Abstract

A subwavelength corrugated metal waveguide is studied and designed to slow down the light at terahertz frequencies. The waveguide consists of two parallel thin metal slabs with periodic corrugations on their inner boundaries. Compared with structures based on engineered surface plasmons, the proposed structure has smaller group velocity dispersion and lower propagation loss. The origin of the slow wave is also explained.

© 2008 Optical Society of America

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    [CrossRef]
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    [CrossRef]
  8. H. Han, H. Park, M. Cho, and J. Kim, “Terahertz pulse propagation in a plastic photonic crystal fiber,” Appl. Phys. Lett. 80, 2634-2636 (2002).
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    [CrossRef]
  25. M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, “Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs,” Phys. Rev. Lett. 87, 253902 (2001).
    [CrossRef] [PubMed]
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    [CrossRef]
  30. V. Kuzmiak, A. A. Maradudin, and A. R. McGurn, “Photonic band structures of two-dimensional systems fabricated from rods of a cubic polar crystal,” Phys. Rev. B 55, 4298-4311(1997).
    [CrossRef]
  31. Q. Xu, B. Schmidt, S. Pradhan, and M. Lipson, “Micrometre-scale silicon electro-optic modulator,” Nature 435, 325-327(2005).
    [CrossRef] [PubMed]
  32. Y. Jiang, W. Jiang, L. Gu, X. Chen, and R. T. Chen, “80-micron interaction length silicon photonic crystal waveguide modulator,” Appl. Phys. Lett. 87, 221105 (2005).
    [CrossRef]

2007 (1)

2006 (2)

G. Reyes, A. Quema, C. Ponseca, R. Pobre, R. Quirogab, S. Ono, H. Murakami, E. Estacio, N. Sarukura, K. Aosaki, Y. Sakane, and H. Sato, “Low-loss single-mode terahertz waveguiding using Cytop,” Appl. Phys. Lett. 89, 211119 (2006).
[CrossRef]

S. A. Maier, S. R. Andrews, L. Martín-Moreno, and F. J. García-Vidal, “Terahertz surface plasmon-polariton propagation and focusing on periodically corrugated metal wires,” Phys. Rev. Lett. 97, 176805 (2006).
[CrossRef] [PubMed]

2005 (6)

T. Jeon, J. Zhang, and D. Grischkowsky, “THz Sommerfeld wave propagation on a single metal wire,” Appl. Phys. Lett. 86, 161904 (2005).
[CrossRef]

Y. A. Vlasov, M. O'Boyle, H. F. Hamann, and S. J. McNab, “Active control of slow light on a chip with photonic crystal waveguides,” Nature 438, 65-69 (2005).
[CrossRef] [PubMed]

H. Gersen, T. J. Karle, R. J. P. Engelen, W. Bogaerts, J. P. Korterik, N. F. van Hulst, T. F. Krauss, and L. Kuipers, “Real-space observation of ultraslow light in photonic crystal waveguides,” Phys. Rev. Lett. 94, 073903 (2005).
[CrossRef] [PubMed]

A. Bingham, Y. Zhao, and D. Grischkowsky, “THz parallel plate photonic waveguides,” Appl. Phys. Lett. 87, 051101(2005).
[CrossRef]

Q. Xu, B. Schmidt, S. Pradhan, and M. Lipson, “Micrometre-scale silicon electro-optic modulator,” Nature 435, 325-327(2005).
[CrossRef] [PubMed]

Y. Jiang, W. Jiang, L. Gu, X. Chen, and R. T. Chen, “80-micron interaction length silicon photonic crystal waveguide modulator,” Appl. Phys. Lett. 87, 221105 (2005).
[CrossRef]

2004 (4)

2003 (2)

R. Mendis and D. Grischkowsky, “A THz transverse electromagnetic mode two-dimensional interconnect layer incorporating quasi-optics,” Appl. Phys. Lett. 83, 3656-3658 (2003).
[CrossRef]

Y. Tanaka, T. Asano, Y. Akahane, B. S. Song, and S. Noda, “Theoretical investigation of a two-dimensional photonic crystal slab with truncated cone air holes,” Appl. Phys. Lett. 82, 1661-1663 (2003).
[CrossRef]

