Abstract

We numerically calculate optical property maps for hexagonally arranged nonlinear holey fibers made of silica, lead silicate, and bismuth oxide-based glass and employ them to design tapered fibers with enhanced stimulated Brillouin scattering threshold and a simultaneous control of the average dispersion.

© 2007 Optical Society of America

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References

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  1. 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, 3728-3736 (2005).
    [CrossRef] [PubMed]
  2. G. P. Agrawal, Nonlinear Fiber Optics, 3rd ed. (Academic Press, 2001).
  3. A. Hirose, Y. Takushima, and T. Okoshi, "Suppression of stimulated Brillouin scattering and Brillouin crosstalk by frequency-sweeping spread-spectrum scheme," J. Opt. Commun. 12, 82-85 (1991).
    [CrossRef]
  4. X. P. Mao, R. W. Tkach, A. R. Chraplyvy, R. M. Jopson, and R. M. Derosier, "Stimulated Brillouin threshold dependence on fiber type and uniformity," IEEE Photon. Technol. Lett. 4, 66-69 (1992).
    [CrossRef]
  5. K. Shiraki, M. Ohashi, and M. Tateda, "SBS threshold of a fiber with a Brillouin frequency shift distribution," J. Lightwave Technol. 14, 50-57 (1996).
    [CrossRef]
  6. M. J. Li, S. Li, D. A. Nolan, U. G. Achmetshin, M. M. Bubnov, A. N. Guryanov, E. M. Dianov, V. F. Khopin, and A. A. Sysoliatin, "New dispersion decreasing fiber with high SBS threshold for nonlinear signal processing," in Proceedings of Optical Fiber Communication Conference (OFC) (Optical Society of America, 2005), paper OFH5.
  7. J. H. Lee, Z. Yusoff, W. Belardi, M. Ibsen, T. M. Monro, and D. J. Richardson, "Investigation of Brillouin effects in small-core holey optical fiber: lasing and scattering," Opt. Lett. 27, 927-929 (2002).
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  8. K. Furusawa, Y. Yusoff, F. Poletti, T. M. Monro, N. G. R. Broderick, and D. J. Richardson, "On the Brillouin characterization of holey optical fibers," Opt. Lett. 31, 2541-2543 (2006).
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  9. M. Nikles, L. Thevenaz, and P. A. Robert, "Brillouin gain spectrum characterization in single-mode optical fibers," J. Lightwave Technol. 15, 1842-1851 (1997).
    [CrossRef]
  10. M. L. Tse, P. Horak, J. H. V. Price, F. Poletti, F. He, and D. J. Richardson, "Pulse compression at 1.06μm in dispersion-decreasing holey fibers," Opt. Lett. 31, 3504-3506 (2006).
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  12. P. Dainese, P. S. J. Russell, N. Joly, J. C. Knight, G. S. Wiederhecker, H. L. Fragnito, V. Laude, and A. Khelif, "Stimulated Brillouin scattering from multi-GHz-guided acoustic phonons in nanostructured photonic crystal fibers," Nat. Phys. 2, 388-392 (2006).
    [CrossRef]
  13. J. H. Lee, T. Tanemura, K. Kikuchi, T. Nagashima, T. Hasegawa, S. Ohara, and N. Sugimoto, "Experimental comparison of a Kerr nonlinearity figure of merit including the stimulated Brillouin scattering threshold for state-of-the-art nonlinear optical fibers," Opt. Lett. 30, 1698-1700 (2005).
