Abstract

We present the design of a low bending loss hole-assisted fiber for a 180°-bend fiber socket application, including a tolerance analysis for manufacturability. To this aim, we make use of statistical design methodology, combined with a fully vectorial mode solver. Two resulting designs are presented and their performance in terms of bending loss, coupling loss to Corning SMF-28 standard telecom fiber, and cut-off wavelength is calculated.

© 2008 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. D. B. Payne and R. P. Davey, "The future of fibre access systems?," B T Technol. J. 20, 104-114 (2002).
    [CrossRef]
  2. K. Himeno, S. Matsuo, N. Guan, and A. Wada, "Low-bending-loss single-mode fibers for fiber-to-the-home," J. Lightwave Technol. 23, 3494-3499 (2005).
    [CrossRef]
  3. K. Nakajima, K. Hogari, J. Zhou, K. Tajima, and I. Sankawa, "Hole-assisted fiber for small bending and splice losses," IEEE Photon. Technol. Lett. 15, 1737-1739 (2003).
    [CrossRef]
  4. Y. Tsuchida, K. Saitoh, and M. Koshiba, "Design and characterization of single-mode holey fibers with low bending losses," Opt. Express 13, 4770-4779 (2005).
    [CrossRef] [PubMed]
  5. N. Guan,  et al., "Holey fibers for low bending loss," IEICE Trans. Electron. E89, 191-196 (2006).
    [CrossRef]
  6. Y. Bing, K. Oshono, Y. Kurosawa, T. Kumagai, and M. Tachikura, "Low-loss holey fiber," Hitachi Cable Review 24, 1-4 (2005).
  7. D. C. Montgomery, Design and Analysis of Experiments, 5th ed. (John Wiley & Sons, New York, 2001).
  8. T. J. Santner, B. J. Williams, and W. I. Notz, The Design and Analysis of Computer Experiment (Springer-Verlag, 2003).
  9. J. Van Erps,  et al., "Mass manufacturable 180◦-bend single mode fiber socket using hole-assisted low bending loss fiber," IEEE Photon. Technol. Lett. 20, 187-189 (2008).
    [CrossRef]
  10. LumericalMODE  Solutions™, http://www.lumerical.com/mode.php.
  11. H. R. D. Sunak and S. P. Bastien, "Refractive index and material dispersion of doped silica in the 0.6-1.8um wavelength region," IEEE Photon. Technol. Lett. 1, 142-145 (1989).
    [CrossRef]
  12. L. Faustini and G. Martini, "Bend loss in single-mode fibers," J. Lightwave Technol. 15, 671-679 (1997).
    [CrossRef]
  13. Corning HPFS® Standard Grade, http://www.corning.com/docs/specialtymaterials/pisheets/H0607 hpfs Standard ProductSheet.pdf.
  14. J. Berenger, "A perfectly matched layer for the absorption of electromagnetic waves," J. Computational Phys. 114, 185-200 (1994).
    [CrossRef]
  15. A. S. Webb, F. Poletti, D. J. Richardson, and J. K. Sahu, "Suspended-core holey fiber for evanescent-field sensing," Opt. Eng. 46, 010503 (2007).
    [CrossRef]
  16. A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983).
  17. J. D. Love and C. Durniak, "Bend loss, tapering, and cladding-mode coupling in single-mode fibers," IEEE Photon. Technol. Lett. 191257-1259 (2007).
    [CrossRef]
  18. R. L. Plackett and J. P. Burman, "The design of multifactorial experiments," Biometrika 33, 305-325 (1946).
    [CrossRef]
  19. G. E. P. Box and D.W. Behnken, "Some new three level designs for the study of quantitative variables," Technometrics 2, 455-476 (1960).
    [CrossRef]
  20. Minitab Statistical Software, http://www.minitab.com/products/minitab/.
  21. G. E. P. Box, W. G. Hunter, and J. S. Hunter, Statistics for experimenters: An Introduction to Design, Data Analysis and Model Building (John Wiley & Sons, New York, 1978).
  22. I. M. Sobol, A Primer for the Monte Carlo Method (CRC Press, 1994).
  23. Crystal ball predictive modeling software, http://www.crystalball.com/cbpro/index.html.
  24. T. Martynkien, J. Olszewski, M. Szpulak, G. Golojuch, W. Urbanczyk, T. Nasilowski, F. Berghmans, and H. Thienpont, "Experimental investigations of bending loss oscillations in large mode area photonic crystal fibers," Opt. Express 15, 13547-13556 (2007).
    [CrossRef] [PubMed]
  25. K. Nakajima,  et al., "Cutoff wavelength measurement in a fiber with improved bending loss," IEEE Photon. Technol. Lett. 16, 1918-1920 (2004).
    [CrossRef]

