Abstract

Large-mode-area (LMA) silica holey fibers (HFs) are investigated both theoretically and experimentally with special attention paid to the effect of a limited number of air channels in the cladding on the main modal characteristics of the fibers. We applied the method of integral equations to model the LMA HF modes, and the results of our calculations are compared with the experimental data obtained for the so-called large-hole–large-spacing silica HFs. The effect of the relative holes’ diameter in the case of a few layers in the cladding on the LMA HF properties is addressed in detail because this parameter basically determines the limits of single-mode waveguide operation and transmission loss of the fabricated LMA HFs.

© 2004 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J. C. Baggett, T. M. Monro, K. Furusawa, and D. J. Richardson, “Comparative study of large-mode holey and conventional fibers,” Opt. Lett. 26, 1045–1047 (2001).
    [CrossRef]
  2. W. J. Wadsworth, R. M. Persival, G. Bouwmans, J. C. Knight, and P. St. J. Russell, “High power air-clad photonic crystal fiber laser,” Opt. Exp. 11, 48–53 (2003), http://www.opticsexpress.org.
    [CrossRef]
  3. N. A. Mortensen, M. D. Nielsen, J. R. Folkenberg, A. Petersson, and H. R. Simonsen, “Improved large-mode-area endlessly single-mode photonic crystal fibers,” Opt. Lett. 28, 393–395 (2003).
    [CrossRef] [PubMed]
  4. T. M. Monro, D. J. Richardson, N. G. R. Broderick, and P. J. Bennett, “Holey optical fibers: an efficient modal model,” J. Lightwave Technol. 19, 1093–1102 (1999).
    [CrossRef]
  5. D. Mogilevtsev, T. A. Birks, and P. St. J. Russell, “Localized function method for modeling defect modes in 2-D photonic crystal,” J. Lightwave Technol. 11, 2078–2081 (1999).
    [CrossRef]
  6. A. Ferrando, E. Silvestre, J. J. Miret, P. Andres, and M. V. Andres, “Vector description of higher-order modes in photonic crystal fibers,” J. Opt. Soc. Am. A 17, 1333–1340 (2000).
    [CrossRef]
  7. T. M. Monro, D. J. Richardson, N. G. R. Broderick, and D. J. Bennett, “Modeling large air fraction holey optical fibers,” J. Lightwave Technol. 18, 50–56 (2000).
    [CrossRef]
  8. Z. Zhu and T. G. Brown, “Full-vectorial finite-difference analysis of microstructured optical fibers,” Opt. Exp. 10, 853–864 (2002), http://www.opticsexpress.org.
    [CrossRef]
  9. M. Koshida and K. Saitoh, “Structural dependence of effec-tive area and mode field diameter for holey fibers,” Opt. Exp., 11, 1746–1756 (2003), http://www.opticsexpress.org.
    [CrossRef]
  10. M. A. van Eijkelenborg, M. C. J. Large, A. Argyros, J. Zagari, S. Manos, N. A. Issa, I. Bassett, S. Fleming, R. C. McPhedran, C. M. de Sterke, and A. P. Nicorovici, “Microstructured polymer optical fiber,” Opt. Exp. 9, 319–327 (2001), http://www.opticsexpress.org.
    [CrossRef]
  11. 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, 2322–2330 (2002).
    [CrossRef]
  12. B. T. Kuhlmey, T. P. White, G. Renversez, D. Maystre, L. C. Botten, C. M. de Sterke, and R. S. McPhedran, “Multipole method for microstructured optical fibers. II. Implementation and results,” J. Opt. Soc. Am. B 19, 2331–2340 (2002).
    [CrossRef]
  13. A. B. Sotsky and L. I. Sotskaya, “The properties of modes of microstructures optical fibers in the vicinity of critical conditions,” Tech. Phys. Lett. 29, 764–767 (2003).
    [CrossRef]
  14. A. B. Sotsky and L. I. Sotskya, “Leaky modes in optical fibers with transverse anisotropy,” Opt. Spectrosc. 88, 415–422 (2000).
    [CrossRef]
