Abstract

We investigate photonic band-gap (PBG) profiles of a modified honeycomb lattice structure and we identify the structural parameters that possess the largest band-gap. By incorporating the identified profile into the cladding, the wavelength dependence of the dispersion properties and confinement losses of air-guiding modified honeycomb PBG fibers (PBGFs) is investigated through a full-vector modal solver based on finite element method. In particular, we find that broadband effectively single-mode operation from 1450 nm to 1850 nm can be achieved using a modified honeycomb PBGF with a defected core realized by removing 7 air holes.

© 2006 Optical Society of America

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  1. T. A. Birks, P. J. Roberts, P. S. J. Russell, D. M. Atkin, and T. J. Shepherd, "Full 2-D photonic bandgaps in silica/air structures," Electron. Lett. 31, 1941-1943 (1995).
    [CrossRef]
  2. R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. S. J. Russell, P. J. Roberts, and D. C. Allan, "Single-mode photonic band gap guidance of light in air," Science 285, 1537-1539 (1999).
    [CrossRef] [PubMed]
  3. J. Broeng, S. E. Barkou, T. Sφndergaard, and A. Bjarklev, "Analysis of air-guiding photonic bandgap fibers," Opt. Lett. 25, 96-98 (2000).
    [CrossRef]
  4. C. M. Smith, N. Venkataraman, M. T. Gallagher, D. Müller, J. A. West, N. F. Borrelli, D. C. Allan, and K. W. Koch, "Low-loss hollow-core silica/air photonic bandgap fibre," Nature 424, 657-659 (2003).
    [CrossRef] [PubMed]
  5. K. Saitoh and M. Koshiba, "Leakage loss and group velocity dispersion in air-core photonic bandgap fibers," Opt. Express 11,3100-3109 (2003). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-23-3100.
    [CrossRef] [PubMed]
  6. K. Saitoh, N. A. Mortensen, and M. Koshiba, "Air-core photonic band-gap fibers: the impact of surface modes," Opt. Express 12,394-400 (2004). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-3-394.
    [CrossRef] [PubMed]
  7. H. K. Kim, J. Shin, S. Fan, M. J. F. Digonnet, and G. S. Kino, "Designing air-core photonic bandgap fibers free of surface modes," IEEE J. Quantum Electron. 40, 551-556 (2004).
    [CrossRef]
  8. M. Yan and P. Shum, "Air guiding with honeycomb photonic bandgap fiber," IEEE Photon. Technol. Lett. 17, 64-66 (2005).
    [CrossRef]
  9. M. Yan, P. Shum, and J. Hu, "Design of air-guiding honeycomb photonic bandgap fiber," Opt. Lett. 30, 465-467 (2005).
    [CrossRef] [PubMed]
  10. J. Broeng, S. E. Barkou, A. Bjarklev, J. C. Knight, T. A. Birks, and P. S. J. Russell, "Highly increased photonic band gaps in silica/air structures," Opt. Commun. 156, 240-244 (1998).
    [CrossRef]
  11. Y. Li, C. Wang, M. Hu, B. Liu, X. Sun, and L. Chai, "Honeycomb photonic bandgap fibers with and without interstitial air holes," Opt. Express 13,6856-6863 (2005). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-18-6856.
    [CrossRef] [PubMed]
  12. T. Haas, S. Belau, and T. Doll, "Realistic monomode air-core honeycomb photonic bandgap fiber with pockets," J. Lightwave Technol. 23, 2702-2706 (2005).
    [CrossRef]
  13. M. Chen and R. Yu, "Analysis of photonic bandgaps in modified honeycomb structures," IEEE Photon. Technol. Lett. 16, 819-821 (2004).
    [CrossRef]
  14. S. Selleri, L. Vincetti, F. Poli, A. Cucinotta, and M. Foroni, "Air-guiding photonic crystal fibers with modified honeycomb lattice," in Proceedings of 2005 IEEE/LEOS Workshop on Fibers and Optical Passive Components (WFOPC), 20-25 (2005).
  15. L. Vincetti, F. Poli, and S. Selleri, "Confinement loss and nonlinearity analysis of air-guiding modified honeycomb photonic bandgap fibers," IEEE Photon. Technol. Lett. 18, 508-510 (2006).
    [CrossRef]
  16. K. Saitoh and M. Koshiba, "Full-vectorial imaginary-distance beam propagation method based on finite element scheme: Application to photonic crystal fibers," IEEE J. Quantum Electron. 38, 927-933 (2002).
    [CrossRef]

