Abstract

We present a new approach to the design of the holey fibers that have ultra-high nonlinearity and dispersion properties optimized for tunable fiber parametric wavelength converters based on degenerated four wave mixing. This hybrid approach combines downhill simplex algorithms with four wave mixing modeling. Exploiting the relations between fiber properties and the converter’s characteristics, this method is not only much faster than other methods proposed before but also enables an inverse design of the holey fibers according to the pre-set device characteristics, like conversion gain, tuning range, fiber length and pump power. We then investigate the sensitivity of these characteristics to the small variations in the fiber structural parameters and find adjusting the pump power can to some extent mitigate the impact of the fabrication errors.

© 2010 OSA

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  1. S. J. B. Yoo, “Wavelength conversion technologies for WDM network applications,” J. Lightwave Technol. 14(6), 955–966 (1996).
    [CrossRef]
  2. R. W. McKerracher, J. L. Blows, and C. de Sterke, “Wavelength conversion bandwidth in fiber based optical parametric amplifiers,” Opt. Express 11(9), 1002–1007 (2003).
    [CrossRef] [PubMed]
  3. G. P. Agrawal, Nonlinear Fiber Optics, (Academic Press, San Diego, 2001), Chap. 10.
  4. M. Galili, J. Xu, H. C. Mulvad, L. K. Oxenløwe, A. T. Clausen, P. Jeppesen, B. Luther-Davies, S. Madden, A. Rode, D.-Y. Choi, M. Pelusi, F. Luan, and B. J. Eggleton, “Breakthrough switching speed with an all-optical chalcogenide glass chip: 640 Gbit/s demultiplexing,” Opt. Express 17(4), 2182–2187 (2009).
    [CrossRef] [PubMed]
  5. K. Croussore and G. Li, “Amplitude regeneration of RZ-DPSK signals based on four-wave mixing in fibre,” Electron. Lett. 43(3), 177–178 (2007).
    [CrossRef]
  6. M. L. F. Abbade, J. D. Marconi, R. L. Cassiolato, V. Ishizuca, I. E. Fonseca, and H. L. Fragnito, “Field-Trial Evaluation of Cross-Layer Effect Caused by All-Optical Wavelength Converters on IP Network Applications,” J. Lightwave Technol. 27(12), 1816–1826 (2009).
    [CrossRef]
  7. K. K. Chow, K. Kikuchi, T. Nagashima, T. Hasegawa, S. Ohara, and N. Sugimoto, “Four-wave mixing based widely tunable wavelength conversion using 1-m dispersion-shifted bismuth-oxide photonic crystal fiber,” Opt. Express 15(23), 15418–15423 (2007).
    [CrossRef] [PubMed]
  8. D. I. Yeom, E. C. Mägi, M. R. Lamont, M. A. Roelens, L. Fu, and B. J. Eggleton, “Low-threshold supercontinuum generation in highly nonlinear chalcogenide nanowires,” Opt. Lett. 33(7), 660–662 (2008).
    [CrossRef] [PubMed]
  9. J. J. Miret, E. Silvestre, and P. Andrés, “Octave-spanning ultraflat supercontinuum with soft-glass photonic crystal fibers,” Opt. Express 17(11), 9197–9203 (2009).
    [CrossRef] [PubMed]
  10. J. Kaňka, “Design of photonic crystal fibers with highly nonlinear glasses for four-wave-mixing based telecom applications,” Opt. Express 16(25), 20395–20408 (2008).
    [CrossRef] [PubMed]
  11. F. Poletti, V. Finazzi, T. M. Monro, N. G. R. Broderick, V. Tse, and D. J. Richardson, “Inverse design and fabrication tolerances of ultra-flattened dispersion holey fibers,” Opt. Express 13(10), 3728–3736 (2005).
    [CrossRef] [PubMed]
  12. W. Q. Zhang, V. Shahraam Afshar, and T. M. Monro, “A genetic algorithm based approach to fiber design for high coherence and large bandwidth supercontinuum generation,” Opt. Express 17, 19312–19328 (2009).
  13. J. C. Lagarias, J. A. Reeds, M. H. Wright, and P. E. Wright, “Convergence properties of the Nelder-Mead Simplex Method in low dimensions,” SIAM J. Optim. 9(1), 112–147 (1998).
    [CrossRef]
  14. S. Cui, D. Liu, Y. Wang, and F. Tu, “Method for effectively utilizing tunable one-pump fiber parametric wavelength converters as an enabling device for WDM routers,” Opt. Express 17(3), 1454–1465 (2009).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
  18. T.-L. Wu and C.-H. Chao, “A novel ultra-flattened dispersion photonic crystal fiber,” IEEE Photon. Technol. Lett. 17(1), 67–69 (2005).
    [CrossRef]
  19. T. P. White, B. T. Kuhlmey, R. C. McPhedran, D. Maystre, G. Renversez, C. M. de Sterke, and L. C. Botten, “Multipole method for microstructured optical fibers. I. Formulation,” J. Opt. Soc. Am. B 19(10), 2322–2330 (2002).
    [CrossRef]
  20. B. T. Kuhlmey, T. P. White, G. Renversez, D. Maystre, L. C. Botten, C. M. de Sterke, and R. C. McPhedran, “Multipole method for microstructured optical fibers II. Implementation and results,” J. Opt. Soc. Am. B 19(10), 2331–2340 (2002).
    [CrossRef]
  21. M. Karlsson, “Four-wave mixing in fibers with randomly varying zero-dispersion wavelength,” J. Opt. Soc. Am. B 15(8), 2269–2275 (1998).
    [CrossRef]
  22. M. Farahmand and M. de Sterke, “Parametric amplification in presence of dispersion fluctuations,” Opt. Express 12(1), 136–142 (2004).
    [CrossRef] [PubMed]
  23. H. Ebendorff-Heidepriem and T. M. Monro, “Extrusion of complex preforms for microstructured optical fibers,” Opt. Express 15(23), 15086–15092 (2007).
    [CrossRef] [PubMed]
  24. M. Hirano, T. Nakanishi, T. Okuno, and M. Onishi, ““Silica-Based Highly Nonlinear Fibers and Their Application,” IEEE Sel. Top. Quantum Electron. 15(1), 103–113 (2009).
    [CrossRef]
  25. M. Westlund, H. Hansryd, P. A. Andrekson, and S. N. Knudsen, “Transparent wavelength conversion in fibre with 24nm pump tuning range,” Electron. Lett. 38(2), 85–86 (2002).
    [CrossRef]
  26. K. M. Gundu, M. Kolesik, J. V. Moloney, and K. S. Lee, “Ultra-flattened-dispersion selectively liquid-filled photonic crystal fibers,” Opt. Express 14(15), 6870–6878 (2006).
    [CrossRef] [PubMed]

