Abstract

We characterize coupling between two identical collinear hollow-core Bragg fibers, assuming a TE01 launching condition. Using a multipole method and a finite-element method, we have investigated the dependence of the beat length between supermodes of the coupled fibers and supermode radiation losses as a function of the interfiber separation, the fiber core radius, and the index of the cladding. We established that coupling is maximal when the fibers are touching each other and decreases dramatically during the first hundreds of nanometers of separation. However, residual coupling with the strength proportional to the fiber radiation loss decreased over a long range as an inverse square root of the interfiber separation and exhibited periodic variation with interfiber separation. Finally, we considered coupling between the TE01 modes with a view to designing a directional coupler. We found that for fibers with large enough core radii one can identify broad frequency ranges in which the intermodal coupling strength exceeds supermode radiation losses by 1 order of magnitude, thus opening the possibility of building a directional coupler. We attribute such unusually strong intermode coupling both to the resonant effects in the intermirror cavity and to proximity interaction between the leaky modes localized in the mirror.

© 2004 Optical Society of America

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References

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  1. C. M. Smith, N. Venkataraman, M. T. Gallagher, D. Muller, J. A. West, N. F. Borrelli, D. C. Allan, and K. W. Koch, “Low-loss hollow-core silica/air photonic bandgap fibre,” Nature (London) 424, 657–659 (2003).
    [CrossRef]
  2. B. Temelkuran, S. D. Hart, G. Benoit, J. D. Joannopoulos, and Y. Fink, “Wavelength-scalable hollow optical fibres with large photonic bandgaps for CO2 laser transmission,” Nature (London) 420, 650–653 (2002).
    [CrossRef]
  3. M. A. van Eijkelenborg, A. Argyros, G. Barton, I. M. Bassett, M. Fellew, G. Henry, N. A. Issa, M. C. J. Large, S. Manos, W. Padden, L. Poladian, and J. Zagari, “Recent progress in microstructured polymer optical fibre fabrication and characterisation,” Opt. Fiber Technol. 9, 199–209 (2003).
    [CrossRef]
  4. B. H. Lee, J. B. Eom, J. Kim, D. S. Moon, U.-C. Paek, and G.-H. Yang, “Photonic crystal fiber coupler,” Opt. Lett. 27, 812–814 (2002).
    [CrossRef]
  5. G. Kakarantzas, B. J. Mangan, T. A. Birks, J. C. Knight, and P. St. J. Russell, “Directional coupling in a twin core photonic crystal fiber using heat treatment,” in Conference on Lasers and Electro-Optics, Vol. 56 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2001), pp. 599–600.
  6. M. Kristensen, “Mode-coupling in photonic crystal fibers with multiple cores,” in Conference on Lasers and Electro-optics (Washington, D.C., 2000).
  7. B. J. Mangan, J. C. Knight, T. A. Birks, P. St. J. Russell, and A. H. Greenaway, “Experimental study of dualcore photonic crystal fibre,” Electron. Lett. 36, 1358–1359 (2000).
    [CrossRef]
  8. K. Saitoh, Y. Sato, and M. Koshiba, “Coupling characteristics of dual-core photonic crystal fiber couplers,” Opt. Express 11, 3188–3195 (2003), http://www.opticsexpress.org.
    [CrossRef] [PubMed]
  9. L. Zhang and C. Yang, “Polarization splitter based on photonic crystal fibers,” Opt. Express 11, 1015–1020 (2003), http://www.opticsexpress.org.
    [CrossRef] [PubMed]
  10. K. Saitoh and M. Koshiba, “Full-vectorial imaginary-distance beam propagation method based on a finite element scheme: application to photonic crystal fibers,” IEEE J. Quantum Electron. 38, 927–933 (2002).
    [CrossRef]
  11. F. Fogli, L. Saccomandi, P. Bassi, G. Bellanca, and S. Trillo, “Full vectorial BPM modeling of indexguiding photonic crystal fibers and couplers,” Opt. Express 10, 54–59 (2002), http://www.opticsexpress.org.
    [CrossRef] [PubMed]
  12. S. G. Johnson, M. Ibanescu, M. Skorobogatiy, O. Weisberg, T. D. Engeness, M. Soljačić, S. A. Jacobs, J. D. Joannopoulos, and Y. Fink, “Low-loss asymptotically single-mode propagation in large-core OmniGuide fibers,” Opt. Express 9, 748–779 (2001), www.opticsexpress.org.
    [CrossRef] [PubMed]
  13. T. P. White, B. T. Kuhlmey, R. C. McPhedran, D. Maystre, G. C. Martijn de Sterke, and L. C. Botten, “Multipole method for microstructured optical fibers. I. Formulation,” J. Opt. Soc. Am. B 19, 2322–2330 (2002).
    [CrossRef]
  14. R. A. Minasian, K. E. Alameh, and E. H. W. Chan, “Photonics-based interference mitigation filters,” IEEE Trans. Microwave Theory Tech. 49, 1894–1899 (2001).
    [CrossRef]
  15. P. Yeh, A. Yariv, and E. Marom, “Theory of Bragg fiber,” J. Opt. Soc. Am. 68, 1196–1201 (1978).
    [CrossRef]