  15. C. A. Korn and T. M. Korn, Mathematical Handbook (McGraw-Hill, New York, 1968), p. 831.
  16. M. Born and E. Wolf, Principles of Optics (Pergamon, Oxford, UK, 1968), p. 710.
  17. V. I. Krylov, V. V. Bobkov, and P. I. Monasturnyi, Methods of Computing (Nauka, Moscow, 1977), p. 399 (in Russian).
  18. A. B. Sotsky, “To computing complex zeros of transcendental equations,” Dokl. NASB 45, 19–22 (2001) (in Russian).
  19. T. P. White, R. C. McPhedran, C. M. de Sterke, L. C. Botten, and M. J. Steel, “Confinement losses in microstructured optical fibers,” Opt. Lett. 26, 1660–1662 (2001).
    [CrossRef]
  20. M. J. Steel, T. P. White, C. M. de Sterke, R. C. McPhedran, and L. C. Botten, “Symmetry and degeneracy in microstructured optical fibers,” Opt. Lett. 26, 488–490 (2001).
    [CrossRef]
  21. A. B. Sotsky and L. I. Sotskaya, “Modes of capillary optical fibers,” Opt. Commun. 230, 67–79 (2004).
    [CrossRef]
  22. N. A. Mortensen, “Effective area of photonic crystal fibers,” Opt. Exp. 10, 341–348 (2002), http://www.opticsexpress.org.
    [CrossRef]
  23. B. T. Kuhlmey, R. C. McPhedran, and C. M. De Sterke, “Modal cutoff in microstructured optical fiber,” Opt. Lett. 27, 1684–1686 (2002).
    [CrossRef]
  24. N. A. Mortensen and J. R. Folkenberg, “Low-loss criterion and effective area considerations for photonic crystal fibers,” J. Opt. A. Pure Appl. Opt. 5, 163–167 (2003).
    [CrossRef]
  25. M. D. Nielsen, N. A. Mortensen, and J. R. Folkeberg, “Reduced microdeformation attenuation spectra in large-mode-area photonic crystal fibers for visible applications,” Opt. Lett. 28, 1645–1647 (2003).
    [CrossRef] [PubMed]
  26. T. A. Birks, J. C. Knight, and P. St. J. Russell, “Endlessly single-mode photonic crystal fiber,” Opt. Lett. 22, 961–963 (1997).
    [CrossRef] [PubMed]
  27. B. T. Kuhlmey, R. C. McPhedran, C. M. de Sterke, D. A. Robinson, G. Renversez, and D. Mayster, “Microstructured optical fibers: where’s the edge?,” Opt. Exp. 10, 1285–1290 (2002), http://www.opticsexpress.org.
    [CrossRef]
  28. V. V. Shevchenko, “Spectral expansion eigen and attached functions of an non-self-adjoint problem on an entire axis,” Diffirencialnye Uravnenia 15, 2004–2020 (1979) (in Russian).
  29. M. J. Adams, An Introduction to Optical Waveguides (Wiley, New York, 1981), p. 512.
  30. M. D. Nielsen, J. R. Folkenberg, and N. A. Mortensen, “Single-mode photonic crystal fiber with an effective area of 600 μm2 and low bending loss,” Electron. Lett. 39, 1802–1803 (2003), www:arxiv.org./abs/physics/0311065.
    [CrossRef]
  31. A. D. Fitt, K. Furusava, T. M. Monro, and C. P. Please, “Modeling the fabrication of hollow fibers: capillary drawing,” J. Lightwave Technol. 17, 1093–1102 (1999).
  32. V. P. Minkovich, A. V. Kir’yanov, and S. Calixto, “Large-hole-large-spacing holey fibers with a few air holes—fabrication and measurements of light-delivering properties and optical losses,” Laser Phys. 14, 000–000 (2004).
  33. N. A. Mortensen and J. R. Folkenberg, “Near-field to far-field transition of photonic crystal fibers: symmetries and interference phenomena,” Opt. Exp. 10, 475–481 (2002), http://www.opticsexpress.org.
    [CrossRef]
  34. M. D. Nielsen, N. A. Mortensen, J. R. Folkenberg, and A. Bjarklev, “Mode-field radius of photonic crystal fibers expressed by the V parameter,” Opt. Lett. 28, 2309–2311 (2003).
    [CrossRef] [PubMed]
  35. M. D. Nielsen and N. A. Mortensen, “Photonic crystal fiber design based on the V-parameter,” Opt. Express 11, 2762–2768 (2003), http://www.opticsexpress.org.
    [CrossRef] [PubMed]