2008 (1)

J. Van Erps,  et al., "Mass manufacturable 180◦-bend single mode fiber socket using hole-assisted low bending loss fiber," IEEE Photon. Technol. Lett. 20, 187-189 (2008).
[CrossRef]

2007 (3)

A. S. Webb, F. Poletti, D. J. Richardson, and J. K. Sahu, "Suspended-core holey fiber for evanescent-field sensing," Opt. Eng. 46, 010503 (2007).
[CrossRef]

J. D. Love and C. Durniak, "Bend loss, tapering, and cladding-mode coupling in single-mode fibers," IEEE Photon. Technol. Lett. 191257-1259 (2007).
[CrossRef]

T. Martynkien, J. Olszewski, M. Szpulak, G. Golojuch, W. Urbanczyk, T. Nasilowski, F. Berghmans, and H. Thienpont, "Experimental investigations of bending loss oscillations in large mode area photonic crystal fibers," Opt. Express 15, 13547-13556 (2007).
[CrossRef] [PubMed]

2006 (1)

N. Guan,  et al., "Holey fibers for low bending loss," IEICE Trans. Electron. E89, 191-196 (2006).
[CrossRef]

2005 (3)

2004 (1)

K. Nakajima,  et al., "Cutoff wavelength measurement in a fiber with improved bending loss," IEEE Photon. Technol. Lett. 16, 1918-1920 (2004).
[CrossRef]

2003 (1)

K. Nakajima, K. Hogari, J. Zhou, K. Tajima, and I. Sankawa, "Hole-assisted fiber for small bending and splice losses," IEEE Photon. Technol. Lett. 15, 1737-1739 (2003).
[CrossRef]

2002 (1)

D. B. Payne and R. P. Davey, "The future of fibre access systems?," B T Technol. J. 20, 104-114 (2002).
[CrossRef]

1997 (1)

L. Faustini and G. Martini, "Bend loss in single-mode fibers," J. Lightwave Technol. 15, 671-679 (1997).
[CrossRef]

1994 (1)

J. Berenger, "A perfectly matched layer for the absorption of electromagnetic waves," J. Computational Phys. 114, 185-200 (1994).
[CrossRef]

1989 (1)

H. R. D. Sunak and S. P. Bastien, "Refractive index and material dispersion of doped silica in the 0.6-1.8um wavelength region," IEEE Photon. Technol. Lett. 1, 142-145 (1989).
[CrossRef]

1960 (1)

G. E. P. Box and D.W. Behnken, "Some new three level designs for the study of quantitative variables," Technometrics 2, 455-476 (1960).
[CrossRef]

1946 (1)

R. L. Plackett and J. P. Burman, "The design of multifactorial experiments," Biometrika 33, 305-325 (1946).
[CrossRef]

Bastien, S. P.

H. R. D. Sunak and S. P. Bastien, "Refractive index and material dispersion of doped silica in the 0.6-1.8um wavelength region," IEEE Photon. Technol. Lett. 1, 142-145 (1989).
[CrossRef]

Behnken, D.W.

G. E. P. Box and D.W. Behnken, "Some new three level designs for the study of quantitative variables," Technometrics 2, 455-476 (1960).
[CrossRef]

Berenger, J.

J. Berenger, "A perfectly matched layer for the absorption of electromagnetic waves," J. Computational Phys. 114, 185-200 (1994).
[CrossRef]

Berghmans, F.

Bing, Y.

Y. Bing, K. Oshono, Y. Kurosawa, T. Kumagai, and M. Tachikura, "Low-loss holey fiber," Hitachi Cable Review 24, 1-4 (2005).

Box, G. E. P.

G. E. P. Box and D.W. Behnken, "Some new three level designs for the study of quantitative variables," Technometrics 2, 455-476 (1960).
[CrossRef]

Burman, J. P.

