Abstract

We employ a Genetic Algorithm for the dispersion optimization of a range of holey fibers (HF) with a small number of air holes but good confinement loss. We demonstrate that a dispersion of 0±0.1 ps/nm/km in the wavelength range between 1.5 and 1.6µm is achievable for HFs with a range of different transversal structures, and discuss some of the trade-offs in terms of dispersion slope, nonlinearity and confinement loss. We then analyze the sensitivity of the total dispersion to small variations from the optimal value of specific structural parameters, and estimate the fabrication accuracy required for the reliable fabrication of such fibers.

© 2005 Optical Society of America

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References

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  1. T. Okuno, M. Hirano, T. Kato, M. Shigematsu, and M. Onishi, “Highly nonlinear and perfectly dispersion-flattened fibers for efficient optical signal processing applications,” Electronics Letters 39, 972–974 (2003).
    [CrossRef]
  2. T. M. Monro, D. J. Richardson, N. G. R. Broderick, and P. J. Bennett, “Holey optical fibers: an efficient modal model,” J. Lightwave Technol. 17, 1093–1102, (1999).
    [CrossRef]
  3. A. Ferrando, E. Silvestre, and P. Andres, “Designing the properties of dispersion-flattened photonic crystal fibers,” Opt. Express 9, 687–697 (2001). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-9-13-687
    [CrossRef] [PubMed]
  4. W. H. Reeves, J. C. Knight, P. St. J. Russell, and P. J. Roberts “Demonstration of ultra-flattened dispersion in photonic crystal fibers,” Opt. Express 10, 609–613 (2002). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-14-609
    [PubMed]
  5. K. P. Hansen,“Dispersion flattened hybrid-core nonlinear photonic crystal fiber,” Opt. Express 11, 1503–1509 (2003). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-13-1503
    [CrossRef] [PubMed]
  6. K. Saitoh, M. Koshiba, T. Hasegawa, and E. Sasaoka, “Chromatic dispersion control in photonic crystal fibers: application to ultra-flattened dispersion,” Opt. Express 11, 843–852 (2003). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-8-843
    [CrossRef] [PubMed]
  7. F. Poli, A. Cucinotta, S. Selleri, and A. H. Bouk, “Tailoring of flattened dispersion in highly nonlinear photonic crystal fibers,” IEEE Photon. Technol. Lett. 16, 1065–1067 (2004).
    [CrossRef]
  8. G. Renversez, B. Kuhlmey, and R. McPhaedran, “Dispersion Management with microstructured optical fibers: ultraflattened chromatic dispersion with low losses,” Opt. Lett. 28, 989–991 (2003).
    [CrossRef] [PubMed]
  9. T. Wu and C. Chao, “A novel ultra-flattened dispersion photonic crystal fiber,” IEEE Photon. Technol. Lett. 17, 67–69 (2005).
    [CrossRef]
  10. A. Cucinotta, S. Selleri, L. Vincetti, and M. Zoboli, “Perturbation analysis of dispersion properties in photonic crystal fibers trough the finite element method”, J. Lightwave Technol. 20, 1433–1441,(2002).
    [CrossRef]
  11. E. Kerrinckx, L. Bigot, M. Douay, and Y. Quiquempois, “Photonic crystal fiber design by means of a genetic algorithm,” Opt. Express 12, 1990–1995 (2004). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-9-382
    [CrossRef] [PubMed]
  12. T. P. Wite, B. T. Kuhlmey, R. C. McPhaedran, D. Maystre, G. Renversez, C. M. de Sterke, and L. C. Botten,“Multipole method for microstrucutred optical fibers. I. Formulation,” J. Opt. Soc. Am. B 19, 2322–2330 (2002).
    [CrossRef]
  13. D. E. Goldberg, Genetic algorithms in search, optimization and machine learning, (Addison-Wesley, New York, 1989).
  14. J. Skaar and K. M. Risvik, “A genetic algorithm for the inverse problem in synthesis of fiber gratings,” J. Lightwave Technol. 16, 1928, (1998).
    [CrossRef]
  15. H. Ebendorff-Heidepriem, P. Petropoulos, S. Asimakis, V. Finazzi, R. C. Moore, K. Frampton, F. Koizumi, D. J. Richardson, and T. M. Monro, “Bismuth glass holey fibers with high nonlinearity,” Opt. Express 12, 5082–5087 (2004). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-21-5082
    [CrossRef] [PubMed]
  16. K. M. Hilligse, T. V. Andersen, H. N. Paulsen, C. K. Nielsen, K. Mlmer, S. Keiding, R. Kristiansen, K. P. Hansen, and J. J. Larsen, “Supercontinuum generation in a photonic crystal fiber with two zero dispersion wavelengths,” Opt. Express 12, 1045–1054 (2004). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-6-1045
    [CrossRef]

2005 (1)

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

2004 (4)

2003 (4)

2002 (3)

2001 (1)

1999 (1)

1998 (1)

Andersen, T. V.

