Abstract

In this study, a Gaussian amp function related to the Gaussian family is employed to approximate the output intensity profile of various arrangements of air holes in photonic crystal fibers (PCFs) with a fixed number of air rings (N=4). It is shown that d/Λ=0.5 can be the best minimum value of air-filling fraction for all of the studied PCFs when λ=1.35μm, whereas, for λ=1.55 and 1.65 μm, d/Λ=0.6 is suitable for achieving the maximum output intensity with very low confinement loss.

© 2014 Optical Society of America

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  1. H. Demir and S. Ozsoy, “Large-solid-core square-lattice photonic crystal fibers,” Opt. Fiber Technol. 17, 594–600 (2011).
    [CrossRef]
  2. S. Kunimasa and K. Masanori, “Numerical modeling of photonic crystal fibers,” J. Lightwave Technol. 23, 3580–3590 (2005).
    [CrossRef]
  3. J. C. Knight, T. A. Birks, P. St. J. Russell, and R. F. Cregan, “Large mode area photonic crystal fiber,” Electron. Lett. 34, 1347–1348 (1998).
    [CrossRef]
  4. J. C. Knight, T. A. Birks, P. St. J. Russell, and D. M. Atkin, “All-silica single-mode optical fiber with photonic crystal cladding,” Opt. Lett. 21, 1547–1549 (1996).
    [CrossRef]
  5. F. Begum and Y. Namihira, “Photonic crystal fiber for medical applications,” in The Recent Progress in Optical Fiber Research, M. Yasin, ed. (In Tech, 2012), pp. 230–246.
  6. S. Olyaee and F. Taghipour, “Design of new square-lattice photonic crystal fibers for optical communication applications,” Inter. J. Phys. Sci. 6, 4405–4411 (2011).
  7. M. N. Hoque, A. Sayeem, and N. Akter, “Octagonal photonic crystal fibers: application to ultra-flattened dispersion,” Australian J. Basic Appl. Sci. 4, 2274–2279 (2010).
  8. H. Demir and S. Ozsoy, “A theoretical study of large solid-core square-lattice silica photonic crystal fibers with square air-holes,” Opt. Mater. 35, 205–210 (2012).
  9. H. Demir and S. Ozsoy, “Solid-core square-lattice photonic crystal fibers: comparative studies of the single-mode regime and numerical aperture for circular and square air-holes,” Opt. Quantum Electron. 42, 851–862 (2011).
    [CrossRef]
  10. N. Ding, H. Lihong, L. Yumin, and Y. Zhongyuan, “Investigation of the index profile of photonic crystal fibers on dispersion characteristics,” in Proceedings of IEEE Conference on Photonics and Optoelectronics (IEEE, 2010).
  11. S. A. Bopart, B. E. Bonma, C. Pitris, J. F. Southern, M. E. Brezinski, and J. G. Fujimoto, “In vivo cellular optical coherence tomography imaging,” Nat. Med. 4, 861–865 (1998).
    [CrossRef]
  12. J. H. Lee, E. J. Jung, and C. Kim, “Incoherent, CW supercontinuum source based on erbium fiber ASE for optical coherence tomography imaging,” in Proceedings of IEEE Conference on OptoEelectronics and Communication (IEEE, 2009), paper FD3.
  13. T. Hirooka, Y. Hori, and M. Nakazawa, “Gaussian and Sech approximations of mode field profiles in photonic crystal fibers,” IEEE Photon. Technol. Lett. 16, 1071–1073 (2004).
    [CrossRef]
  14. L. Zhang, Z. Wu, S. Gao, and M. Cui, “Study of a constructed function for approximating mode field in photonic crystal fiber,” Opt. Eng. 51, 065003 (2012).
    [CrossRef]
  15. A. Zendehnam, M. Mirzaei, and R. Solgi, “Confinement loss and G.V.D for HF and AHAOF by FEM,” Int. J. Opt. Appl. 2, 34–37 (2012).
    [CrossRef]
  16. M. Hosseinpour, “Investigation of different arrangements on loss and GVD in photonic crystal optical fibers and study of distribution function in them,” M.S. thesis (Physics Department, Science Faculty, Arak University, 2013).
  17. J. T. Verdeyen, “Laser electron.,” Science 2, 69–70 (1995).
  18. M. Hosseinpour and A. Zendehnam, Department of Physics, Science Faculty, University of Arak, Arak, Iran, are preparing a manuscript to be called “Study of PCF’s output intensity profiles with various configurations for low d/Λ values.”
  19. W. Math World, “Gaussian function,” http://mathworld.wolfram.com/GaussianFunction.html .
  20. F. Stutzki, F. Jansen, C. Jauregui, J. Limpert, and A. Tünnermann, “Non-hexagonal large-pitch fibers for enhanced mode discrimination,” Opt. Express 19, 12081–12086 (2011).
    [CrossRef]