R. L. Plackett and J. P. Burman, "The design of multifactorial experiments," Biometrika 33, 305-325 (1946).
[CrossRef]

Davey, R. P.

D. B. Payne and R. P. Davey, "The future of fibre access systems?," B T Technol. J. 20, 104-114 (2002).
[CrossRef]

Durniak, C.

J. D. Love and C. Durniak, "Bend loss, tapering, and cladding-mode coupling in single-mode fibers," IEEE Photon. Technol. Lett. 191257-1259 (2007).
[CrossRef]

Faustini, L.

L. Faustini and G. Martini, "Bend loss in single-mode fibers," J. Lightwave Technol. 15, 671-679 (1997).
[CrossRef]

Golojuch, G.

Guan, N.

Himeno, K.

Hogari, K.

K. Nakajima, K. Hogari, J. Zhou, K. Tajima, and I. Sankawa, "Hole-assisted fiber for small bending and splice losses," IEEE Photon. Technol. Lett. 15, 1737-1739 (2003).
[CrossRef]

Koshiba, M.

Kumagai, T.

Y. Bing, K. Oshono, Y. Kurosawa, T. Kumagai, and M. Tachikura, "Low-loss holey fiber," Hitachi Cable Review 24, 1-4 (2005).

Kurosawa, Y.

Y. Bing, K. Oshono, Y. Kurosawa, T. Kumagai, and M. Tachikura, "Low-loss holey fiber," Hitachi Cable Review 24, 1-4 (2005).

Love, J. D.

J. D. Love and C. Durniak, "Bend loss, tapering, and cladding-mode coupling in single-mode fibers," IEEE Photon. Technol. Lett. 191257-1259 (2007).
[CrossRef]

Martini, G.

L. Faustini and G. Martini, "Bend loss in single-mode fibers," J. Lightwave Technol. 15, 671-679 (1997).
[CrossRef]

Martynkien, T.

Matsuo, S.

Nakajima, K.

K. Nakajima,  et al., "Cutoff wavelength measurement in a fiber with improved bending loss," IEEE Photon. Technol. Lett. 16, 1918-1920 (2004).
[CrossRef]

K. Nakajima, K. Hogari, J. Zhou, K. Tajima, and I. Sankawa, "Hole-assisted fiber for small bending and splice losses," IEEE Photon. Technol. Lett. 15, 1737-1739 (2003).
[CrossRef]

Nasilowski, T.

Olszewski, J.

Oshono, K.

Y. Bing, K. Oshono, Y. Kurosawa, T. Kumagai, and M. Tachikura, "Low-loss holey fiber," Hitachi Cable Review 24, 1-4 (2005).

Payne, D. B.

D. B. Payne and R. P. Davey, "The future of fibre access systems?," B T Technol. J. 20, 104-114 (2002).
[CrossRef]

Plackett, R. L.

R. L. Plackett and J. P. Burman, "The design of multifactorial experiments," Biometrika 33, 305-325 (1946).
[CrossRef]

Poletti, F.

A. S. Webb, F. Poletti, D. J. Richardson, and J. K. Sahu, "Suspended-core holey fiber for evanescent-field sensing," Opt. Eng. 46, 010503 (2007).
[CrossRef]

Richardson, D. J.

A. S. Webb, F. Poletti, D. J. Richardson, and J. K. Sahu, "Suspended-core holey fiber for evanescent-field sensing," Opt. Eng. 46, 010503 (2007).
[CrossRef]

Sahu, J. K.

A. S. Webb, F. Poletti, D. J. Richardson, and J. K. Sahu, "Suspended-core holey fiber for evanescent-field sensing," Opt. Eng. 46, 010503 (2007).
[CrossRef]

Saitoh, K.

Sankawa, I.

K. Nakajima, K. Hogari, J. Zhou, K. Tajima, and I. Sankawa, "Hole-assisted fiber for small bending and splice losses," IEEE Photon. Technol. Lett. 15, 1737-1739 (2003).
[CrossRef]

Sunak, H. R. D.

H. R. D. Sunak and S. P. Bastien, "Refractive index and material dispersion of doped silica in the 0.6-1.8um wavelength region," IEEE Photon. Technol. Lett. 1, 142-145 (1989).
[CrossRef]

Szpulak, M.