2006

L. Vincetti, F. Poli, and S. Selleri, "Confinement loss and nonlinearity analysis of air-guiding modified honeycomb photonic bandgap fibers," IEEE Photon. Technol. Lett. 18, 508-510 (2006).
[CrossRef]

2005

2004

M. Chen and R. Yu, "Analysis of photonic bandgaps in modified honeycomb structures," IEEE Photon. Technol. Lett. 16, 819-821 (2004).
[CrossRef]

K. Saitoh, N. A. Mortensen, and M. Koshiba, "Air-core photonic band-gap fibers: the impact of surface modes," Opt. Express 12,394-400 (2004). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-3-394.
[CrossRef] [PubMed]

H. K. Kim, J. Shin, S. Fan, M. J. F. Digonnet, and G. S. Kino, "Designing air-core photonic bandgap fibers free of surface modes," IEEE J. Quantum Electron. 40, 551-556 (2004).
[CrossRef]

2003

C. M. Smith, N. Venkataraman, M. T. Gallagher, D. Müller, J. A. West, N. F. Borrelli, D. C. Allan, and K. W. Koch, "Low-loss hollow-core silica/air photonic bandgap fibre," Nature 424, 657-659 (2003).
[CrossRef] [PubMed]

K. Saitoh and M. Koshiba, "Leakage loss and group velocity dispersion in air-core photonic bandgap fibers," Opt. Express 11,3100-3109 (2003). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-23-3100.
[CrossRef] [PubMed]

2002

K. Saitoh and M. Koshiba, "Full-vectorial imaginary-distance beam propagation method based on finite element scheme: Application to photonic crystal fibers," IEEE J. Quantum Electron. 38, 927-933 (2002).
[CrossRef]

2000

1999

R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. S. J. Russell, P. J. Roberts, and D. C. Allan, "Single-mode photonic band gap guidance of light in air," Science 285, 1537-1539 (1999).
[CrossRef] [PubMed]

1998

J. Broeng, S. E. Barkou, A. Bjarklev, J. C. Knight, T. A. Birks, and P. S. J. Russell, "Highly increased photonic band gaps in silica/air structures," Opt. Commun. 156, 240-244 (1998).
[CrossRef]

1995

T. A. Birks, P. J. Roberts, P. S. J. Russell, D. M. Atkin, and T. J. Shepherd, "Full 2-D photonic bandgaps in silica/air structures," Electron. Lett. 31, 1941-1943 (1995).
[CrossRef]

Allan, D. C.

C. M. Smith, N. Venkataraman, M. T. Gallagher, D. Müller, J. A. West, N. F. Borrelli, D. C. Allan, and K. W. Koch, "Low-loss hollow-core silica/air photonic bandgap fibre," Nature 424, 657-659 (2003).
[CrossRef] [PubMed]

R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. S. J. Russell, P. J. Roberts, and D. C. Allan, "Single-mode photonic band gap guidance of light in air," Science 285, 1537-1539 (1999).
[CrossRef] [PubMed]

Atkin, D. M.

T. A. Birks, P. J. Roberts, P. S. J. Russell, D. M. Atkin, and T. J. Shepherd, "Full 2-D photonic bandgaps in silica/air structures," Electron. Lett. 31, 1941-1943 (1995).
[CrossRef]

Barkou, S. E.

J. Broeng, S. E. Barkou, T. Sφndergaard, and A. Bjarklev, "Analysis of air-guiding photonic bandgap fibers," Opt. Lett. 25, 96-98 (2000).
[CrossRef]

J. Broeng, S. E. Barkou, A. Bjarklev, J. C. Knight, T. A. Birks, and P. S. J. Russell, "Highly increased photonic band gaps in silica/air structures," Opt. Commun. 156, 240-244 (1998).
[CrossRef]

Belau, S.