2004 (2)

A. B. Sotsky and L. I. Sotskaya, “Modes of capillary optical fibers,” Opt. Commun. 230, 67–79 (2004).
[CrossRef]

V. P. Minkovich, A. V. Kir’yanov, and S. Calixto, “Large-hole-large-spacing holey fibers with a few air holes—fabrication and measurements of light-delivering properties and optical losses,” Laser Phys. 14, 000–000 (2004).

2003 (9)

N. A. Mortensen and J. R. Folkenberg, “Low-loss criterion and effective area considerations for photonic crystal fibers,” J. Opt. A. Pure Appl. Opt. 5, 163–167 (2003).
[CrossRef]

W. J. Wadsworth, R. M. Persival, G. Bouwmans, J. C. Knight, and P. St. J. Russell, “High power air-clad photonic crystal fiber laser,” Opt. Exp. 11, 48–53 (2003), http://www.opticsexpress.org.
[CrossRef]

M. Koshida and K. Saitoh, “Structural dependence of effec-tive area and mode field diameter for holey fibers,” Opt. Exp., 11, 1746–1756 (2003), http://www.opticsexpress.org.
[CrossRef]

A. B. Sotsky and L. I. Sotskaya, “The properties of modes of microstructures optical fibers in the vicinity of critical conditions,” Tech. Phys. Lett. 29, 764–767 (2003).
[CrossRef]

N. A. Mortensen, M. D. Nielsen, J. R. Folkenberg, A. Petersson, and H. R. Simonsen, “Improved large-mode-area endlessly single-mode photonic crystal fibers,” Opt. Lett. 28, 393–395 (2003).
[CrossRef] [PubMed]

M. D. Nielsen, N. A. Mortensen, and J. R. Folkeberg, “Reduced microdeformation attenuation spectra in large-mode-area photonic crystal fibers for visible applications,” Opt. Lett. 28, 1645–1647 (2003).
[CrossRef] [PubMed]

M. D. Nielsen and N. A. Mortensen, “Photonic crystal fiber design based on the V-parameter,” Opt. Express 11, 2762–2768 (2003), http://www.opticsexpress.org.
[CrossRef] [PubMed]

M. D. Nielsen, N. A. Mortensen, J. R. Folkenberg, and A. Bjarklev, “Mode-field radius of photonic crystal fibers expressed by the V parameter,” Opt. Lett. 28, 2309–2311 (2003).
[CrossRef] [PubMed]

M. D. Nielsen, J. R. Folkenberg, and N. A. Mortensen, “Single-mode photonic crystal fiber with an effective area of 600 μm2 and low bending loss,” Electron. Lett. 39, 1802–1803 (2003), www:arxiv.org./abs/physics/0311065.
[CrossRef]

2002 (7)

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, 2322–2330 (2002).
[CrossRef]

B. T. Kuhlmey, T. P. White, G. Renversez, D. Maystre, L. C. Botten, C. M. de Sterke, and R. S. McPhedran, “Multipole method for microstructured optical fibers. II. Implementation and results,” J. Opt. Soc. Am. B 19, 2331–2340 (2002).
[CrossRef]

B. T. Kuhlmey, R. C. McPhedran, and C. M. De Sterke, “Modal cutoff in microstructured optical fiber,” Opt. Lett. 27, 1684–1686 (2002).
[CrossRef]