2002 (1)

H. Han, H. Park, M. Cho, and J. Kim, “Terahertz pulse propagation in a plastic photonic crystal fiber,” Appl. Phys. Lett. 80, 2634-2636 (2002).
[CrossRef]

2001 (3)

R. Mendis and D. Grischkowsky, “Undistorted guided-wave propagation of subpicosecond terahertz pulses,” Opt. Lett. 26, 846-848 (2001).
[CrossRef]

R. Mendis and D. Grischkowsky, “THz interconnect with low loss and low group velocity dispersion,” IEEE Microw. Wireless Compon. Lett. 11, 444-446 (2001).
[CrossRef]

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, “Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs,” Phys. Rev. Lett. 87, 253902 (2001).
[CrossRef] [PubMed]

2000 (4)

G. Gallot, S. P. Jamison, R. W. McGowan, and D. Grischkowsky, “Terahertz waveguides,” J. Opt. Soc. Am. B 17, 851-863 (2000).
[CrossRef]

R. Mendis and D. Grischkowsky, “Plastic ribbon THz waveguides,” J. Appl. Phys. 88, 4449-4451 (2000).
[CrossRef]

S. P. Jamison, R. W. McGowan, and D. Grischkowsky, “Single-mode waveguide propagation and reshaping of sub-ps terahertz pulses in sapphire fiber,” Appl. Phys. Lett. 76, 1987-1989(2000).
[CrossRef]

Q. Chen, Z. Jiang, G. X. Xu, and X. C. Zhang, “Near-field terahertz imaging with a dynamic aperture,” Opt. Lett. 25, 1122-1124 (2000).
[CrossRef]

1999 (1)

1997 (1)

V. Kuzmiak, A. A. Maradudin, and A. R. McGurn, “Photonic band structures of two-dimensional systems fabricated from rods of a cubic polar crystal,” Phys. Rev. B 55, 4298-4311(1997).
[CrossRef]

1996 (1)

1954 (1)

R. S. Elliott, “On the theory of corrugated plane surfaces,” IRE Trans. Antennas Propag. 2, 71-81 (1954).

1952 (1)

R. Kompfner, “Travelling-wave tubes,” Rep. Prog. Phys. 15275-327 (1952).
[CrossRef]

1951 (1)

W. Rotman, “A study of single surface corrugated guides,” Proc. IRE 39, 952-959 (1951).
[CrossRef]

1950 (1)

G. Goubau, “Surface waves and their application to transmission lines,” J. Appl. Phys. 21, 1119 (1950).
[CrossRef]

Ahopelto, J.

Akahane, Y.

Y. Tanaka, T. Asano, Y. Akahane, B. S. Song, and S. Noda, “Theoretical investigation of a two-dimensional photonic crystal slab with truncated cone air holes,” Appl. Phys. Lett. 82, 1661-1663 (2003).
[CrossRef]

Andrews, S. R.

S. A. Maier, S. R. Andrews, L. Martín-Moreno, and F. J. García-Vidal, “Terahertz surface plasmon-polariton propagation and focusing on periodically corrugated metal wires,” Phys. Rev. Lett. 97, 176805 (2006).
[CrossRef] [PubMed]

Aosaki, K.

G. Reyes, A. Quema, C. Ponseca, R. Pobre, R. Quirogab, S. Ono, H. Murakami, E. Estacio, N. Sarukura, K. Aosaki, Y. Sakane, and H. Sato, “Low-loss single-mode terahertz waveguiding using Cytop,” Appl. Phys. Lett. 89, 211119 (2006).
[CrossRef]

Asano, T.

Y. Tanaka, T. Asano, Y. Akahane, B. S. Song, and S. Noda, “Theoretical investigation of a two-dimensional photonic crystal slab with truncated cone air holes,” Appl. Phys. Lett. 82, 1661-1663 (2003).
[CrossRef]

Barkan, A.

K. Wang, A. Barkan, and D. M. Mittleman, “Propagation effects in apertureless near-field optical antennas,” Appl. Phys. Lett. 84, 305-307 (2004).
[CrossRef]

Bingham, A.