2012 (3)

H. Demir and S. Ozsoy, “A theoretical study of large solid-core square-lattice silica photonic crystal fibers with square air-holes,” Opt. Mater. 35, 205–210 (2012).

L. Zhang, Z. Wu, S. Gao, and M. Cui, “Study of a constructed function for approximating mode field in photonic crystal fiber,” Opt. Eng. 51, 065003 (2012).
[CrossRef]

A. Zendehnam, M. Mirzaei, and R. Solgi, “Confinement loss and G.V.D for HF and AHAOF by FEM,” Int. J. Opt. Appl. 2, 34–37 (2012).
[CrossRef]

2011 (4)

H. Demir and S. Ozsoy, “Large-solid-core square-lattice photonic crystal fibers,” Opt. Fiber Technol. 17, 594–600 (2011).
[CrossRef]

H. Demir and S. Ozsoy, “Solid-core square-lattice photonic crystal fibers: comparative studies of the single-mode regime and numerical aperture for circular and square air-holes,” Opt. Quantum Electron. 42, 851–862 (2011).
[CrossRef]

S. Olyaee and F. Taghipour, “Design of new square-lattice photonic crystal fibers for optical communication applications,” Inter. J. Phys. Sci. 6, 4405–4411 (2011).

F. Stutzki, F. Jansen, C. Jauregui, J. Limpert, and A. Tünnermann, “Non-hexagonal large-pitch fibers for enhanced mode discrimination,” Opt. Express 19, 12081–12086 (2011).
[CrossRef]

2010 (1)

M. N. Hoque, A. Sayeem, and N. Akter, “Octagonal photonic crystal fibers: application to ultra-flattened dispersion,” Australian J. Basic Appl. Sci. 4, 2274–2279 (2010).

2005 (1)

2004 (1)

T. Hirooka, Y. Hori, and M. Nakazawa, “Gaussian and Sech approximations of mode field profiles in photonic crystal fibers,” IEEE Photon. Technol. Lett. 16, 1071–1073 (2004).
[CrossRef]

1998 (2)

S. A. Bopart, B. E. Bonma, C. Pitris, J. F. Southern, M. E. Brezinski, and J. G. Fujimoto, “In vivo cellular optical coherence tomography imaging,” Nat. Med. 4, 861–865 (1998).
[CrossRef]

J. C. Knight, T. A. Birks, P. St. J. Russell, and R. F. Cregan, “Large mode area photonic crystal fiber,” Electron. Lett. 34, 1347–1348 (1998).
[CrossRef]

1996 (1)

1995 (1)

J. T. Verdeyen, “Laser electron.,” Science 2, 69–70 (1995).

Akter, N.

M. N. Hoque, A. Sayeem, and N. Akter, “Octagonal photonic crystal fibers: application to ultra-flattened dispersion,” Australian J. Basic Appl. Sci. 4, 2274–2279 (2010).

Atkin, D. M.

Begum, F.

F. Begum and Y. Namihira, “Photonic crystal fiber for medical applications,” in The Recent Progress in Optical Fiber Research, M. Yasin, ed. (In Tech, 2012), pp. 230–246.

Birks, T. A.

J. C. Knight, T. A. Birks, P. St. J. Russell, and R. F. Cregan, “Large mode area photonic crystal fiber,” Electron. Lett. 34, 1347–1348 (1998).
[CrossRef]

J. C. Knight, T. A. Birks, P. St. J. Russell, and D. M. Atkin, “All-silica single-mode optical fiber with photonic crystal cladding,” Opt. Lett. 21, 1547–1549 (1996).
[CrossRef]

Bonma, B. E.