2003 (4)

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

M. A. van Eijkelenborg, A. Argyros, G. Barton, I. M. Bassett, M. Fellew, G. Henry, N. A. Issa, M. C. J. Large, S. Manos, W. Padden, L. Poladian, and J. Zagari, “Recent progress in microstructured polymer optical fibre fabrication and characterisation,” Opt. Fiber Technol. 9, 199–209 (2003).
[CrossRef]

L. Zhang and C. Yang, “Polarization splitter based on photonic crystal fibers,” Opt. Express 11, 1015–1020 (2003), http://www.opticsexpress.org.
[CrossRef] [PubMed]

K. Saitoh, Y. Sato, and M. Koshiba, “Coupling characteristics of dual-core photonic crystal fiber couplers,” Opt. Express 11, 3188–3195 (2003), http://www.opticsexpress.org.
[CrossRef] [PubMed]

2002 (5)

2001 (2)

2000 (1)

B. J. Mangan, J. C. Knight, T. A. Birks, P. St. J. Russell, and A. H. Greenaway, “Experimental study of dualcore photonic crystal fibre,” Electron. Lett. 36, 1358–1359 (2000).
[CrossRef]

1978 (1)

Alameh, K. E.

R. A. Minasian, K. E. Alameh, and E. H. W. Chan, “Photonics-based interference mitigation filters,” IEEE Trans. Microwave Theory Tech. 49, 1894–1899 (2001).
[CrossRef]

Allan, D. C.

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

Argyros, A.

M. A. van Eijkelenborg, A. Argyros, G. Barton, I. M. Bassett, M. Fellew, G. Henry, N. A. Issa, M. C. J. Large, S. Manos, W. Padden, L. Poladian, and J. Zagari, “Recent progress in microstructured polymer optical fibre fabrication and characterisation,” Opt. Fiber Technol. 9, 199–209 (2003).
[CrossRef]

Barton, G.

M. A. van Eijkelenborg, A. Argyros, G. Barton, I. M. Bassett, M. Fellew, G. Henry, N. A. Issa, M. C. J. Large, S. Manos, W. Padden, L. Poladian, and J. Zagari, “Recent progress in microstructured polymer optical fibre fabrication and characterisation,” Opt. Fiber Technol. 9, 199–209 (2003).
[CrossRef]

Bassett, I. M.

M. A. van Eijkelenborg, A. Argyros, G. Barton, I. M. Bassett, M. Fellew, G. Henry, N. A. Issa, M. C. J. Large, S. Manos, W. Padden, L. Poladian, and J. Zagari, “Recent progress in microstructured polymer optical fibre fabrication and characterisation,” Opt. Fiber Technol. 9, 199–209 (2003).
[CrossRef]

Bassi, P.

Bellanca, G.

Benoit, G.

B. Temelkuran, S. D. Hart, G. Benoit, J. D. Joannopoulos, and Y. Fink, “Wavelength-scalable hollow optical fibres with large photonic bandgaps for CO2 laser transmission,” Nature (London) 420, 650–653 (2002).
[CrossRef]

Birks, T. A.

B. J. Mangan, J. C. Knight, T. A. Birks, P. St. J. Russell, and A. H. Greenaway, “Experimental study of dualcore photonic crystal fibre,” Electron. Lett. 36, 1358–1359 (2000).
[CrossRef]

Borrelli, N. F.

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

Botten, L. C.