A. Bingham, Y. Zhao, and D. Grischkowsky, “THz parallel plate photonic waveguides,” Appl. Phys. Lett. 87, 051101(2005).
[CrossRef]

Bogaerts, W.

H. Gersen, T. J. Karle, R. J. P. Engelen, W. Bogaerts, J. P. Korterik, N. F. van Hulst, T. F. Krauss, and L. Kuipers, “Real-space observation of ultraslow light in photonic crystal waveguides,” Phys. Rev. Lett. 94, 073903 (2005).
[CrossRef] [PubMed]

Chen, C.

Chen, Q.

Chen, R. T.

Y. Jiang, W. Jiang, L. Gu, X. Chen, and R. T. Chen, “80-micron interaction length silicon photonic crystal waveguide modulator,” Appl. Phys. Lett. 87, 221105 (2005).
[CrossRef]

Chen, X.

Y. Jiang, W. Jiang, L. Gu, X. Chen, and R. T. Chen, “80-micron interaction length silicon photonic crystal waveguide modulator,” Appl. Phys. Lett. 87, 221105 (2005).
[CrossRef]

Cho, M.

H. Han, H. Park, M. Cho, and J. Kim, “Terahertz pulse propagation in a plastic photonic crystal fiber,” Appl. Phys. Lett. 80, 2634-2636 (2002).
[CrossRef]

Elliott, R. S.

R. S. Elliott, “On the theory of corrugated plane surfaces,” IRE Trans. Antennas Propag. 2, 71-81 (1954).

Engelen, R. J. P.

H. Gersen, T. J. Karle, R. J. P. Engelen, W. Bogaerts, J. P. Korterik, N. F. van Hulst, T. F. Krauss, and L. Kuipers, “Real-space observation of ultraslow light in photonic crystal waveguides,” Phys. Rev. Lett. 94, 073903 (2005).
[CrossRef] [PubMed]

Estacio, E.

G. Reyes, A. Quema, C. Ponseca, R. Pobre, R. Quirogab, S. Ono, H. Murakami, E. Estacio, N. Sarukura, K. Aosaki, Y. Sakane, and H. Sato, “Low-loss single-mode terahertz waveguiding using Cytop,” Appl. Phys. Lett. 89, 211119 (2006).
[CrossRef]

Gallot, G.

García-Vidal, F. J.

S. A. Maier, S. R. Andrews, L. Martín-Moreno, and F. J. García-Vidal, “Terahertz surface plasmon-polariton propagation and focusing on periodically corrugated metal wires,” Phys. Rev. Lett. 97, 176805 (2006).
[CrossRef] [PubMed]

Gersen, H.

H. Gersen, T. J. Karle, R. J. P. Engelen, W. Bogaerts, J. P. Korterik, N. F. van Hulst, T. F. Krauss, and L. Kuipers, “Real-space observation of ultraslow light in photonic crystal waveguides,” Phys. Rev. Lett. 94, 073903 (2005).
[CrossRef] [PubMed]

Goubau, G.

G. Goubau, “Surface waves and their application to transmission lines,” J. Appl. Phys. 21, 1119 (1950).
[CrossRef]

Grischkowsky, D.

T. Jeon, J. Zhang, and D. Grischkowsky, “THz Sommerfeld wave propagation on a single metal wire,” Appl. Phys. Lett. 86, 161904 (2005).
[CrossRef]

A. Bingham, Y. Zhao, and D. Grischkowsky, “THz parallel plate photonic waveguides,” Appl. Phys. Lett. 87, 051101(2005).
[CrossRef]

J. Zhang and D. Grischkowsky, “Waveguide terahertz time-domain spectroscopy of nanometer wave layers,” Opt. Lett. 29, 1617-1619 (2004).
[CrossRef] [PubMed]

R. Mendis and D. Grischkowsky, “A THz transverse electromagnetic mode two-dimensional interconnect layer incorporating quasi-optics,” Appl. Phys. Lett. 83, 3656-3658 (2003).
[CrossRef]