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  14. B. T. Kuhlmey, R. C. McPhedran, and C. Martijn de Sterke, "Modal cutoff in microstructured optical fibers," Opt. Lett. 27, 1684-1686 (2002).
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  15. J. R. Folkenberg, N. A. Mortensen, K. P. Hansen, T. P. Hansen, H. R. Simonsen, and C. Jakobsen, "Experimental investigation of cutoff phenomena in nonlinear photonic crystal fibers," Opt. Lett. 28, 1882-1884 (2003).
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  17. J. Y. Y. Leong, S. Asimakis, F. Poletti, P. Petropoulos, X. Feng, R. C. Moore, K. E. Frampton, T. M. Monro, H. Ebendorff-Heidepriem, W. H. Loh, and D. J. Richardson, "Towards zero dispersion highly nonlinear lead silicate glass holey fiber at 1550nm by structured-element-stacking," in Proceedings of European Conference on Optical Communications (ECOC) (ECOC, 2005), Vol. 6, pp. 45-46.
  18. N. A. Wolchover, F. Luan, A. K. George, J. C. Knight, and F. G. Omenetto, "High nonlinearity photonic crystal nanowires," Opt. Express 15, 829-833 (2007).
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  19. H. Ebendorff-Heidepriem, M. Bammann, and T. M. Monro, "Single step fabrication of soft glass and polymer preforms with large numbers of transverse features," in Proceedings of Lasers and Electro-Optics Society (LEOS) (IEEE-LEOS, 2005), paper PD1.3.
  20. 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).
    [CrossRef] [PubMed]
  21. T. Nagashima, T. Hasegawa, S. Ohara, and N. Sugimoto, "Dispersion shifted Bi2O3-based photonic crystal fiber," in Proceedings of European Conference on Optical Communications (ECOC) (ECOC, 2006), paper We1.3.2.
  22. T. Hasegawa, T. Nagashima, and N. Sugimoto, "Z-scan study of third-order optical nonlinearities in bismuth-based glasses," Opt. Commun. 250, 411-415 (2005).
    [CrossRef]
  23. Among the several possible models for fitting the refractive index variation with λ, we found that the polynomial expansion based on a Laurent series and shown in Eq. (9) provided particularly accurate interpolated results:n(λ)+1=A0+A1λ2+A2λ2+A3λ4+A4λ6+A5λ8.The resulting coefficients we obtained are A0=4.8270881A1=3.9929852×10−3A2=1.7852359×10−1A3=9.3099043×10−3A4= −7.977633×10−5A5=1.7116618×10−4..
  24. M. Koshiba and K. Saitoh, "Structural dependence of effective area and mode field diameter for holey fibers," Opt. Express 11, 1746-1756 (2003).
    [CrossRef] [PubMed]
  25. C. Jauregui, P. Petropoulos, and D. J. Richardson, "Slowing of pulses to c/10 with subwatt power levels and low latency using Brillouin amplification in a bismuth-oxide optical fiber," J. Lightwave Technol. 25, 216-221 (2007).
    [CrossRef]
  26. M. L. V. Tse, P. Horak, F. Poletti, and D. J. Richardson, "Designing tapered holey fibers for soliton compression," IEEE J. Quantum Electron, submitted for publication.

