulation for the development of novel terahertz radiation devices,” Proc. SPIE 8980, 89801V (2014).
[CrossRef]

Pure Appl. Opt.

F. J. Garcia-Vidal, L. Martin-Moreno, and J. B. Pendry, “Surfaces with holes in them: new plasmonic metamaterials,” Pure Appl. Opt. 7(2), S97–S101 (2005).
[CrossRef]

Science

J. B. Pendry, L. Martín-Moreno, and F. J. Garcia-Vidal, “Mimicking surface plasmons with structured surfaces,” Science 305(5685), 847–848 (2004).
[CrossRef] [PubMed]

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Figures (3)

Fig. 1
Fig. 1

(a) Schematic representation of the analyzed 2D system and definitions of dimensions of the graded grating. The Ag graded grating is placed at the center of the bottom of analyzed domain in vacuum. The total area of the analyzed domain has a dimension of approximately 20 mm × 40 mm. The grating period (Λ) and groove width (s) are 170 μm and 60 μm, respectively. The number of grooves of the grating (N) is set to be 35. The groove depth (d) is gradually made deeper or shallower and the shallowest and the deepest groove depths (ds and dd) are variable parameters. Δd is the groove depth variation. A 20-μm-wide bunched e-beam with Gaussian charge distribution was sent 20-μm (w) above the grating. (b) Dispersion relations of induced surface waves on periodic grating with d = 100, 168, and 236 μm, along with that of the e-beam (beam line).

Fig. 2
Fig. 2

(a) Snapshot of Hz field after the e-beam passed over GG[100, 168, 2]. (b) FFT spectra of near field (surface wave) Hz monitored at several positions 10 μm above each groove with d = 160, 150, 140, 130, 120, 110, or 100 μm, along with that of the far-field radiation monitored at the observation point P (from top to bottom), in GG[100, 168, 2]. (c) Spatial distributions of Hz fields long after the exciting quasi-monochromatic electromagnetic pulse has been damped when the frequency of the mode is 0.314 (A), 0.329 (B), and 0.347 (C) THz (from top to bottom) in GG[100, 168, 2]. Each mode and its name (A, B, C) correspond to the peaks in the far-field radiation spectrum in the bottom panel of (b).

Fig. 3
Fig. 3

(a) Snapshot of Hz field after the e-beam passed over GG[100, 168, −2]. (b) FFT spectrum of Hz field monitored at the observation point Q in GG[100, 168, −2] (dashed line), along with that monitored at the point P in GG[100, 168, 2] (solid line). (c) FFT spectra of Hz fields monitored at the observation point P in GG[100, 168, 2] (solid line) and GG[168, 236, 2] (dashed line). (d) FFT spectra of Hz fields monitored at the observation point P in GG[100, 236, 4].

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