R. Mendis and D. Grischkowsky, “Undistorted guided-wave propagation of subpicosecond terahertz pulses,” Opt. Lett. 26, 846-848 (2001).
[CrossRef]

R. Mendis and D. Grischkowsky, “THz interconnect with low loss and low group velocity dispersion,” IEEE Microw. Wireless Compon. Lett. 11, 444-446 (2001).
[CrossRef]

S. P. Jamison, R. W. McGowan, and D. Grischkowsky, “Single-mode waveguide propagation and reshaping of sub-ps terahertz pulses in sapphire fiber,” Appl. Phys. Lett. 76, 1987-1989(2000).
[CrossRef]

G. Gallot, S. P. Jamison, R. W. McGowan, and D. Grischkowsky, “Terahertz waveguides,” J. Opt. Soc. Am. B 17, 851-863 (2000).
[CrossRef]

R. Mendis and D. Grischkowsky, “Plastic ribbon THz waveguides,” J. Appl. Phys. 88, 4449-4451 (2000).
[CrossRef]

R. W. McGowan, G. Gallot, and D. Grischkowsky, “Propagation of ultrawideband short pulses of THz radiation through submillimeter-diameter circular waveguides,” Opt. Lett. 24, 1431-1433 (1999).
[CrossRef]

Gu, L.

Y. Jiang, W. Jiang, L. Gu, X. Chen, and R. T. Chen, “80-micron interaction length silicon photonic crystal waveguide modulator,” Appl. Phys. Lett. 87, 221105 (2005).
[CrossRef]

Hamann, H. F.

Y. A. Vlasov, M. O'Boyle, H. F. Hamann, and S. J. McNab, “Active control of slow light on a chip with photonic crystal waveguides,” Nature 438, 65-69 (2005).
[CrossRef] [PubMed]

Han, H.

H. Han, H. Park, M. Cho, and J. Kim, “Terahertz pulse propagation in a plastic photonic crystal fiber,” Appl. Phys. Lett. 80, 2634-2636 (2002).
[CrossRef]

Jacobson, R. H.

Jamison, S. P.

G. Gallot, S. P. Jamison, R. W. McGowan, and D. Grischkowsky, “Terahertz waveguides,” J. Opt. Soc. Am. B 17, 851-863 (2000).
[CrossRef]

S. P. Jamison, R. W. McGowan, and D. Grischkowsky, “Single-mode waveguide propagation and reshaping of sub-ps terahertz pulses in sapphire fiber,” Appl. Phys. Lett. 76, 1987-1989(2000).
[CrossRef]

Jeon, T.

T. Jeon, J. Zhang, and D. Grischkowsky, “THz Sommerfeld wave propagation on a single metal wire,” Appl. Phys. Lett. 86, 161904 (2005).
[CrossRef]

Jiang, W.

Y. Jiang, W. Jiang, L. Gu, X. Chen, and R. T. Chen, “80-micron interaction length silicon photonic crystal waveguide modulator,” Appl. Phys. Lett. 87, 221105 (2005).
[CrossRef]

Jiang, Y.

Y. Jiang, W. Jiang, L. Gu, X. Chen, and R. T. Chen, “80-micron interaction length silicon photonic crystal waveguide modulator,” Appl. Phys. Lett. 87, 221105 (2005).
[CrossRef]

Jiang, Z.

Karle, T. J.

H. Gersen, T. J. Karle, R. J. P. Engelen, W. Bogaerts, J. P. Korterik, N. F. van Hulst, T. F. Krauss, and L. Kuipers, “Real-space observation of ultraslow light in photonic crystal waveguides,” Phys. Rev. Lett. 94, 073903 (2005).
[CrossRef] [PubMed]

Kim, J.

H. Han, H. Park, M. Cho, and J. Kim, “Terahertz pulse propagation in a plastic photonic crystal fiber,” Appl. Phys. Lett. 80, 2634-2636 (2002).
[CrossRef]

Kompfner, R.

R. Kompfner, “Travelling-wave tubes,” Rep. Prog. Phys. 15275-327 (1952).
[CrossRef]

Korterik, J. P.