2007 (2)

2006 (3)

2005 (4)

2004 (2)

2003 (2)

2002 (2)

1997 (1)

M. Nikles, L. Thevenaz, and P. A. Robert, "Brillouin gain spectrum characterization in single-mode optical fibers," J. Lightwave Technol. 15, 1842-1851 (1997).
[CrossRef]

1996 (1)

K. Shiraki, M. Ohashi, and M. Tateda, "SBS threshold of a fiber with a Brillouin frequency shift distribution," J. Lightwave Technol. 14, 50-57 (1996).
[CrossRef]

1992 (1)

X. P. Mao, R. W. Tkach, A. R. Chraplyvy, R. M. Jopson, and R. M. Derosier, "Stimulated Brillouin threshold dependence on fiber type and uniformity," IEEE Photon. Technol. Lett. 4, 66-69 (1992).
[CrossRef]

1991 (1)

A. Hirose, Y. Takushima, and T. Okoshi, "Suppression of stimulated Brillouin scattering and Brillouin crosstalk by frequency-sweeping spread-spectrum scheme," J. Opt. Commun. 12, 82-85 (1991).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

X. P. Mao, R. W. Tkach, A. R. Chraplyvy, R. M. Jopson, and R. M. Derosier, "Stimulated Brillouin threshold dependence on fiber type and uniformity," IEEE Photon. Technol. Lett. 4, 66-69 (1992).
[CrossRef]

J. Lightwave Technol. (3)

K. Shiraki, M. Ohashi, and M. Tateda, "SBS threshold of a fiber with a Brillouin frequency shift distribution," J. Lightwave Technol. 14, 50-57 (1996).
[CrossRef]

M. Nikles, L. Thevenaz, and P. A. Robert, "Brillouin gain spectrum characterization in single-mode optical fibers," J. Lightwave Technol. 15, 1842-1851 (1997).
[CrossRef]

C. Jauregui, P. Petropoulos, and D. J. Richardson, "Slowing of pulses to c/10 with subwatt power levels and low latency using Brillouin amplification in a bismuth-oxide optical fiber," J. Lightwave Technol. 25, 216-221 (2007).
[CrossRef]

J. Opt. Commun. (1)

A. Hirose, Y. Takushima, and T. Okoshi, "Suppression of stimulated Brillouin scattering and Brillouin crosstalk by frequency-sweeping spread-spectrum scheme," J. Opt. Commun. 12, 82-85 (1991).
[CrossRef]

Nat. Phys. (1)

P. Dainese, P. S. J. Russell, N. Joly, J. C. Knight, G. S. Wiederhecker, H. L. Fragnito, V. Laude, and A. Khelif, "Stimulated Brillouin scattering from multi-GHz-guided acoustic phonons in nanostructured photonic crystal fibers," Nat. Phys. 2, 388-392 (2006).
[CrossRef]

Opt. Commun. (1)

T. Hasegawa, T. Nagashima, and N. Sugimoto, "Z-scan study of third-order optical nonlinearities in bismuth-based glasses," Opt. Commun. 250, 411-415 (2005).
[CrossRef]

Opt. Express (5)

Opt. Lett. (7)

Other (7)

J. Y. Y. Leong, S. Asimakis, F. Poletti, P. Petropoulos, X. Feng, R. C. Moore, K. E. Frampton, T. M. Monro, H. Ebendorff-Heidepriem, W. H. Loh, and D. J. Richardson, "Towards zero dispersion highly nonlinear lead silicate glass holey fiber at 1550nm by structured-element-stacking," in Proceedings of European Conference on Optical Communications (ECOC) (ECOC, 2005), Vol. 6, pp. 45-46.

H. Ebendorff-Heidepriem, M. Bammann, and T. M. Monro, "Single step fabrication of soft glass and polymer preforms with large numbers of transverse features," in Proceedings of Lasers and Electro-Optics Society (LEOS) (IEEE-LEOS, 2005), paper PD1.3.

G. P. Agrawal, Nonlinear Fiber Optics, 3rd ed. (Academic Press, 2001).

M. J. Li, S. Li, D. A. Nolan, U. G. Achmetshin, M. M. Bubnov, A. N. Guryanov, E. M. Dianov, V. F. Khopin, and A. A. Sysoliatin, "New dispersion decreasing fiber with high SBS threshold for nonlinear signal processing," in Proceedings of Optical Fiber Communication Conference (OFC) (Optical Society of America, 2005), paper OFH5.

M. L. V. Tse, P. Horak, F. Poletti, and D. J. Richardson, "Designing tapered holey fibers for soliton compression," IEEE J. Quantum Electron, submitted for publication.

T. Nagashima, T. Hasegawa, S. Ohara, and N. Sugimoto, "Dispersion shifted Bi2O3-based photonic crystal fiber," in Proceedings of European Conference on Optical Communications (ECOC) (ECOC, 2006), paper We1.3.2.