S. A. Bopart, B. E. Bonma, C. Pitris, J. F. Southern, M. E. Brezinski, and J. G. Fujimoto, “In vivo cellular optical coherence tomography imaging,” Nat. Med. 4, 861–865 (1998).
[CrossRef]

Bopart, S. A.

S. A. Bopart, B. E. Bonma, C. Pitris, J. F. Southern, M. E. Brezinski, and J. G. Fujimoto, “In vivo cellular optical coherence tomography imaging,” Nat. Med. 4, 861–865 (1998).
[CrossRef]

Brezinski, M. E.

S. A. Bopart, B. E. Bonma, C. Pitris, J. F. Southern, M. E. Brezinski, and J. G. Fujimoto, “In vivo cellular optical coherence tomography imaging,” Nat. Med. 4, 861–865 (1998).
[CrossRef]

Cregan, R. F.

J. C. Knight, T. A. Birks, P. St. J. Russell, and R. F. Cregan, “Large mode area photonic crystal fiber,” Electron. Lett. 34, 1347–1348 (1998).
[CrossRef]

Cui, M.

L. Zhang, Z. Wu, S. Gao, and M. Cui, “Study of a constructed function for approximating mode field in photonic crystal fiber,” Opt. Eng. 51, 065003 (2012).
[CrossRef]

Demir, H.

H. Demir and S. Ozsoy, “A theoretical study of large solid-core square-lattice silica photonic crystal fibers with square air-holes,” Opt. Mater. 35, 205–210 (2012).

H. Demir and S. Ozsoy, “Large-solid-core square-lattice photonic crystal fibers,” Opt. Fiber Technol. 17, 594–600 (2011).
[CrossRef]

H. Demir and S. Ozsoy, “Solid-core square-lattice photonic crystal fibers: comparative studies of the single-mode regime and numerical aperture for circular and square air-holes,” Opt. Quantum Electron. 42, 851–862 (2011).
[CrossRef]

Ding, N.

N. Ding, H. Lihong, L. Yumin, and Y. Zhongyuan, “Investigation of the index profile of photonic crystal fibers on dispersion characteristics,” in Proceedings of IEEE Conference on Photonics and Optoelectronics (IEEE, 2010).

Fujimoto, J. G.

S. A. Bopart, B. E. Bonma, C. Pitris, J. F. Southern, M. E. Brezinski, and J. G. Fujimoto, “In vivo cellular optical coherence tomography imaging,” Nat. Med. 4, 861–865 (1998).
[CrossRef]

Gao, S.

L. Zhang, Z. Wu, S. Gao, and M. Cui, “Study of a constructed function for approximating mode field in photonic crystal fiber,” Opt. Eng. 51, 065003 (2012).
[CrossRef]

Hirooka, T.

T. Hirooka, Y. Hori, and M. Nakazawa, “Gaussian and Sech approximations of mode field profiles in photonic crystal fibers,” IEEE Photon. Technol. Lett. 16, 1071–1073 (2004).
[CrossRef]

Hoque, M. N.

M. N. Hoque, A. Sayeem, and N. Akter, “Octagonal photonic crystal fibers: application to ultra-flattened dispersion,” Australian J. Basic Appl. Sci. 4, 2274–2279 (2010).

Hori, Y.

T. Hirooka, Y. Hori, and M. Nakazawa, “Gaussian and Sech approximations of mode field profiles in photonic crystal fibers,” IEEE Photon. Technol. Lett. 16, 1071–1073 (2004).
[CrossRef]

Hosseinpour, M.

M. Hosseinpour and A. Zendehnam, Department of Physics, Science Faculty, University of Arak, Arak, Iran, are preparing a manuscript to be called “Study of PCF’s output intensity profiles with various configurations for low d/Λ values.”

M. Hosseinpour, “Investigation of different arrangements on loss and GVD in photonic crystal optical fibers and study of distribution function in them,” M.S. thesis (Physics Department, Science Faculty, Arak University, 2013).

Jansen, F.

Jauregui, C.

Jung, E. J.

J. H. Lee, E. J. Jung, and C. Kim, “Incoherent, CW supercontinuum source based on erbium fiber ASE for optical coherence tomography imaging,” in Proceedings of IEEE Conference on OptoEelectronics and Communication (IEEE, 2009), paper FD3.