Birks, T. A.

R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. S. J. Russell, P. J. Roberts, and D. C. Allan, "Single-mode photonic band gap guidance of light in air," Science 285, 1537-1539 (1999).
[CrossRef] [PubMed]

J. Broeng, S. E. Barkou, A. Bjarklev, J. C. Knight, T. A. Birks, and P. S. J. Russell, "Highly increased photonic band gaps in silica/air structures," Opt. Commun. 156, 240-244 (1998).
[CrossRef]

T. A. Birks, P. J. Roberts, P. S. J. Russell, D. M. Atkin, and T. J. Shepherd, "Full 2-D photonic bandgaps in silica/air structures," Electron. Lett. 31, 1941-1943 (1995).
[CrossRef]

Bjarklev, A.

J. Broeng, S. E. Barkou, A. Bjarklev, J. C. Knight, T. A. Birks, and P. S. J. Russell, "Highly increased photonic band gaps in silica/air structures," Opt. Commun. 156, 240-244 (1998).
[CrossRef]

Borrelli, N. F.

C. M. Smith, N. Venkataraman, M. T. Gallagher, D. Müller, J. A. West, N. F. Borrelli, D. C. Allan, and K. W. Koch, "Low-loss hollow-core silica/air photonic bandgap fibre," Nature 424, 657-659 (2003).
[CrossRef] [PubMed]

Broeng, J.

J. Broeng, S. E. Barkou, T. Sφndergaard, and A. Bjarklev, "Analysis of air-guiding photonic bandgap fibers," Opt. Lett. 25, 96-98 (2000).
[CrossRef]

J. Broeng, S. E. Barkou, A. Bjarklev, J. C. Knight, T. A. Birks, and P. S. J. Russell, "Highly increased photonic band gaps in silica/air structures," Opt. Commun. 156, 240-244 (1998).
[CrossRef]

Chai, L.

Chen, M.

M. Chen and R. Yu, "Analysis of photonic bandgaps in modified honeycomb structures," IEEE Photon. Technol. Lett. 16, 819-821 (2004).
[CrossRef]

Cregan, R. F.

R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. S. J. Russell, P. J. Roberts, and D. C. Allan, "Single-mode photonic band gap guidance of light in air," Science 285, 1537-1539 (1999).
[CrossRef] [PubMed]

Digonnet, M. J. F.

H. K. Kim, J. Shin, S. Fan, M. J. F. Digonnet, and G. S. Kino, "Designing air-core photonic bandgap fibers free of surface modes," IEEE J. Quantum Electron. 40, 551-556 (2004).
[CrossRef]

Doll, T.

Fan, S.

H. K. Kim, J. Shin, S. Fan, M. J. F. Digonnet, and G. S. Kino, "Designing air-core photonic bandgap fibers free of surface modes," IEEE J. Quantum Electron. 40, 551-556 (2004).
[CrossRef]

Gallagher, M. T.

C. M. Smith, N. Venkataraman, M. T. Gallagher, D. Müller, J. A. West, N. F. Borrelli, D. C. Allan, and K. W. Koch, "Low-loss hollow-core silica/air photonic bandgap fibre," Nature 424, 657-659 (2003).
[CrossRef] [PubMed]

Haas, T.

Hu, J.

Hu, M.

Kim, H. K.

H. K. Kim, J. Shin, S. Fan, M. J. F. Digonnet, and G. S. Kino, "Designing air-core photonic bandgap fibers free of surface modes," IEEE J. Quantum Electron. 40, 551-556 (2004).
[CrossRef]

Kino, G. S.

H. K. Kim, J. Shin, S. Fan, M. J. F. Digonnet, and G. S. Kino, "Designing air-core photonic bandgap fibers free of surface modes," IEEE J. Quantum Electron. 40, 551-556 (2004).
[CrossRef]

Knight, J. C.