Among the several possible models for fitting the refractive index variation with λ, we found that the polynomial expansion based on a Laurent series and shown in Eq. (9) provided particularly accurate interpolated results:n(λ)+1=A0+A1λ2+A2λ2+A3λ4+A4λ6+A5λ8.The resulting coefficients we obtained are A0=4.8270881A1=3.9929852×10−3A2=1.7852359×10−1A3=9.3099043×10−3A4= −7.977633×10−5A5=1.7116618×10−4..

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Figures (9)

Fig. 1
Fig. 1

Main parameters of the fabricated, tapered HF1: (a) measured Λ and d Λ , (b) measured BFS and simulated n eff , (c) simulated D and A eff .

Fig. 2
Fig. 2

Optical property map for nonlinear silica HFs at 1550 nm . The background gray scale contours represent n eff variations; D contours (in units of ps/nm/km) are shown in dashed curves; γ contours (in W 1 km 1 ) are in dashed–dotted curves; the fabricated ( HF ref and HF1) and proposed (HF2 and HF3) fibers are shown with a black marker and solid lines. The curve with circular markers shows the separation between single mode (SM) and multimode (MM) regime (after [14]).

Fig. 3
Fig. 3

Simulated properties of HF2 and HF3.

Fig. 4
Fig. 4

Optical property map for nonlinear SF57 HFs at 1550 nm . The background gray scale contours represent n eff variations; D contours (in units of ps/nm/km) are shown in dashed curves; the D slope = 0 ps nm 2 km contour is shown in dotted curves; γ contours (in W 1 km 1 ) are in dashed–dotted curves; the proposed fibers are shown with a black marker (HF4) and solid lines (HF5 and HF6).

Fig. 5
Fig. 5

Measured Brillouin gain of the reference SF57 SEST fiber shown in the inset.

Fig. 6
Fig. 6

Simulated properties of HF5 and HF6.

Fig. 7
Fig. 7

Optical property map for nonlinear bismuth HFs at 1550 nm . The background gray scale contours represent n eff variations; D contours (in units of ps/nm/km) are shown in dashed curves; the D slope = 0 ps nm 2 km contour is shown in dotted curves; γ contours (in W 1 km 1 ) are in dashed–dotted curves; the proposed fibers are shown with a black marker (HF7) and solid lines (HF8 and HF9).

Fig. 8
Fig. 8

Group velocity dispersion of HF7; 2 dB contour plot of the y-polarized fundamental mode of (b) HF7 and (c) the SC-SIF, both calculated at 1550 nm .

Fig. 9
Fig. 9

Simulated properties of HF8 and HF9.

Tables (3)

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Table 1 Comparison of Optical Properties for Silica Fibers a

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Table 2 Comparison of Optical Properties for SF57 Fibers a

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Table 3 Comparison of Optical Properties for Bi 2 O 3 Fibers a

Equations (12)

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

ν B ( z ) = 2 n eff ( z ) v A λ ,
g B ( ν , z ) = g B 0 ( Δ ν B 2 ) 2 [ ν ν B ( z ) ] 2 + ( Δ ν B 2 ) 2 ,
G ( ν ) = 0 L g B ( ν , z ) e α z d z ,
G ( ν B ) = G 0 = g B 0 L eff ,
P th 21 K A eff G ( ν max ) ,
P th 21 K A eff g B 0 L eff ,
P inc = 10 log 10 [ g B 0 L eff G ( ν max ) ] .
FOM = γ L eff P th 42 π λ n 2 L eff G ( ν max ) ,
n ( λ ) + 1 = A 0 + A 1 λ 2 + A 2 λ 2 + A 3 λ 4 + A 4 λ 6 + A 5 λ 8 .
A 0 = 4.8270881 A 1 = 3.9929852 × 10 3
A 2 = 1.7852359 × 10 1 A 3 = 9.3099043 × 10 3
A 4 = 7.977633 × 10 5 A 5 = 1.7116618 × 10 4 .

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