Z. Zhu and T. G. Brown, “Full-vectorial finite-difference analysis of microstructured optical fibers,” Opt. Exp. 10, 853–864 (2002), http://www.opticsexpress.org.
[CrossRef]

B. T. Kuhlmey, R. C. McPhedran, C. M. de Sterke, D. A. Robinson, G. Renversez, and D. Mayster, “Microstructured optical fibers: where’s the edge?,” Opt. Exp. 10, 1285–1290 (2002), http://www.opticsexpress.org.
[CrossRef]

N. A. Mortensen, “Effective area of photonic crystal fibers,” Opt. Exp. 10, 341–348 (2002), http://www.opticsexpress.org.
[CrossRef]

N. A. Mortensen and J. R. Folkenberg, “Near-field to far-field transition of photonic crystal fibers: symmetries and interference phenomena,” Opt. Exp. 10, 475–481 (2002), http://www.opticsexpress.org.
[CrossRef]

2001 (5)

M. A. van Eijkelenborg, M. C. J. Large, A. Argyros, J. Zagari, S. Manos, N. A. Issa, I. Bassett, S. Fleming, R. C. McPhedran, C. M. de Sterke, and A. P. Nicorovici, “Microstructured polymer optical fiber,” Opt. Exp. 9, 319–327 (2001), http://www.opticsexpress.org.
[CrossRef]

A. B. Sotsky, “To computing complex zeros of transcendental equations,” Dokl. NASB 45, 19–22 (2001) (in Russian).

M. J. Steel, T. P. White, C. M. de Sterke, R. C. McPhedran, and L. C. Botten, “Symmetry and degeneracy in microstructured optical fibers,” Opt. Lett. 26, 488–490 (2001).
[CrossRef]

J. C. Baggett, T. M. Monro, K. Furusawa, and D. J. Richardson, “Comparative study of large-mode holey and conventional fibers,” Opt. Lett. 26, 1045–1047 (2001).
[CrossRef]

T. P. White, R. C. McPhedran, C. M. de Sterke, L. C. Botten, and M. J. Steel, “Confinement losses in microstructured optical fibers,” Opt. Lett. 26, 1660–1662 (2001).
[CrossRef]

2000 (3)

1999 (3)

1997 (1)

1979 (1)

V. V. Shevchenko, “Spectral expansion eigen and attached functions of an non-self-adjoint problem on an entire axis,” Diffirencialnye Uravnenia 15, 2004–2020 (1979) (in Russian).

Andres, M. V.

Andres, P.

Argyros, A.

M. A. van Eijkelenborg, M. C. J. Large, A. Argyros, J. Zagari, S. Manos, N. A. Issa, I. Bassett, S. Fleming, R. C. McPhedran, C. M. de Sterke, and A. P. Nicorovici, “Microstructured polymer optical fiber,” Opt. Exp. 9, 319–327 (2001), http://www.opticsexpress.org.
[CrossRef]

Baggett, J. C.

Bassett, I.

M. A. van Eijkelenborg, M. C. J. Large, A. Argyros, J. Zagari, S. Manos, N. A. Issa, I. Bassett, S. Fleming, R. C. McPhedran, C. M. de Sterke, and A. P. Nicorovici, “Microstructured polymer optical fiber,” Opt. Exp. 9, 319–327 (2001), http://www.opticsexpress.org.
[CrossRef]

Bennett, D. J.

Bennett, P. J.

Birks, T. A.

D. Mogilevtsev, T. A. Birks, and P. St. J. Russell, “Localized function method for modeling defect modes in 2-D photonic crystal,” J. Lightwave Technol. 11, 2078–2081 (1999).
[CrossRef]

T. A. Birks, J. C. Knight, and P. St. J. Russell, “Endlessly single-mode photonic crystal fiber,” Opt. Lett. 22, 961–963 (1997).
[CrossRef] [PubMed]

Bjarklev, A.