2009 (6)

2008 (2)

2007 (4)

2006 (1)

2005 (2)

2004 (2)

2003 (1)

2002 (3)

1998 (2)

M. Karlsson, “Four-wave mixing in fibers with randomly varying zero-dispersion wavelength,” J. Opt. Soc. Am. B 15(8), 2269–2275 (1998).
[CrossRef]

J. C. Lagarias, J. A. Reeds, M. H. Wright, and P. E. Wright, “Convergence properties of the Nelder-Mead Simplex Method in low dimensions,” SIAM J. Optim. 9(1), 112–147 (1998).
[CrossRef]

1996 (2)

M. E. Marhic, N. Kagi, T.-K. Chiang, and L. G. Kazovsky, “Broadband fiber optical parametric amplifiers,” Opt. Lett. 21(8), 573–575 (1996).
[CrossRef] [PubMed]

S. J. B. Yoo, “Wavelength conversion technologies for WDM network applications,” J. Lightwave Technol. 14(6), 955–966 (1996).
[CrossRef]

Abbade, M. L. F.

Alic, N.

Andersen, T. V.

Andrekson, P. A.

M. Westlund, H. Hansryd, P. A. Andrekson, and S. N. Knudsen, “Transparent wavelength conversion in fibre with 24nm pump tuning range,” Electron. Lett. 38(2), 85–86 (2002).
[CrossRef]

Andrés, P.

Blows, J. L.

Botten, L. C.

Broderick, N. G. R.

Cassiolato, R. L.

Chao, C.-H.

T.-L. Wu and C.-H. Chao, “A novel ultra-flattened dispersion photonic crystal fiber,” IEEE Photon. Technol. Lett. 17(1), 67–69 (2005).
[CrossRef]

Chiang, T.-K.