Kim, C.

J. H. Lee, E. J. Jung, and C. Kim, “Incoherent, CW supercontinuum source based on erbium fiber ASE for optical coherence tomography imaging,” in Proceedings of IEEE Conference on OptoEelectronics and Communication (IEEE, 2009), paper FD3.

Knight, J. C.

J. C. Knight, T. A. Birks, P. St. J. Russell, and R. F. Cregan, “Large mode area photonic crystal fiber,” Electron. Lett. 34, 1347–1348 (1998).
[CrossRef]

J. C. Knight, T. A. Birks, P. St. J. Russell, and D. M. Atkin, “All-silica single-mode optical fiber with photonic crystal cladding,” Opt. Lett. 21, 1547–1549 (1996).
[CrossRef]

Kunimasa, S.

Lee, J. H.

J. H. Lee, E. J. Jung, and C. Kim, “Incoherent, CW supercontinuum source based on erbium fiber ASE for optical coherence tomography imaging,” in Proceedings of IEEE Conference on OptoEelectronics and Communication (IEEE, 2009), paper FD3.

Lihong, H.

N. Ding, H. Lihong, L. Yumin, and Y. Zhongyuan, “Investigation of the index profile of photonic crystal fibers on dispersion characteristics,” in Proceedings of IEEE Conference on Photonics and Optoelectronics (IEEE, 2010).

Limpert, J.

Masanori, K.

Mirzaei, M.

A. Zendehnam, M. Mirzaei, and R. Solgi, “Confinement loss and G.V.D for HF and AHAOF by FEM,” Int. J. Opt. Appl. 2, 34–37 (2012).
[CrossRef]

Nakazawa, M.

T. Hirooka, Y. Hori, and M. Nakazawa, “Gaussian and Sech approximations of mode field profiles in photonic crystal fibers,” IEEE Photon. Technol. Lett. 16, 1071–1073 (2004).
[CrossRef]

Namihira, Y.

F. Begum and Y. Namihira, “Photonic crystal fiber for medical applications,” in The Recent Progress in Optical Fiber Research, M. Yasin, ed. (In Tech, 2012), pp. 230–246.

Olyaee, S.

S. Olyaee and F. Taghipour, “Design of new square-lattice photonic crystal fibers for optical communication applications,” Inter. J. Phys. Sci. 6, 4405–4411 (2011).

Ozsoy, S.

H. Demir and S. Ozsoy, “A theoretical study of large solid-core square-lattice silica photonic crystal fibers with square air-holes,” Opt. Mater. 35, 205–210 (2012).

H. Demir and S. Ozsoy, “Large-solid-core square-lattice photonic crystal fibers,” Opt. Fiber Technol. 17, 594–600 (2011).
[CrossRef]

H. Demir and S. Ozsoy, “Solid-core square-lattice photonic crystal fibers: comparative studies of the single-mode regime and numerical aperture for circular and square air-holes,” Opt. Quantum Electron. 42, 851–862 (2011).
[CrossRef]

Pitris, C.

S. A. Bopart, B. E. Bonma, C. Pitris, J. F. Southern, M. E. Brezinski, and J. G. Fujimoto, “In vivo cellular optical coherence tomography imaging,” Nat. Med. 4, 861–865 (1998).
[CrossRef]

Russell, P. St. J.

J. C. Knight, T. A. Birks, P. St. J. Russell, and R. F. Cregan, “Large mode area photonic crystal fiber,” Electron. Lett. 34, 1347–1348 (1998).
[CrossRef]

J. C. Knight, T. A. Birks, P. St. J. Russell, and D. M. Atkin, “All-silica single-mode optical fiber with photonic crystal cladding,” Opt. Lett. 21, 1547–1549 (1996).
[CrossRef]

Sayeem, A.

M. N. Hoque, A. Sayeem, and N. Akter, “Octagonal photonic crystal fibers: application to ultra-flattened dispersion,” Australian J. Basic Appl. Sci. 4, 2274–2279 (2010).

Solgi, R.

A. Zendehnam, M. Mirzaei, and R. Solgi, “Confinement loss and G.V.D for HF and AHAOF by FEM,” Int. J. Opt. Appl. 2, 34–37 (2012).
[CrossRef]

Southern, J. F.