Chan, E. H. W.

R. A. Minasian, K. E. Alameh, and E. H. W. Chan, “Photonics-based interference mitigation filters,” IEEE Trans. Microwave Theory Tech. 49, 1894–1899 (2001).
[CrossRef]

Engeness, T. D.

Eom, J. B.

Fellew, M.

M. A. van Eijkelenborg, A. Argyros, G. Barton, I. M. Bassett, M. Fellew, G. Henry, N. A. Issa, M. C. J. Large, S. Manos, W. Padden, L. Poladian, and J. Zagari, “Recent progress in microstructured polymer optical fibre fabrication and characterisation,” Opt. Fiber Technol. 9, 199–209 (2003).
[CrossRef]

Fink, Y.

B. Temelkuran, S. D. Hart, G. Benoit, J. D. Joannopoulos, and Y. Fink, “Wavelength-scalable hollow optical fibres with large photonic bandgaps for CO2 laser transmission,” Nature (London) 420, 650–653 (2002).
[CrossRef]

S. G. Johnson, M. Ibanescu, M. Skorobogatiy, O. Weisberg, T. D. Engeness, M. Soljačić, S. A. Jacobs, J. D. Joannopoulos, and Y. Fink, “Low-loss asymptotically single-mode propagation in large-core OmniGuide fibers,” Opt. Express 9, 748–779 (2001), www.opticsexpress.org.
[CrossRef] [PubMed]

Fogli, F.

Gallagher, M. T.

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

Greenaway, A. H.

B. J. Mangan, J. C. Knight, T. A. Birks, P. St. J. Russell, and A. H. Greenaway, “Experimental study of dualcore photonic crystal fibre,” Electron. Lett. 36, 1358–1359 (2000).
[CrossRef]

Hart, S. D.

B. Temelkuran, S. D. Hart, G. Benoit, J. D. Joannopoulos, and Y. Fink, “Wavelength-scalable hollow optical fibres with large photonic bandgaps for CO2 laser transmission,” Nature (London) 420, 650–653 (2002).
[CrossRef]

Henry, G.

M. A. van Eijkelenborg, A. Argyros, G. Barton, I. M. Bassett, M. Fellew, G. Henry, N. A. Issa, M. C. J. Large, S. Manos, W. Padden, L. Poladian, and J. Zagari, “Recent progress in microstructured polymer optical fibre fabrication and characterisation,” Opt. Fiber Technol. 9, 199–209 (2003).
[CrossRef]

Ibanescu, M.

Issa, N. A.

M. A. van Eijkelenborg, A. Argyros, G. Barton, I. M. Bassett, M. Fellew, G. Henry, N. A. Issa, M. C. J. Large, S. Manos, W. Padden, L. Poladian, and J. Zagari, “Recent progress in microstructured polymer optical fibre fabrication and characterisation,” Opt. Fiber Technol. 9, 199–209 (2003).
[CrossRef]

Jacobs, S. A.

Joannopoulos, J. D.

B. Temelkuran, S. D. Hart, G. Benoit, J. D. Joannopoulos, and Y. Fink, “Wavelength-scalable hollow optical fibres with large photonic bandgaps for CO2 laser transmission,” Nature (London) 420, 650–653 (2002).
[CrossRef]

S. G. Johnson, M. Ibanescu, M. Skorobogatiy, O. Weisberg, T. D. Engeness, M. Soljačić, S. A. Jacobs, J. D. Joannopoulos, and Y. Fink, “Low-loss asymptotically single-mode propagation in large-core OmniGuide fibers,” Opt. Express 9, 748–779 (2001), www.opticsexpress.org.
[CrossRef] [PubMed]

Johnson, S. G.

Kim, J.

Knight, J. C.

B. J. Mangan, J. C. Knight, T. A. Birks, P. St. J. Russell, and A. H. Greenaway, “Experimental study of dualcore photonic crystal fibre,” Electron. Lett. 36, 1358–1359 (2000).
[CrossRef]

Koch, K. W.

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

Koshiba, M.

K. Saitoh, Y. Sato, and M. Koshiba, “Coupling characteristics of dual-core photonic crystal fiber couplers,” Opt. Express 11, 3188–3195 (2003), http://www.opticsexpress.org.
[CrossRef] [PubMed]

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

Kuhlmey, B. T.