Tachikura, M.

Y. Bing, K. Oshono, Y. Kurosawa, T. Kumagai, and M. Tachikura, "Low-loss holey fiber," Hitachi Cable Review 24, 1-4 (2005).

Tajima, K.

K. Nakajima, K. Hogari, J. Zhou, K. Tajima, and I. Sankawa, "Hole-assisted fiber for small bending and splice losses," IEEE Photon. Technol. Lett. 15, 1737-1739 (2003).
[CrossRef]

Thienpont, H.

Tsuchida, Y.

Urbanczyk, W.

Van Erps, J.

J. Van Erps,  et al., "Mass manufacturable 180◦-bend single mode fiber socket using hole-assisted low bending loss fiber," IEEE Photon. Technol. Lett. 20, 187-189 (2008).
[CrossRef]

Wada, A.

Webb, A. S.

A. S. Webb, F. Poletti, D. J. Richardson, and J. K. Sahu, "Suspended-core holey fiber for evanescent-field sensing," Opt. Eng. 46, 010503 (2007).
[CrossRef]

Zhou, J.

K. Nakajima, K. Hogari, J. Zhou, K. Tajima, and I. Sankawa, "Hole-assisted fiber for small bending and splice losses," IEEE Photon. Technol. Lett. 15, 1737-1739 (2003).
[CrossRef]

B T Technol. J. (1)

D. B. Payne and R. P. Davey, "The future of fibre access systems?," B T Technol. J. 20, 104-114 (2002).
[CrossRef]

Biometrika (1)

R. L. Plackett and J. P. Burman, "The design of multifactorial experiments," Biometrika 33, 305-325 (1946).
[CrossRef]

Hitachi Cable Review (1)

Y. Bing, K. Oshono, Y. Kurosawa, T. Kumagai, and M. Tachikura, "Low-loss holey fiber," Hitachi Cable Review 24, 1-4 (2005).

IEEE Photon. Technol. Lett. (5)

J. Van Erps,  et al., "Mass manufacturable 180◦-bend single mode fiber socket using hole-assisted low bending loss fiber," IEEE Photon. Technol. Lett. 20, 187-189 (2008).
[CrossRef]

K. Nakajima, K. Hogari, J. Zhou, K. Tajima, and I. Sankawa, "Hole-assisted fiber for small bending and splice losses," IEEE Photon. Technol. Lett. 15, 1737-1739 (2003).
[CrossRef]

H. R. D. Sunak and S. P. Bastien, "Refractive index and material dispersion of doped silica in the 0.6-1.8um wavelength region," IEEE Photon. Technol. Lett. 1, 142-145 (1989).
[CrossRef]

J. D. Love and C. Durniak, "Bend loss, tapering, and cladding-mode coupling in single-mode fibers," IEEE Photon. Technol. Lett. 191257-1259 (2007).
[CrossRef]

K. Nakajima,  et al., "Cutoff wavelength measurement in a fiber with improved bending loss," IEEE Photon. Technol. Lett. 16, 1918-1920 (2004).
[CrossRef]

IEICE Trans. Electron. (1)

N. Guan,  et al., "Holey fibers for low bending loss," IEICE Trans. Electron. E89, 191-196 (2006).
[CrossRef]

J. Computational Phys. (1)

J. Berenger, "A perfectly matched layer for the absorption of electromagnetic waves," J. Computational Phys. 114, 185-200 (1994).
[CrossRef]

J. Lightwave Technol. (2)

Opt. Eng. (1)

A. S. Webb, F. Poletti, D. J. Richardson, and J. K. Sahu, "Suspended-core holey fiber for evanescent-field sensing," Opt. Eng. 46, 010503 (2007).
[CrossRef]

Opt. Express (2)

Technometrics (1)

G. E. P. Box and D.W. Behnken, "Some new three level designs for the study of quantitative variables," Technometrics 2, 455-476 (1960).
[CrossRef]

Other (9)

Minitab Statistical Software, http://www.minitab.com/products/minitab/.

G. E. P. Box, W. G. Hunter, and J. S. Hunter, Statistics for experimenters: An Introduction to Design, Data Analysis and Model Building (John Wiley & Sons, New York, 1978).

I. M. Sobol, A Primer for the Monte Carlo Method (CRC Press, 1994).

Crystal ball predictive modeling software, http://www.crystalball.com/cbpro/index.html.