S. A. Bopart, B. E. Bonma, C. Pitris, J. F. Southern, M. E. Brezinski, and J. G. Fujimoto, “In vivo cellular optical coherence tomography imaging,” Nat. Med. 4, 861–865 (1998).
[CrossRef]

Stutzki, F.

Taghipour, F.

S. Olyaee and F. Taghipour, “Design of new square-lattice photonic crystal fibers for optical communication applications,” Inter. J. Phys. Sci. 6, 4405–4411 (2011).

Tünnermann, A.

Verdeyen, J. T.

J. T. Verdeyen, “Laser electron.,” Science 2, 69–70 (1995).

Wu, Z.

L. Zhang, Z. Wu, S. Gao, and M. Cui, “Study of a constructed function for approximating mode field in photonic crystal fiber,” Opt. Eng. 51, 065003 (2012).
[CrossRef]

Yumin, L.

N. Ding, H. Lihong, L. Yumin, and Y. Zhongyuan, “Investigation of the index profile of photonic crystal fibers on dispersion characteristics,” in Proceedings of IEEE Conference on Photonics and Optoelectronics (IEEE, 2010).

Zendehnam, A.

A. Zendehnam, M. Mirzaei, and R. Solgi, “Confinement loss and G.V.D for HF and AHAOF by FEM,” Int. J. Opt. Appl. 2, 34–37 (2012).
[CrossRef]

M. Hosseinpour and A. Zendehnam, Department of Physics, Science Faculty, University of Arak, Arak, Iran, are preparing a manuscript to be called “Study of PCF’s output intensity profiles with various configurations for low d/Λ values.”

Zhang, L.

L. Zhang, Z. Wu, S. Gao, and M. Cui, “Study of a constructed function for approximating mode field in photonic crystal fiber,” Opt. Eng. 51, 065003 (2012).
[CrossRef]

Zhongyuan, Y.

N. Ding, H. Lihong, L. Yumin, and Y. Zhongyuan, “Investigation of the index profile of photonic crystal fibers on dispersion characteristics,” in Proceedings of IEEE Conference on Photonics and Optoelectronics (IEEE, 2010).

Australian J. Basic Appl. Sci. (1)

M. N. Hoque, A. Sayeem, and N. Akter, “Octagonal photonic crystal fibers: application to ultra-flattened dispersion,” Australian J. Basic Appl. Sci. 4, 2274–2279 (2010).

Electron. Lett. (1)

J. C. Knight, T. A. Birks, P. St. J. Russell, and R. F. Cregan, “Large mode area photonic crystal fiber,” Electron. Lett. 34, 1347–1348 (1998).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

T. Hirooka, Y. Hori, and M. Nakazawa, “Gaussian and Sech approximations of mode field profiles in photonic crystal fibers,” IEEE Photon. Technol. Lett. 16, 1071–1073 (2004).
[CrossRef]

Int. J. Opt. Appl. (1)

A. Zendehnam, M. Mirzaei, and R. Solgi, “Confinement loss and G.V.D for HF and AHAOF by FEM,” Int. J. Opt. Appl. 2, 34–37 (2012).
[CrossRef]

Inter. J. Phys. Sci. (1)

S. Olyaee and F. Taghipour, “Design of new square-lattice photonic crystal fibers for optical communication applications,” Inter. J. Phys. Sci. 6, 4405–4411 (2011).

J. Lightwave Technol. (1)

Nat. Med. (1)

S. A. Bopart, B. E. Bonma, C. Pitris, J. F. Southern, M. E. Brezinski, and J. G. Fujimoto, “In vivo cellular optical coherence tomography imaging,” Nat. Med. 4, 861–865 (1998).
[CrossRef]

Opt. Eng. (1)

L. Zhang, Z. Wu, S. Gao, and M. Cui, “Study of a constructed function for approximating mode field in photonic crystal fiber,” Opt. Eng. 51, 065003 (2012).
[CrossRef]

Opt. Express (1)

Opt. Fiber Technol. (1)

H. Demir and S. Ozsoy, “Large-solid-core square-lattice photonic crystal fibers,” Opt. Fiber Technol. 17, 594–600 (2011).
[CrossRef]

Opt. Lett. (1)

Opt. Mater. (1)

H. Demir and S. Ozsoy, “A theoretical study of large solid-core square-lattice silica photonic crystal fibers with square air-holes,” Opt. Mater. 35, 205–210 (2012).