Large, M. C. J.

M. A. van Eijkelenborg, A. Argyros, G. Barton, I. M. Bassett, M. Fellew, G. Henry, N. A. Issa, M. C. J. Large, S. Manos, W. Padden, L. Poladian, and J. Zagari, “Recent progress in microstructured polymer optical fibre fabrication and characterisation,” Opt. Fiber Technol. 9, 199–209 (2003).
[CrossRef]

Lee, B. H.

Mangan, B. J.

B. J. Mangan, J. C. Knight, T. A. Birks, P. St. J. Russell, and A. H. Greenaway, “Experimental study of dualcore photonic crystal fibre,” Electron. Lett. 36, 1358–1359 (2000).
[CrossRef]

Manos, S.

M. A. van Eijkelenborg, A. Argyros, G. Barton, I. M. Bassett, M. Fellew, G. Henry, N. A. Issa, M. C. J. Large, S. Manos, W. Padden, L. Poladian, and J. Zagari, “Recent progress in microstructured polymer optical fibre fabrication and characterisation,” Opt. Fiber Technol. 9, 199–209 (2003).
[CrossRef]

Marom, E.

Martijn de Sterke, G. C.

Maystre, D.

McPhedran, R. C.

Minasian, R. A.

R. A. Minasian, K. E. Alameh, and E. H. W. Chan, “Photonics-based interference mitigation filters,” IEEE Trans. Microwave Theory Tech. 49, 1894–1899 (2001).
[CrossRef]

Moon, D. S.

Muller, D.

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

Padden, W.

M. A. van Eijkelenborg, A. Argyros, G. Barton, I. M. Bassett, M. Fellew, G. Henry, N. A. Issa, M. C. J. Large, S. Manos, W. Padden, L. Poladian, and J. Zagari, “Recent progress in microstructured polymer optical fibre fabrication and characterisation,” Opt. Fiber Technol. 9, 199–209 (2003).
[CrossRef]

Paek, U.-C.

Poladian, L.

M. A. van Eijkelenborg, A. Argyros, G. Barton, I. M. Bassett, M. Fellew, G. Henry, N. A. Issa, M. C. J. Large, S. Manos, W. Padden, L. Poladian, and J. Zagari, “Recent progress in microstructured polymer optical fibre fabrication and characterisation,” Opt. Fiber Technol. 9, 199–209 (2003).
[CrossRef]

Russell, P. St. J.

B. J. Mangan, J. C. Knight, T. A. Birks, P. St. J. Russell, and A. H. Greenaway, “Experimental study of dualcore photonic crystal fibre,” Electron. Lett. 36, 1358–1359 (2000).
[CrossRef]

Saccomandi, L.

Saitoh, K.

K. Saitoh, Y. Sato, and M. Koshiba, “Coupling characteristics of dual-core photonic crystal fiber couplers,” Opt. Express 11, 3188–3195 (2003), http://www.opticsexpress.org.
[CrossRef] [PubMed]

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

Sato, Y.

Skorobogatiy, M.

Smith, C. M.

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

Soljacic, M.

Temelkuran, B.

B. Temelkuran, S. D. Hart, G. Benoit, J. D. Joannopoulos, and Y. Fink, “Wavelength-scalable hollow optical fibres with large photonic bandgaps for CO2 laser transmission,” Nature (London) 420, 650–653 (2002).
[CrossRef]

Trillo, S.

van Eijkelenborg, M. A.

M. A. van Eijkelenborg, A. Argyros, G. Barton, I. M. Bassett, M. Fellew, G. Henry, N. A. Issa, M. C. J. Large, S. Manos, W. Padden, L. Poladian, and J. Zagari, “Recent progress in microstructured polymer optical fibre fabrication and characterisation,” Opt. Fiber Technol. 9, 199–209 (2003).
[CrossRef]

Venkataraman, N.

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

Weisberg, O.

West, J. A.

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

White, T. P.

Yang, C.

Yang, G.-H.

Yariv, A.

Yeh, P.

Zagari, J.

M. A. van Eijkelenborg, A. Argyros, G. Barton, I. M. Bassett, M. Fellew, G. Henry, N. A. Issa, M. C. J. Large, S. Manos, W. Padden, L. Poladian, and J. Zagari, “Recent progress in microstructured polymer optical fibre fabrication and characterisation,” Opt. Fiber Technol. 9, 199–209 (2003).
[CrossRef]

Zhang, L.