A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983).

Corning HPFS® Standard Grade, http://www.corning.com/docs/specialtymaterials/pisheets/H0607 hpfs Standard ProductSheet.pdf.

LumericalMODE  Solutions™, http://www.lumerical.com/mode.php.

D. C. Montgomery, Design and Analysis of Experiments, 5th ed. (John Wiley & Sons, New York, 2001).

T. J. Santner, B. J. Williams, and W. I. Notz, The Design and Analysis of Computer Experiment (Springer-Verlag, 2003).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (9)

Fig. 1.
Fig. 1.

Schematic representation of a 180°-bend fiber socket using low bending loss hole-assisted fiber bent on a 5mm radius to interconnect two SMF-28 fibers.

Fig. 2.
Fig. 2.

Definition of the simulation area of 50µm×50µm and the boundary conditions of SMF-28 in MODE Solutions.

Fig. 3.
Fig. 3.

Bending loss of SMF-28 as a function of bending radius at 1310nm and at 1550nm.

Fig. 4.
Fig. 4.

Low bending loss hole-assisted fiber, design Type A (left) and Type B (right). The GeO2-doped core, indicated in light gray, has a radius c (not indicated). The white zones represent air holes, the gray zones represent Corning fused silica.

Fig. 5.
Fig. 5.

Pareto charts resulting from the Plackett-Burman design analysis, showing that the important factors at 1310nm are the inner cladding radius r, hole width w and bridge thickness t. At 1550nm, the core radius c is also significant.

Fig. 6.
Fig. 6.

Results of the Monte-Carlo simulations for design Type A: 2.8×10-4 dB±3.2×10-4 dB for 1310nm and 1.0×10-3 dB±2.0×10-4 dB for 1550nm.

Fig. 7.
Fig. 7.

Pareto charts resulting from the Plackett-Burman design analysis for Type B, showing that the inner cladding radius r is the only significant factor at significance level α=0.05.

Fig. 8.
Fig. 8.

Results of the Monte-Carlo simulations for design Type B: 5.2×10-5 dB±4.5×10-6 dB for 1310nm and 9.0×10-4 dB±6.0×10-5 dB for 1550nm.

Fig. 9.
Fig. 9.

Bend loss performance of hole-assisted fiber Type A (3 bridges), Type A (24 bridges) and Type B versus conventional single mode fiber SMF-28 at 1550nm.

Tables (6)

Tables Icon

Table 1. Plackett-Burman design table for hole-assisted fiber Type A. The factors are the core radius c, the inner cladding radius r, the bridge thickness t and the hole width w. Two responses, the loss at 1310nm and at 1550nm, are calculated using MODE Solutions.

Tables Icon

Table 2. Refined Box-Behnken design table for hole-assisted fiber Type A. The factors are the core radius c, the inner cladding radius r, the bridge thickness t and the hole width w. Two responses, the loss at 1310nm and at 1550nm, are calculated using MODE Solutions.

Tables Icon

Table 3. Quadratic surface response model coefficients resulting from the refined Box-Behnken analysis of hole-assisted fiber design Type A for the following parameters: core radius c, inner cladding radius r, bridge thickness t and hole width w. R 2=100%.

Tables Icon

Table 4. Simulation results of the hole-assisted fiber design Type A: coupling loss, bending loss of the fundamental mode and bending loss BL calculated using Eq. (3).

Tables Icon

Table 5. Simulation results of the hole-assisted fiber design Type B: coupling loss, bending loss of the fundamental mode and bending loss BL calculated using Eq. (3).

Tables Icon

Table 6. Simulation results of the design Type A with 24 bridges instead of 3: coupling loss, bending loss of the fundamental mode and bending loss BL calculated using Eq. (3).

Equations (4)

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

n 2 1 n 2 + 2 = i = 1 3 ( A i + B i f ) λ 2 λ 2 z i 2
η = [ ( E × H S M F * · d S ) ( E SMF × H * · d S ) E × H * · d S ] 1 [ E SMF × H SMF * · d S ]
B L = i = 1 n L i η i
y = β 0 + i = 1 k β i x i + i = 1 k β i i x i 2 + j = 1 k i < j k β i j x i x j + ε

Metrics