H. Gersen, T. J. Karle, R. J. P. Engelen, W. Bogaerts, J. P. Korterik, N. F. van Hulst, T. F. Krauss, and L. Kuipers, “Real-space observation of ultraslow light in photonic crystal waveguides,” Phys. Rev. Lett. 94, 073903 (2005).
[CrossRef] [PubMed]

Krauss, T. F.

H. Gersen, T. J. Karle, R. J. P. Engelen, W. Bogaerts, J. P. Korterik, N. F. van Hulst, T. F. Krauss, and L. Kuipers, “Real-space observation of ultraslow light in photonic crystal waveguides,” Phys. Rev. Lett. 94, 073903 (2005).
[CrossRef] [PubMed]

Kuipers, L.

H. Gersen, T. J. Karle, R. J. P. Engelen, W. Bogaerts, J. P. Korterik, N. F. van Hulst, T. F. Krauss, and L. Kuipers, “Real-space observation of ultraslow light in photonic crystal waveguides,” Phys. Rev. Lett. 94, 073903 (2005).
[CrossRef] [PubMed]

Kuzmiak, V.

V. Kuzmiak, A. A. Maradudin, and A. R. McGurn, “Photonic band structures of two-dimensional systems fabricated from rods of a cubic polar crystal,” Phys. Rev. B 55, 4298-4311(1997).
[CrossRef]

Lin, C.

Lipsanen, H.

Lipson, M.

Q. Xu, B. Schmidt, S. Pradhan, and M. Lipson, “Micrometre-scale silicon electro-optic modulator,” Nature 435, 325-327(2005).
[CrossRef] [PubMed]

Maier, S. A.

S. A. Maier, S. R. Andrews, L. Martín-Moreno, and F. J. García-Vidal, “Terahertz surface plasmon-polariton propagation and focusing on periodically corrugated metal wires,” Phys. Rev. Lett. 97, 176805 (2006).
[CrossRef] [PubMed]

Maradudin, A. A.

V. Kuzmiak, A. A. Maradudin, and A. R. McGurn, “Photonic band structures of two-dimensional systems fabricated from rods of a cubic polar crystal,” Phys. Rev. B 55, 4298-4311(1997).
[CrossRef]

Martín-Moreno, L.

S. A. Maier, S. R. Andrews, L. Martín-Moreno, and F. J. García-Vidal, “Terahertz surface plasmon-polariton propagation and focusing on periodically corrugated metal wires,” Phys. Rev. Lett. 97, 176805 (2006).
[CrossRef] [PubMed]

McGowan, R. W.

McGurn, A. R.

V. Kuzmiak, A. A. Maradudin, and A. R. McGurn, “Photonic band structures of two-dimensional systems fabricated from rods of a cubic polar crystal,” Phys. Rev. B 55, 4298-4311(1997).
[CrossRef]

McNab, S. J.

Y. A. Vlasov, M. O'Boyle, H. F. Hamann, and S. J. McNab, “Active control of slow light on a chip with photonic crystal waveguides,” Nature 438, 65-69 (2005).
[CrossRef] [PubMed]

Mendis, R.

R. Mendis and D. Grischkowsky, “A THz transverse electromagnetic mode two-dimensional interconnect layer incorporating quasi-optics,” Appl. Phys. Lett. 83, 3656-3658 (2003).
[CrossRef]

R. Mendis and D. Grischkowsky, “THz interconnect with low loss and low group velocity dispersion,” IEEE Microw. Wireless Compon. Lett. 11, 444-446 (2001).
[CrossRef]

R. Mendis and D. Grischkowsky, “Undistorted guided-wave propagation of subpicosecond terahertz pulses,” Opt. Lett. 26, 846-848 (2001).
[CrossRef]

R. Mendis and D. Grischkowsky, “Plastic ribbon THz waveguides,” J. Appl. Phys. 88, 4449-4451 (2000).
[CrossRef]

Mittleman, D. M.