Electron. Lett. (1)

B. J. Mangan, J. C. Knight, T. A. Birks, P. St. J. Russell, and A. H. Greenaway, “Experimental study of dualcore photonic crystal fibre,” Electron. Lett. 36, 1358–1359 (2000).
[CrossRef]

IEEE J. Quantum Electron. (1)

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

IEEE Trans. Microwave Theory Tech. (1)

R. A. Minasian, K. E. Alameh, and E. H. W. Chan, “Photonics-based interference mitigation filters,” IEEE Trans. Microwave Theory Tech. 49, 1894–1899 (2001).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. B (1)

Nature (London) (2)

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

B. Temelkuran, S. D. Hart, G. Benoit, J. D. Joannopoulos, and Y. Fink, “Wavelength-scalable hollow optical fibres with large photonic bandgaps for CO2 laser transmission,” Nature (London) 420, 650–653 (2002).
[CrossRef]

Opt. Express (4)

Opt. Fiber Technol. (1)

M. A. van Eijkelenborg, A. Argyros, G. Barton, I. M. Bassett, M. Fellew, G. Henry, N. A. Issa, M. C. J. Large, S. Manos, W. Padden, L. Poladian, and J. Zagari, “Recent progress in microstructured polymer optical fibre fabrication and characterisation,” Opt. Fiber Technol. 9, 199–209 (2003).
[CrossRef]

Opt. Lett. (1)

Other (2)

G. Kakarantzas, B. J. Mangan, T. A. Birks, J. C. Knight, and P. St. J. Russell, “Directional coupling in a twin core photonic crystal fiber using heat treatment,” in Conference on Lasers and Electro-Optics, Vol. 56 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2001), pp. 599–600.

M. Kristensen, “Mode-coupling in photonic crystal fibers with multiple cores,” in Conference on Lasers and Electro-optics (Washington, D.C., 2000).

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Figures (6)

Fig. 1
Fig. 1

Schematics of the two identical collinear hollow Bragg fibers separated by intermirror distance d. The Dielectric profile along the interfiber center line resembles a one-dimensional Bragg grating with a central defect corresponding to the intermirror cavity.

Fig. 2
Fig. 2

Normalized coupling strength |Re(δβ)|/Im(βTE) and supermode radiation losses Im(β+)/Im(βTE) and Im(β-)/Im(βTE) in a system of two collinear hollow Bragg fibers as a function of intermirror separation d. The cladding index is the same as the core index: nc=nclad. All the curves are normalized by the radiation losses of the TE01 mode of a stand-alone hollow Bragg fiber.

Fig. 3
Fig. 3

Normalized coupling strength and supermode radiation losses of coupled hollow Bragg fibers as a function of intermirror fiber separation d. The cladding index is the same as the core index: nc=nclad. Bragg fibers of three core radii are studied: solid curves, Rc=10 µm; dashed curves, Rc=15 µm; dotted curves, Rc=20 µm. At the left is a blowup of the region where fibers nearly touch (0.2 µm<d<1 µm), showing a dramatic increase in the fiber coupling compared to the almost constant radiation losses of the supermodes.

Fig. 4
Fig. 4

Normalized coupling strength and supermode radiation losses of coupled hollow Bragg fibers as a function of intermirror fiber separation d near second resonance. The cladding index is larger than the core index: nclad=1.3, nc=1. Bragg fibers of three core radii are shown: solid curves, Rc=5 µm; dashed curves, Rc=10 µm; dotted curves, Rc=20 µm. The maximum of the coupling strength slowly decreases as the fiber core radius increases.

Fig. 5
Fig. 5

Normalized coupling strength and supermode radiation losses as a function of fiber core radii Rc at λ=1.45 µm. With increasing core radius one observes a tendency for a gradual increase of the coupling strength relative to the highest radiation loss of the supermodes.

Fig. 6
Fig. 6

Normalized coupling strength and supermode radiation losses as functions of wave-length λ for Rc=15 µm and interfiber separations d=0, 0.2, 0.5 µm. Dotted curve, Im(βTE01); solid curve below dotted curve, Im(β-); solid curve with filled circles, Im(β+); solid curve above dotted curve, |Re(δβ)|.

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