Botten, L. C.

Bouwmans, G.

W. J. Wadsworth, R. M. Persival, G. Bouwmans, J. C. Knight, and P. St. J. Russell, “High power air-clad photonic crystal fiber laser,” Opt. Exp. 11, 48–53 (2003), http://www.opticsexpress.org.
[CrossRef]

Broderick, N. G. R.

Brown, T. G.

Z. Zhu and T. G. Brown, “Full-vectorial finite-difference analysis of microstructured optical fibers,” Opt. Exp. 10, 853–864 (2002), http://www.opticsexpress.org.
[CrossRef]

Calixto, S.

V. P. Minkovich, A. V. Kir’yanov, and S. Calixto, “Large-hole-large-spacing holey fibers with a few air holes—fabrication and measurements of light-delivering properties and optical losses,” Laser Phys. 14, 000–000 (2004).

de Sterke, C. M.

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, 2322–2330 (2002).
[CrossRef]

B. T. Kuhlmey, T. P. White, G. Renversez, D. Maystre, L. C. Botten, C. M. de Sterke, and R. S. McPhedran, “Multipole method for microstructured optical fibers. II. Implementation and results,” J. Opt. Soc. Am. B 19, 2331–2340 (2002).
[CrossRef]

B. T. Kuhlmey, R. C. McPhedran, C. M. de Sterke, D. A. Robinson, G. Renversez, and D. Mayster, “Microstructured optical fibers: where’s the edge?,” Opt. Exp. 10, 1285–1290 (2002), http://www.opticsexpress.org.
[CrossRef]

B. T. Kuhlmey, R. C. McPhedran, and C. M. De Sterke, “Modal cutoff in microstructured optical fiber,” Opt. Lett. 27, 1684–1686 (2002).
[CrossRef]

M. J. Steel, T. P. White, C. M. de Sterke, R. C. McPhedran, and L. C. Botten, “Symmetry and degeneracy in microstructured optical fibers,” Opt. Lett. 26, 488–490 (2001).
[CrossRef]

M. A. van Eijkelenborg, M. C. J. Large, A. Argyros, J. Zagari, S. Manos, N. A. Issa, I. Bassett, S. Fleming, R. C. McPhedran, C. M. de Sterke, and A. P. Nicorovici, “Microstructured polymer optical fiber,” Opt. Exp. 9, 319–327 (2001), http://www.opticsexpress.org.
[CrossRef]

T. P. White, R. C. McPhedran, C. M. de Sterke, L. C. Botten, and M. J. Steel, “Confinement losses in microstructured optical fibers,” Opt. Lett. 26, 1660–1662 (2001).
[CrossRef]

Ferrando, A.

Fitt, A. D.

Fleming, S.

M. A. van Eijkelenborg, M. C. J. Large, A. Argyros, J. Zagari, S. Manos, N. A. Issa, I. Bassett, S. Fleming, R. C. McPhedran, C. M. de Sterke, and A. P. Nicorovici, “Microstructured polymer optical fiber,” Opt. Exp. 9, 319–327 (2001), http://www.opticsexpress.org.
[CrossRef]

Folkeberg, J. R.

Folkenberg, J. R.

M. D. Nielsen, N. A. Mortensen, J. R. Folkenberg, and A. Bjarklev, “Mode-field radius of photonic crystal fibers expressed by the V parameter,” Opt. Lett. 28, 2309–2311 (2003).
[CrossRef] [PubMed]

N. A. Mortensen and J. R. Folkenberg, “Low-loss criterion and effective area considerations for photonic crystal fibers,” J. Opt. A. Pure Appl. Opt. 5, 163–167 (2003).
[CrossRef]

N. A. Mortensen, M. D. Nielsen, J. R. Folkenberg, A. Petersson, and H. R. Simonsen, “Improved large-mode-area endlessly single-mode photonic crystal fibers,” Opt. Lett. 28, 393–395 (2003).
[CrossRef] [PubMed]

M. D. Nielsen, J. R. Folkenberg, and N. A. Mortensen, “Single-mode photonic crystal fiber with an effective area of 600 μm2 and low bending loss,” Electron. Lett. 39, 1802–1803 (2003), www:arxiv.org./abs/physics/0311065.
[CrossRef]

N. A. Mortensen and J. R. Folkenberg, “Near-field to far-field transition of photonic crystal fibers: symmetries and interference phenomena,” Opt. Exp. 10, 475–481 (2002), http://www.opticsexpress.org.
[CrossRef]

Furusava, K.