Andres, P.

Asimakis, S.

Bennett, P. J.

Bigot, L.

Botten, L. C.

Bouk, A. H.

F. Poli, A. Cucinotta, S. Selleri, and A. H. Bouk, “Tailoring of flattened dispersion in highly nonlinear photonic crystal fibers,” IEEE Photon. Technol. Lett. 16, 1065–1067 (2004).
[CrossRef]

Broderick, N. G. R.

Chao, C.

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

Cucinotta, A.

F. Poli, A. Cucinotta, S. Selleri, and A. H. Bouk, “Tailoring of flattened dispersion in highly nonlinear photonic crystal fibers,” IEEE Photon. Technol. Lett. 16, 1065–1067 (2004).
[CrossRef]

A. Cucinotta, S. Selleri, L. Vincetti, and M. Zoboli, “Perturbation analysis of dispersion properties in photonic crystal fibers trough the finite element method”, J. Lightwave Technol. 20, 1433–1441,(2002).
[CrossRef]

de Sterke, C. M.

Douay, M.

Ebendorff-Heidepriem, H.

Ferrando, A.

Finazzi, V.

Frampton, K.

Goldberg, D. E.

D. E. Goldberg, Genetic algorithms in search, optimization and machine learning, (Addison-Wesley, New York, 1989).

Hansen, K. P.

Hasegawa, T.

Hilligse, K. M.

Hirano, M.

T. Okuno, M. Hirano, T. Kato, M. Shigematsu, and M. Onishi, “Highly nonlinear and perfectly dispersion-flattened fibers for efficient optical signal processing applications,” Electronics Letters 39, 972–974 (2003).
[CrossRef]

Kato, T.

T. Okuno, M. Hirano, T. Kato, M. Shigematsu, and M. Onishi, “Highly nonlinear and perfectly dispersion-flattened fibers for efficient optical signal processing applications,” Electronics Letters 39, 972–974 (2003).
[CrossRef]

Keiding, S.

Kerrinckx, E.

Knight, J. C.

Koizumi, F.

Koshiba, M.

Kristiansen, R.

Kuhlmey, B.

Kuhlmey, B. T.

Larsen, J. J.

Maystre, D.

McPhaedran, R.

McPhaedran, R. C.

Mlmer, K.

Monro, T. M.

Moore, R. C.

Nielsen, C. K.

Okuno, T.

T. Okuno, M. Hirano, T. Kato, M. Shigematsu, and M. Onishi, “Highly nonlinear and perfectly dispersion-flattened fibers for efficient optical signal processing applications,” Electronics Letters 39, 972–974 (2003).
[CrossRef]

Onishi, M.

T. Okuno, M. Hirano, T. Kato, M. Shigematsu, and M. Onishi, “Highly nonlinear and perfectly dispersion-flattened fibers for efficient optical signal processing applications,” Electronics Letters 39, 972–974 (2003).
[CrossRef]

Paulsen, H. N.

Petropoulos, P.

Poli, F.

F. Poli, A. Cucinotta, S. Selleri, and A. H. Bouk, “Tailoring of flattened dispersion in highly nonlinear photonic crystal fibers,” IEEE Photon. Technol. Lett. 16, 1065–1067 (2004).
[CrossRef]

Quiquempois, Y.

Reeves, W. H.

Renversez, G.

Richardson, D. J.

Risvik, K. M.

Roberts, P. J.

Russell, P. St. J.

Saitoh, K.

Sasaoka, E.

Selleri, S.

F. Poli, A. Cucinotta, S. Selleri, and A. H. Bouk, “Tailoring of flattened dispersion in highly nonlinear photonic crystal fibers,” IEEE Photon. Technol. Lett. 16, 1065–1067 (2004).
[CrossRef]

A. Cucinotta, S. Selleri, L. Vincetti, and M. Zoboli, “Perturbation analysis of dispersion properties in photonic crystal fibers trough the finite element method”, J. Lightwave Technol. 20, 1433–1441,(2002).
[CrossRef]

Shigematsu, M.