K. Wang and D. M. Mittleman, “Metal wires for THz wave guiding,” Nature 432, 376-379 (2004).
[CrossRef] [PubMed]

K. Wang, A. Barkan, and D. M. Mittleman, “Propagation effects in apertureless near-field optical antennas,” Appl. Phys. Lett. 84, 305-307 (2004).
[CrossRef]

R. H. Jacobson, D. M. Mittleman, and M. C. Nuss, “Chemical recognition of gases and gas mixtures with terahertz waves,” Opt. Lett. 21, 2011-2013 (1996).
[CrossRef]

Mulot, M.

Murakami, H.

G. Reyes, A. Quema, C. Ponseca, R. Pobre, R. Quirogab, S. Ono, H. Murakami, E. Estacio, N. Sarukura, K. Aosaki, Y. Sakane, and H. Sato, “Low-loss single-mode terahertz waveguiding using Cytop,” Appl. Phys. Lett. 89, 211119 (2006).
[CrossRef]

Noda, S.

Y. Tanaka, T. Asano, Y. Akahane, B. S. Song, and S. Noda, “Theoretical investigation of a two-dimensional photonic crystal slab with truncated cone air holes,” Appl. Phys. Lett. 82, 1661-1663 (2003).
[CrossRef]

Notomi, M.

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, “Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs,” Phys. Rev. Lett. 87, 253902 (2001).
[CrossRef] [PubMed]

Nuss, M. C.

O'Boyle, M.

Y. A. Vlasov, M. O'Boyle, H. F. Hamann, and S. J. McNab, “Active control of slow light on a chip with photonic crystal waveguides,” Nature 438, 65-69 (2005).
[CrossRef] [PubMed]

Ono, S.

G. Reyes, A. Quema, C. Ponseca, R. Pobre, R. Quirogab, S. Ono, H. Murakami, E. Estacio, N. Sarukura, K. Aosaki, Y. Sakane, and H. Sato, “Low-loss single-mode terahertz waveguiding using Cytop,” Appl. Phys. Lett. 89, 211119 (2006).
[CrossRef]

Palik, E. D.

E. D. Palik, Handbook of Optical Constants of Solids, 2nd ed. (Academic, 1998).

Park, H.

H. Han, H. Park, M. Cho, and J. Kim, “Terahertz pulse propagation in a plastic photonic crystal fiber,” Appl. Phys. Lett. 80, 2634-2636 (2002).
[CrossRef]

Pobre, R.

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Figures (5)

Fig. 1
Fig. 1

(a) Proposed waveguide structure (structure A) for slow light at THz. (b) Structure B (based on engineered surface plasmons) for comparison.

Fig. 2
Fig. 2

(a) Band structure of structure A with g = 10 μm , d = 30 μm , l = 45 μm , h = 20 μm , and a = 50 μm . Antisymmetric bands are given by curves with red triangles. (b) Band structure of structure B (for comparison) with d = 30 μm , l = 9 μm , h = 21.8 μm , and a = 10 μm . (c) The enlarged band structure of the fourth antisymmetric band of structure A in the wavelength range between 9.05 and 9.085 THz .

Fig. 3
Fig. 3

(a) Group velocity v g . (b) Group velocity dispersion parameter D. (c) Quality factor Q. (d) Product of the quality factor Q and group velocity v g . (e) Propagation loss per period ( a = 50 μm ). Curve with red triangles is for the fourth antisymmetric band of structure A, and curve with blue circles is for the second band of structure B.

Fig. 4
Fig. 4

Distribution of H z and time average Poynting vector (marked by black arrows) of (a) a unit cell of structure A at 9.055 THz , (b) a single isolated metal cavity at 9.074 THz , (c) a unit cell of structure A at 6.120 THz , and (d) a single isolated metal cavity at 6.144 THz . The white boundaries indicate the profile of Ag structures. The units for the magnitude of magnetic field in (a), (b), (c), and (d) are arbitrary.

Fig. 5
Fig. 5

Distribution of (a)  | E x | 2 and (b)  | E y | 2 of a unit cell of structure A at 9.055 THz . The white lines give the profile of Ag structures. The units for the intensity of electric field in (a) and (b) are arbitrary.

Equations (4)

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

ε m = 1 ω p 2 ω ( ω + i γ ) ,
v g = d ω d k x .
D = 1 c d n g d λ ,
loss = exp ( a ω Q v g ) ,

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