Furusawa, K.

Issa, N. A.

M. A. van Eijkelenborg, M. C. J. Large, A. Argyros, J. Zagari, S. Manos, N. A. Issa, I. Bassett, S. Fleming, R. C. McPhedran, C. M. de Sterke, and A. P. Nicorovici, “Microstructured polymer optical fiber,” Opt. Exp. 9, 319–327 (2001), http://www.opticsexpress.org.
[CrossRef]

Kir’yanov, A. V.

V. P. Minkovich, A. V. Kir’yanov, and S. Calixto, “Large-hole-large-spacing holey fibers with a few air holes—fabrication and measurements of light-delivering properties and optical losses,” Laser Phys. 14, 000–000 (2004).

Knight, J. C.

W. J. Wadsworth, R. M. Persival, G. Bouwmans, J. C. Knight, and P. St. J. Russell, “High power air-clad photonic crystal fiber laser,” Opt. Exp. 11, 48–53 (2003), http://www.opticsexpress.org.
[CrossRef]

T. A. Birks, J. C. Knight, and P. St. J. Russell, “Endlessly single-mode photonic crystal fiber,” Opt. Lett. 22, 961–963 (1997).
[CrossRef] [PubMed]

Koshida, M.

M. Koshida and K. Saitoh, “Structural dependence of effec-tive area and mode field diameter for holey fibers,” Opt. Exp., 11, 1746–1756 (2003), http://www.opticsexpress.org.
[CrossRef]

Kuhlmey, B. T.

Large, M. C. J.

M. A. van Eijkelenborg, M. C. J. Large, A. Argyros, J. Zagari, S. Manos, N. A. Issa, I. Bassett, S. Fleming, R. C. McPhedran, C. M. de Sterke, and A. P. Nicorovici, “Microstructured polymer optical fiber,” Opt. Exp. 9, 319–327 (2001), http://www.opticsexpress.org.
[CrossRef]

Manos, S.

M. A. van Eijkelenborg, M. C. J. Large, A. Argyros, J. Zagari, S. Manos, N. A. Issa, I. Bassett, S. Fleming, R. C. McPhedran, C. M. de Sterke, and A. P. Nicorovici, “Microstructured polymer optical fiber,” Opt. Exp. 9, 319–327 (2001), http://www.opticsexpress.org.
[CrossRef]

Mayster, D.

B. T. Kuhlmey, R. C. McPhedran, C. M. de Sterke, D. A. Robinson, G. Renversez, and D. Mayster, “Microstructured optical fibers: where’s the edge?,” Opt. Exp. 10, 1285–1290 (2002), http://www.opticsexpress.org.
[CrossRef]

Maystre, D.

McPhedran, R. C.

McPhedran, R. S.

Minkovich, V. P.

V. P. Minkovich, A. V. Kir’yanov, and S. Calixto, “Large-hole-large-spacing holey fibers with a few air holes—fabrication and measurements of light-delivering properties and optical losses,” Laser Phys. 14, 000–000 (2004).

Miret, J. J.

Mogilevtsev, D.

D. Mogilevtsev, T. A. Birks, and P. St. J. Russell, “Localized function method for modeling defect modes in 2-D photonic crystal,” J. Lightwave Technol. 11, 2078–2081 (1999).
[CrossRef]

Monro, T. M.

Mortensen, N. A.