Choi, D.-Y.

Chow, K. K.

Clausen, A. T.

Croussore, K.

K. Croussore and G. Li, “Amplitude regeneration of RZ-DPSK signals based on four-wave mixing in fibre,” Electron. Lett. 43(3), 177–178 (2007).
[CrossRef]

Cui, S.

de Sterke, C.

de Sterke, C. M.

de Sterke, M.

Ebendorff-Heidepriem, H.

Eggleton, B. J.

Fainman, Y.

Farahmand, M.

Finazzi, V.

Fonseca, I. E.

Ford, J. E.

Fragnito, H. L.

Fu, L.

Galili, M.

Gundu, K. M.

Hansen, K. P.

Hansryd, H.

M. Westlund, H. Hansryd, P. A. Andrekson, and S. N. Knudsen, “Transparent wavelength conversion in fibre with 24nm pump tuning range,” Electron. Lett. 38(2), 85–86 (2002).
[CrossRef]

Hasegawa, T.

Hilligsøe, K. M.

Hirano, M.

M. Hirano, T. Nakanishi, T. Okuno, and M. Onishi, ““Silica-Based Highly Nonlinear Fibers and Their Application,” IEEE Sel. Top. Quantum Electron. 15(1), 103–113 (2009).
[CrossRef]

Ishizuca, V.

Jeppesen, P.

Jiang, R.

Kagi, N.

Kanka, J.

Karlsson, M.

Kazovsky, L. G.

Keiding, S.

Kikuchi, K.

Knudsen, S. N.

M. Westlund, H. Hansryd, P. A. Andrekson, and S. N. Knudsen, “Transparent wavelength conversion in fibre with 24nm pump tuning range,” Electron. Lett. 38(2), 85–86 (2002).
[CrossRef]

Kolesik, M.

Kuhlmey, B. T.

Lagarias, J. C.

J. C. Lagarias, J. A. Reeds, M. H. Wright, and P. E. Wright, “Convergence properties of the Nelder-Mead Simplex Method in low dimensions,” SIAM J. Optim. 9(1), 112–147 (1998).
[CrossRef]

Lamont, M. R.

Larsen, J.

Lee, K. S.

Li, G.

K. Croussore and G. Li, “Amplitude regeneration of RZ-DPSK signals based on four-wave mixing in fibre,” Electron. Lett. 43(3), 177–178 (2007).
[CrossRef]

Liu, D.

Luan, F.

Luther-Davies, B.

Madden, S.

Mägi, E. C.

Marconi, J. D.

Marhic, M. E.

Maystre, D.

McKerracher, R. W.

McKinstrie, C. J.

McPhedran, R. C.

Miret, J. J.

Moloney, J. V.

Monro, T. M.

Mulvad, H. C.

Nagashima, T.

Nakanishi, T.

M. Hirano, T. Nakanishi, T. Okuno, and M. Onishi, ““Silica-Based Highly Nonlinear Fibers and Their Application,” IEEE Sel. Top. Quantum Electron. 15(1), 103–113 (2009).
[CrossRef]

Nezhad, M.

Nielsen, C. K.

Ohara, S.

Okuno, T.

M. Hirano, T. Nakanishi, T. Okuno, and M. Onishi, ““Silica-Based Highly Nonlinear Fibers and Their Application,” IEEE Sel. Top. Quantum Electron. 15(1), 103–113 (2009).
[CrossRef]

Onishi, M.

M. Hirano, T. Nakanishi, T. Okuno, and M. Onishi, ““Silica-Based Highly Nonlinear Fibers and Their Application,” IEEE Sel. Top. Quantum Electron. 15(1), 103–113 (2009).
[CrossRef]

Oxenløwe, L. K.

Pelusi, M.

Poletti, F.

Radic, S.

Reeds, J. A.

J. C. Lagarias, J. A. Reeds, M. H. Wright, and P. E. Wright, “Convergence properties of the Nelder-Mead Simplex Method in low dimensions,” SIAM J. Optim. 9(1), 112–147 (1998).
[CrossRef]

Renversez, G.

Richardson, D. J.

Rode, A.

Roelens, M. A.

Saperstein, R. E.

Shahraam Afshar, V.

W. Q. Zhang, V. Shahraam Afshar, and T. M. Monro, “A genetic algorithm based approach to fiber design for high coherence and large bandwidth supercontinuum generation,” Opt. Express 17, 19312–19328 (2009).