R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. S. J. Russell, P. J. Roberts, and D. C. Allan, "Single-mode photonic band gap guidance of light in air," Science 285, 1537-1539 (1999).
[CrossRef] [PubMed]

J. Broeng, S. E. Barkou, A. Bjarklev, J. C. Knight, T. A. Birks, and P. S. J. Russell, "Highly increased photonic band gaps in silica/air structures," Opt. Commun. 156, 240-244 (1998).
[CrossRef]

Koch, K. W.

C. M. Smith, N. Venkataraman, M. T. Gallagher, D. Müller, J. A. West, N. F. Borrelli, D. C. Allan, and K. W. Koch, "Low-loss hollow-core silica/air photonic bandgap fibre," Nature 424, 657-659 (2003).
[CrossRef] [PubMed]

Koshiba, M.

Li, Y.

Liu, B.

Mangan, B. J.

R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. S. J. Russell, P. J. Roberts, and D. C. Allan, "Single-mode photonic band gap guidance of light in air," Science 285, 1537-1539 (1999).
[CrossRef] [PubMed]

Mortensen, N. A.

Müller, D.

C. M. Smith, N. Venkataraman, M. T. Gallagher, D. Müller, J. A. West, N. F. Borrelli, D. C. Allan, and K. W. Koch, "Low-loss hollow-core silica/air photonic bandgap fibre," Nature 424, 657-659 (2003).
[CrossRef] [PubMed]

Poli, F.

L. Vincetti, F. Poli, and S. Selleri, "Confinement loss and nonlinearity analysis of air-guiding modified honeycomb photonic bandgap fibers," IEEE Photon. Technol. Lett. 18, 508-510 (2006).
[CrossRef]

Roberts, P. J.

R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. S. J. Russell, P. J. Roberts, and D. C. Allan, "Single-mode photonic band gap guidance of light in air," Science 285, 1537-1539 (1999).
[CrossRef] [PubMed]

T. A. Birks, P. J. Roberts, P. S. J. Russell, D. M. Atkin, and T. J. Shepherd, "Full 2-D photonic bandgaps in silica/air structures," Electron. Lett. 31, 1941-1943 (1995).
[CrossRef]

Russell, P. S. J.

R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. S. J. Russell, P. J. Roberts, and D. C. Allan, "Single-mode photonic band gap guidance of light in air," Science 285, 1537-1539 (1999).
[CrossRef] [PubMed]

J. Broeng, S. E. Barkou, A. Bjarklev, J. C. Knight, T. A. Birks, and P. S. J. Russell, "Highly increased photonic band gaps in silica/air structures," Opt. Commun. 156, 240-244 (1998).
[CrossRef]

T. A. Birks, P. J. Roberts, P. S. J. Russell, D. M. Atkin, and T. J. Shepherd, "Full 2-D photonic bandgaps in silica/air structures," Electron. Lett. 31, 1941-1943 (1995).
[CrossRef]

Saitoh, K.

Selleri, S.

L. Vincetti, F. Poli, and S. Selleri, "Confinement loss and nonlinearity analysis of air-guiding modified honeycomb photonic bandgap fibers," IEEE Photon. Technol. Lett. 18, 508-510 (2006).
[CrossRef]

Shepherd, T. J.

T. A. Birks, P. J. Roberts, P. S. J. Russell, D. M. Atkin, and T. J. Shepherd, "Full 2-D photonic bandgaps in silica/air structures," Electron. Lett. 31, 1941-1943 (1995).
[CrossRef]

Shin, J.

H. K. Kim, J. Shin, S. Fan, M. J. F. Digonnet, and G. S. Kino, "Designing air-core photonic bandgap fibers free of surface modes," IEEE J. Quantum Electron. 40, 551-556 (2004).
[CrossRef]

Shum, P.

M. Yan and P. Shum, "Air guiding with honeycomb photonic bandgap fiber," IEEE Photon. Technol. Lett. 17, 64-66 (2005).
[CrossRef]

M. Yan, P. Shum, and J. Hu, "Design of air-guiding honeycomb photonic bandgap fiber," Opt. Lett. 30, 465-467 (2005).
[CrossRef] [PubMed]

Smith, C. M.