T. Okuno, M. Hirano, T. Kato, M. Shigematsu, and M. Onishi, “Highly nonlinear and perfectly dispersion-flattened fibers for efficient optical signal processing applications,” Electronics Letters 39, 972–974 (2003).
[CrossRef]

Silvestre, E.

Skaar, J.

Vincetti, L.

Wite, T. P.

Wu, T.

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

Zoboli, M.

Electronics Letters (1)

T. Okuno, M. Hirano, T. Kato, M. Shigematsu, and M. Onishi, “Highly nonlinear and perfectly dispersion-flattened fibers for efficient optical signal processing applications,” Electronics Letters 39, 972–974 (2003).
[CrossRef]

IEEE Photon. Technol. Lett. (2)

F. Poli, A. Cucinotta, S. Selleri, and A. H. Bouk, “Tailoring of flattened dispersion in highly nonlinear photonic crystal fibers,” IEEE Photon. Technol. Lett. 16, 1065–1067 (2004).
[CrossRef]

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

J. Lightwave Technol. (3)

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

Opt. Express (7)

K. Saitoh, M. Koshiba, T. Hasegawa, and E. Sasaoka, “Chromatic dispersion control in photonic crystal fibers: application to ultra-flattened dispersion,” Opt. Express 11, 843–852 (2003). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-8-843
[CrossRef] [PubMed]

K. P. Hansen,“Dispersion flattened hybrid-core nonlinear photonic crystal fiber,” Opt. Express 11, 1503–1509 (2003). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-13-1503
[CrossRef] [PubMed]

K. M. Hilligse, T. V. Andersen, H. N. Paulsen, C. K. Nielsen, K. Mlmer, S. Keiding, R. Kristiansen, K. P. Hansen, and J. J. Larsen, “Supercontinuum generation in a photonic crystal fiber with two zero dispersion wavelengths,” Opt. Express 12, 1045–1054 (2004). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-6-1045
[CrossRef]

E. Kerrinckx, L. Bigot, M. Douay, and Y. Quiquempois, “Photonic crystal fiber design by means of a genetic algorithm,” Opt. Express 12, 1990–1995 (2004). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-9-382
[CrossRef] [PubMed]

H. Ebendorff-Heidepriem, P. Petropoulos, S. Asimakis, V. Finazzi, R. C. Moore, K. Frampton, F. Koizumi, D. J. Richardson, and T. M. Monro, “Bismuth glass holey fibers with high nonlinearity,” Opt. Express 12, 5082–5087 (2004). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-21-5082
[CrossRef] [PubMed]

A. Ferrando, E. Silvestre, and P. Andres, “Designing the properties of dispersion-flattened photonic crystal fibers,” Opt. Express 9, 687–697 (2001). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-9-13-687
[CrossRef] [PubMed]

W. H. Reeves, J. C. Knight, P. St. J. Russell, and P. J. Roberts “Demonstration of ultra-flattened dispersion in photonic crystal fibers,” Opt. Express 10, 609–613 (2002). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-14-609
[PubMed]

Opt. Lett. (1)

Other (1)

D. E. Goldberg, Genetic algorithms in search, optimization and machine learning, (Addison-Wesley, New York, 1989).

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Figures (5)

Fig. 1.
Fig. 1.

Fiber structures to be optimized by the GA.

Fig. 2.
Fig. 2.

Solutions of the Genetic Algorithm for the 3 fibers in Fig. 1. Plot F4 is the dispersion of an 11 rings structure with constant d/Λ for all the holes. The inset zooms on the wavelength range in which the fibers have been optimized

Fig. 3.
Fig. 3.

Variation of the total dispersion profile as some structural parameters are changed for fiber F2. Dotted lines indicate a ‘-’ variation, while continuous lines represent a ‘+’ variation.

Fig. 4.
Fig. 4.

Variation of the total dispersion profile as all the holes in a ring are displaced from optimum position for fiber F2. Dotted lines indicate a ‘-’ variation, while continuous lines represent a ‘+’ variation.

Fig. 5.
Fig. 5.

Sensitivity of the 4 fibers to an error on the dimension of the first ring of air holes: (a) average dispersion parameter and (b) dispersion slope in the interval 1.5–1.6 µm.

Tables (2)

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Table 1. Structural parameters and optical properties of the best fibers obtained through the GA

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Table 2. Fabrication tolerances for a range of structurally different fibers

Equations (1)

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F = λ i = 1.5 μ m 1.6 μ m D ( λ i )

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