Silvestre, E.

Sugimoto, N.

Thøgersen, J.

Tse, V.

Tu, F.

Wang, Y.

Westlund, M.

M. Westlund, H. Hansryd, P. A. Andrekson, and S. N. Knudsen, “Transparent wavelength conversion in fibre with 24nm pump tuning range,” Electron. Lett. 38(2), 85–86 (2002).
[CrossRef]

White, T. P.

Wright, M. H.

J. C. Lagarias, J. A. Reeds, M. H. Wright, and P. E. Wright, “Convergence properties of the Nelder-Mead Simplex Method in low dimensions,” SIAM J. Optim. 9(1), 112–147 (1998).
[CrossRef]

Wright, P. E.

J. C. Lagarias, J. A. Reeds, M. H. Wright, and P. E. Wright, “Convergence properties of the Nelder-Mead Simplex Method in low dimensions,” SIAM J. Optim. 9(1), 112–147 (1998).
[CrossRef]

Wu, T.-L.

T.-L. Wu and C.-H. Chao, “A novel ultra-flattened dispersion photonic crystal fiber,” IEEE Photon. Technol. Lett. 17(1), 67–69 (2005).
[CrossRef]

Xu, J.

Yeom, D. I.

Yoo, S. J. B.

S. J. B. Yoo, “Wavelength conversion technologies for WDM network applications,” J. Lightwave Technol. 14(6), 955–966 (1996).
[CrossRef]

Zhang, W. Q.

W. Q. Zhang, V. Shahraam Afshar, and T. M. Monro, “A genetic algorithm based approach to fiber design for high coherence and large bandwidth supercontinuum generation,” Opt. Express 17, 19312–19328 (2009).

Electron. Lett. (2)

K. Croussore and G. Li, “Amplitude regeneration of RZ-DPSK signals based on four-wave mixing in fibre,” Electron. Lett. 43(3), 177–178 (2007).
[CrossRef]

M. Westlund, H. Hansryd, P. A. Andrekson, and S. N. Knudsen, “Transparent wavelength conversion in fibre with 24nm pump tuning range,” Electron. Lett. 38(2), 85–86 (2002).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

T.-L. Wu and C.-H. Chao, “A novel ultra-flattened dispersion photonic crystal fiber,” IEEE Photon. Technol. Lett. 17(1), 67–69 (2005).
[CrossRef]

IEEE Sel. Top. Quantum Electron. (1)

M. Hirano, T. Nakanishi, T. Okuno, and M. Onishi, ““Silica-Based Highly Nonlinear Fibers and Their Application,” IEEE Sel. Top. Quantum Electron. 15(1), 103–113 (2009).
[CrossRef]

J. Lightwave Technol. (3)

J. Opt. Soc. Am. B (3)

Opt. Express (12)

M. Farahmand and M. de Sterke, “Parametric amplification in presence of dispersion fluctuations,” Opt. Express 12(1), 136–142 (2004).
[CrossRef] [PubMed]

H. Ebendorff-Heidepriem and T. M. Monro, “Extrusion of complex preforms for microstructured optical fibers,” Opt. Express 15(23), 15086–15092 (2007).
[CrossRef] [PubMed]

R. W. McKerracher, J. L. Blows, and C. de Sterke, “Wavelength conversion bandwidth in fiber based optical parametric amplifiers,” Opt. Express 11(9), 1002–1007 (2003).
[CrossRef] [PubMed]

S. Cui, D. Liu, Y. Wang, and F. Tu, “Method for effectively utilizing tunable one-pump fiber parametric wavelength converters as an enabling device for WDM routers,” Opt. Express 17(3), 1454–1465 (2009).
[CrossRef] [PubMed]

K. K. Chow, K. Kikuchi, T. Nagashima, T. Hasegawa, S. Ohara, and N. Sugimoto, “Four-wave mixing based widely tunable wavelength conversion using 1-m dispersion-shifted bismuth-oxide photonic crystal fiber,” Opt. Express 15(23), 15418–15423 (2007).
[CrossRef] [PubMed]

J. J. Miret, E. Silvestre, and P. Andrés, “Octave-spanning ultraflat supercontinuum with soft-glass photonic crystal fibers,” Opt. Express 17(11), 9197–9203 (2009).
[CrossRef] [PubMed]