C. M. Smith, N. Venkataraman, M. T. Gallagher, D. Müller, J. A. West, N. F. Borrelli, D. C. Allan, and K. W. Koch, "Low-loss hollow-core silica/air photonic bandgap fibre," Nature 424, 657-659 (2003).
[CrossRef] [PubMed]

Sun, X.

Venkataraman, N.

C. M. Smith, N. Venkataraman, M. T. Gallagher, D. Müller, J. A. West, N. F. Borrelli, D. C. Allan, and K. W. Koch, "Low-loss hollow-core silica/air photonic bandgap fibre," Nature 424, 657-659 (2003).
[CrossRef] [PubMed]

Vincetti, L.

L. Vincetti, F. Poli, and S. Selleri, "Confinement loss and nonlinearity analysis of air-guiding modified honeycomb photonic bandgap fibers," IEEE Photon. Technol. Lett. 18, 508-510 (2006).
[CrossRef]

Wang, C.

West, J. A.

C. M. Smith, N. Venkataraman, M. T. Gallagher, D. Müller, J. A. West, N. F. Borrelli, D. C. Allan, and K. W. Koch, "Low-loss hollow-core silica/air photonic bandgap fibre," Nature 424, 657-659 (2003).
[CrossRef] [PubMed]

Yan, M.

M. Yan and P. Shum, "Air guiding with honeycomb photonic bandgap fiber," IEEE Photon. Technol. Lett. 17, 64-66 (2005).
[CrossRef]

M. Yan, P. Shum, and J. Hu, "Design of air-guiding honeycomb photonic bandgap fiber," Opt. Lett. 30, 465-467 (2005).
[CrossRef] [PubMed]

Yu, R.

M. Chen and R. Yu, "Analysis of photonic bandgaps in modified honeycomb structures," IEEE Photon. Technol. Lett. 16, 819-821 (2004).
[CrossRef]

Electron. Lett.

T. A. Birks, P. J. Roberts, P. S. J. Russell, D. M. Atkin, and T. J. Shepherd, "Full 2-D photonic bandgaps in silica/air structures," Electron. Lett. 31, 1941-1943 (1995).
[CrossRef]

IEEE J. Quantum Electron.

H. K. Kim, J. Shin, S. Fan, M. J. F. Digonnet, and G. S. Kino, "Designing air-core photonic bandgap fibers free of surface modes," IEEE J. Quantum Electron. 40, 551-556 (2004).
[CrossRef]

K. Saitoh and M. Koshiba, "Full-vectorial imaginary-distance beam propagation method based on finite element scheme: Application to photonic crystal fibers," IEEE J. Quantum Electron. 38, 927-933 (2002).
[CrossRef]

IEEE Photon. Technol. Lett.

M. Yan and P. Shum, "Air guiding with honeycomb photonic bandgap fiber," IEEE Photon. Technol. Lett. 17, 64-66 (2005).
[CrossRef]

M. Chen and R. Yu, "Analysis of photonic bandgaps in modified honeycomb structures," IEEE Photon. Technol. Lett. 16, 819-821 (2004).
[CrossRef]

L. Vincetti, F. Poli, and S. Selleri, "Confinement loss and nonlinearity analysis of air-guiding modified honeycomb photonic bandgap fibers," IEEE Photon. Technol. Lett. 18, 508-510 (2006).
[CrossRef]

J. Lightwave Technol.

Nature

C. M. Smith, N. Venkataraman, M. T. Gallagher, D. Müller, J. A. West, N. F. Borrelli, D. C. Allan, and K. W. Koch, "Low-loss hollow-core silica/air photonic bandgap fibre," Nature 424, 657-659 (2003).
[CrossRef] [PubMed]

Opt. Commun.

J. Broeng, S. E. Barkou, A. Bjarklev, J. C. Knight, T. A. Birks, and P. S. J. Russell, "Highly increased photonic band gaps in silica/air structures," Opt. Commun. 156, 240-244 (1998).
[CrossRef]

Opt. Express

Opt. Lett.