Opt. Quantum Electron. (1)

H. Demir and S. Ozsoy, “Solid-core square-lattice photonic crystal fibers: comparative studies of the single-mode regime and numerical aperture for circular and square air-holes,” Opt. Quantum Electron. 42, 851–862 (2011).
[CrossRef]

Science (1)

J. T. Verdeyen, “Laser electron.,” Science 2, 69–70 (1995).

Other (6)

M. Hosseinpour and A. Zendehnam, Department of Physics, Science Faculty, University of Arak, Arak, Iran, are preparing a manuscript to be called “Study of PCF’s output intensity profiles with various configurations for low d/Λ values.”

W. Math World, “Gaussian function,” http://mathworld.wolfram.com/GaussianFunction.html .

M. Hosseinpour, “Investigation of different arrangements on loss and GVD in photonic crystal optical fibers and study of distribution function in them,” M.S. thesis (Physics Department, Science Faculty, Arak University, 2013).

N. Ding, H. Lihong, L. Yumin, and Y. Zhongyuan, “Investigation of the index profile of photonic crystal fibers on dispersion characteristics,” in Proceedings of IEEE Conference on Photonics and Optoelectronics (IEEE, 2010).

J. H. Lee, E. J. Jung, and C. Kim, “Incoherent, CW supercontinuum source based on erbium fiber ASE for optical coherence tomography imaging,” in Proceedings of IEEE Conference on OptoEelectronics and Communication (IEEE, 2009), paper FD3.

F. Begum and Y. Namihira, “Photonic crystal fiber for medical applications,” in The Recent Progress in Optical Fiber Research, M. Yasin, ed. (In Tech, 2012), pp. 230–246.

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Figures (11)

Fig. 1.
Fig. 1.

Cross sections of the solid core PCFs with various configurations. The white dots represent the air holes in the silica matrix with refractive index nclad=1.44.

Fig. 2.
Fig. 2.

Simulated 2D intensity distributions of the PCFs investigated at λ=1.55μm, d/Λ=0.6, and N=4.

Fig. 3.
Fig. 3.

Simulated output intensity profiles related to various configurations obtained using COMSOL software while d/Λ=0.6, N=4, and λ=1.55μm. The vertical axis refers to intensity (w/m2), and the horizontal axis represents cross sections of the examined PCFs (in microns).

Fig. 4.
Fig. 4.

Approximated output intensity profiles belonged to the PCFs with different configurations when d/Λ=0.6, N=4, and λ=1.55μm. The vertical axis refers to intensity (w/m2), and the horizontal axis represents cross sections of the examined PCFs (in microns).

Fig. 5.
Fig. 5.

Plots of (a) central intensity and (b) FWHM against the number of edges in cladding region at three wavelengths when d/Λ=0.5 and N=4.

Fig. 6.
Fig. 6.

Plots of (a) central intensity and (b) FWHM against the number of edges in cladding region at three wavelengths when d/Λ=0.6 and N=4.

Fig. 7.
Fig. 7.

Approximated output intensity profiles related to the PCF with heptagonal structure for λ=1.55μm and N=4 when d/Λ is increased. The vertical axis refers to intensity (w/m2) and the horizontal axis represents cross sections of the examined PCFs (in micron).

Fig. 8.
Fig. 8.

2D intensity distribution of the PCFs with square and pentagonal configuration while for both (a) and (c) d/Λ=0.7, and for (b) d/Λ=0.8.

Fig. 9.
Fig. 9.

Plots of the central intensity against various d/Λ values for the PCFs with (a) even number of edges and (b) odd number of edges.

Fig. 10.
Fig. 10.

Plots of CL against the number of edges when N=4 for various d/Λ values.

Fig. 11.
Fig. 11.

Plots of CL against the number of edges when N=4 for various d/Λ at λ=1.35μm.

Tables (1)

Tables Icon

Table 1. Structural Parameters of the Examined PCFs

Equations (2)

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

I(x)=Ioexp[x22w2],
Lc=8.686k0·Im[Neff]

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