J. Kaňka, “Design of photonic crystal fibers with highly nonlinear glasses for four-wave-mixing based telecom applications,” Opt. Express 16(25), 20395–20408 (2008).
[CrossRef] [PubMed]

F. Poletti, V. Finazzi, T. M. Monro, N. G. R. Broderick, V. Tse, and D. J. Richardson, “Inverse design and fabrication tolerances of ultra-flattened dispersion holey fibers,” Opt. Express 13(10), 3728–3736 (2005).
[CrossRef] [PubMed]

W. Q. Zhang, V. Shahraam Afshar, and T. M. Monro, “A genetic algorithm based approach to fiber design for high coherence and large bandwidth supercontinuum generation,” Opt. Express 17, 19312–19328 (2009).

T. V. Andersen, K. M. Hilligsøe, C. K. Nielsen, J. Thøgersen, K. P. Hansen, S. Keiding, and J. Larsen, “Continuous-wave wavelength conversion in a photonic crystal fiber with two zero-dispersion wavelengths,” Opt. Express 12(17), 4113–4122 (2004).
[CrossRef] [PubMed]

M. Galili, J. Xu, H. C. Mulvad, L. K. Oxenløwe, A. T. Clausen, P. Jeppesen, B. Luther-Davies, S. Madden, A. Rode, D.-Y. Choi, M. Pelusi, F. Luan, and B. J. Eggleton, “Breakthrough switching speed with an all-optical chalcogenide glass chip: 640 Gbit/s demultiplexing,” Opt. Express 17(4), 2182–2187 (2009).
[CrossRef] [PubMed]

K. M. Gundu, M. Kolesik, J. V. Moloney, and K. S. Lee, “Ultra-flattened-dispersion selectively liquid-filled photonic crystal fibers,” Opt. Express 14(15), 6870–6878 (2006).
[CrossRef] [PubMed]

Opt. Lett. (2)

SIAM J. Optim. (1)

J. C. Lagarias, J. A. Reeds, M. H. Wright, and P. E. Wright, “Convergence properties of the Nelder-Mead Simplex Method in low dimensions,” SIAM J. Optim. 9(1), 112–147 (1998).
[CrossRef]

Other (1)

G. P. Agrawal, Nonlinear Fiber Optics, (Academic Press, San Diego, 2001), Chap. 10.

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Figures (3)

Fig. 1
Fig. 1

Left: the structure of the HF. Right: the dispersion curve against wavelength for F1 (blue), F2 (red), and F3 (green).

Fig. 2
Fig. 2

Left: change of Δβ against pump wavelength for F1 (blue), F2 (red), and F3 (green), calculated by analytic (dotted) and numerical methods (solid). The two solid black lines represent the boundaries Δβ=4γP0,0 . Right: Conversion gain against pump wavelength for = 1530nm (blue), 1550nm (red), and 1570nm (green)

Fig. 3
Fig. 3

Change of Δβ against pump wavelength when the pitch is optimal (green line) and altered from its optimal value by ± 0.5% (solid blue and red lines), ± 1% (dashed blue and red lines). The three horizontal black dashed lines represent Δβ=4γP0 , when P0 is adjusted to keep the same pump tuning range.

Tables (1)

Tables Icon

Table 1 Structural and characteristic parameters of the HFs. r and Λ are the hole radius and pitch, respectively. γ and CL are caculated at 1550nm. The units for β2,3,4 are 1027s2/m , 1042s3/m and 1054s4/m , respectively.

Equations (11)

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

G=(1+κ24g2)sinh2(gL),
Δβ=βs+βi2βp,
Δβ=β2(ωpωs)2+β42(ωpωc)2(ωpωs)2+β412(ωpωs)4,
4γP0Δβ0,
Gmin=(γP0L)2Gsinh2(γP0L)=Gmax.
ωp1,p2=17β4(6β4ωc+β4ωs±6β42(ωcωs)214β2β4).
Δωp=43β2/7β4.
ωc237β2β4ωpωc+237β2β4,
γP0=3β2228|β4|=|β2|64Δωp2.
ωZDW1,2=ωc±2β2/β4.
FF=(|β2β2aim|/β2aim+k|β3β3aim|/β3aim+|β4β4aim|/β4aim)/3,

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