Science

R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. S. J. Russell, P. J. Roberts, and D. C. Allan, "Single-mode photonic band gap guidance of light in air," Science 285, 1537-1539 (1999).
[CrossRef] [PubMed]

Other

S. Selleri, L. Vincetti, F. Poli, A. Cucinotta, and M. Foroni, "Air-guiding photonic crystal fibers with modified honeycomb lattice," in Proceedings of 2005 IEEE/LEOS Workshop on Fibers and Optical Passive Components (WFOPC), 20-25 (2005).

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Figures (10)

Fig. 1.
Fig. 1.

Modified honeycomb lattice, where d is the diameter of air holes in the basic honeycomb lattice, dc is the diameter of extra air-holes in the center of unit cell, Λ is the distance between adjacent air holes, and n 1 = 1.0 and n 2 = 1.45 are the refractive indices of air and silica, respectively.

Fig. 2.
Fig. 2.

PBG diagrams for a modified honeycomb lattice at (a) βΛ = 6.0 and (b) βΛ = 11.0, where d/Λ = 0.60 and dc /Λ = 1.30. The shaded regions represent complete PBGs. (c) PBG diagram in k-β space for a modified honeycomb lattice with d/Λ = 0.60 and dc /Λ = 1.30.

Fig. 3.
Fig. 3.

The spans of the air line over the PBG regions calculated for all the realistic structural parameters. (a) d/Λ = 0.30 to 0.60, (b) d/Λ = 0.65 to 0.85, and (c) d/Λ = 0.90 to 0.98. The solid red line corresponds to the triangular lattice (dc /Λ = d/Λ) and the solid cyan line represents the upper limit of the size of dc /Λ (dc /Λ = 1.96 - d/Λ). Lower order gaps (band 6–7) are represented by blue curves and the others are represented by green curves.

Fig. 4.
Fig. 4.

Cross sections of the proposed modified honeycomb PBGFs with (a) the defected core realized by removing 13 air holes and (b) the defected core realized by removing 7 air holes.

Fig. 5.
Fig. 5.

Dispersion curves for the type-A PBGF with d/Λ = 0.60 and dc /Λ = 1.36. The black solid curves represent PBG region. The fundamental mode is shown in red curve, the second-order mode is shown in blue curve, and the third-order mode is shown in green curve.

Fig. 6.
Fig. 6.

Surface plots for the x-component of the electric field distribution |Ex | for (a) the x-polarized HE11 and (b) the TE01 modes for type-A PBGF with d/Λ = 0.60, dc /Λ = 1.36, and Λ = 1.747 μm at a wavelength of 1.55 μm.

Fig. 7.
Fig. 7.

Confinement losses of the type-A PBGF with d/Λ = 0.60, dc /Λ = 1.36, and Λ = 1.747 μm for (a) six cell rings and (b) ten cell rings. Red, blue, and green curves correspond to the confinement losses for the fundamental, second-order, and third-order modes, respectively.

Fig. 8.
Fig. 8.

Dispersion curves for the type-B PBGF with d/Λ = 0.60 and dc /Λ = 1.36. The black solid curves represent PBG region. The fundamental mode is shown in red curve and the second-order mode is shown in blue curve.

Fig. 9.
Fig. 9.

Surface plots for the x-component of the electric field distribution |Ex | for (a) the x-polarized HE11 and (b) the TE01 modes for type-B PBGF with d/Λ = 0.60, dc /Λ = 1.36, and Λ = 1.747 μm at a wavelength of 1.55 μm.

Fig. 10.
Fig. 10.

Confinement losses of the type-B PBGF with d/Λ = 0.60, dc /Λ = 1.36, and Λ = 1.747 μm for (a) six cell rings and (b) ten cell rings. Red and blue curves correspond to the confinement losses for the fundamental and second-order modes, respectively.

Equations (2)

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W = k 1 Λ k 2 Λ k 1 Λ + k 2 Λ ,
confinement loss = 8.686 Im [ β ] ,

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