N. A. Mortensen and J. R. Folkenberg, “Low-loss criterion and effective area considerations for photonic crystal fibers,” J. Opt. A. Pure Appl. Opt. 5, 163–167 (2003).
[CrossRef]

M. D. Nielsen and N. A. Mortensen, “Photonic crystal fiber design based on the V-parameter,” Opt. Express 11, 2762–2768 (2003), http://www.opticsexpress.org.
[CrossRef] [PubMed]

N. A. Mortensen, M. D. Nielsen, J. R. Folkenberg, A. Petersson, and H. R. Simonsen, “Improved large-mode-area endlessly single-mode photonic crystal fibers,” Opt. Lett. 28, 393–395 (2003).
[CrossRef] [PubMed]

M. D. Nielsen, J. R. Folkenberg, and N. A. Mortensen, “Single-mode photonic crystal fiber with an effective area of 600 μm2 and low bending loss,” Electron. Lett. 39, 1802–1803 (2003), www:arxiv.org./abs/physics/0311065.
[CrossRef]

M. D. Nielsen, N. A. Mortensen, J. R. Folkenberg, and A. Bjarklev, “Mode-field radius of photonic crystal fibers expressed by the V parameter,” Opt. Lett. 28, 2309–2311 (2003).
[CrossRef] [PubMed]

M. D. Nielsen, N. A. Mortensen, and J. R. Folkeberg, “Reduced microdeformation attenuation spectra in large-mode-area photonic crystal fibers for visible applications,” Opt. Lett. 28, 1645–1647 (2003).
[CrossRef] [PubMed]

N. A. Mortensen and J. R. Folkenberg, “Near-field to far-field transition of photonic crystal fibers: symmetries and interference phenomena,” Opt. Exp. 10, 475–481 (2002), http://www.opticsexpress.org.
[CrossRef]

N. A. Mortensen, “Effective area of photonic crystal fibers,” Opt. Exp. 10, 341–348 (2002), http://www.opticsexpress.org.
[CrossRef]

Nicorovici, A. P.

M. A. van Eijkelenborg, M. C. J. Large, A. Argyros, J. Zagari, S. Manos, N. A. Issa, I. Bassett, S. Fleming, R. C. McPhedran, C. M. de Sterke, and A. P. Nicorovici, “Microstructured polymer optical fiber,” Opt. Exp. 9, 319–327 (2001), http://www.opticsexpress.org.
[CrossRef]

Nielsen, M. D.

Persival, R. M.

W. J. Wadsworth, R. M. Persival, G. Bouwmans, J. C. Knight, and P. St. J. Russell, “High power air-clad photonic crystal fiber laser,” Opt. Exp. 11, 48–53 (2003), http://www.opticsexpress.org.
[CrossRef]

Petersson, A.

Please, C. P.

Renversez, G.

Richardson, D. J.

Robinson, D. A.

B. T. Kuhlmey, R. C. McPhedran, C. M. de Sterke, D. A. Robinson, G. Renversez, and D. Mayster, “Microstructured optical fibers: where’s the edge?,” Opt. Exp. 10, 1285–1290 (2002), http://www.opticsexpress.org.
[CrossRef]

Russell, P. St. J.

W. J. Wadsworth, R. M. Persival, G. Bouwmans, J. C. Knight, and P. St. J. Russell, “High power air-clad photonic crystal fiber laser,” Opt. Exp. 11, 48–53 (2003), http://www.opticsexpress.org.
[CrossRef]

D. Mogilevtsev, T. A. Birks, and P. St. J. Russell, “Localized function method for modeling defect modes in 2-D photonic crystal,” J. Lightwave Technol. 11, 2078–2081 (1999).
[CrossRef]

T. A. Birks, J. C. Knight, and P. St. J. Russell, “Endlessly single-mode photonic crystal fiber,” Opt. Lett. 22, 961–963 (1997).
[CrossRef] [PubMed]

Saitoh, K.

M. Koshida and K. Saitoh, “Structural dependence of effec-tive area and mode field diameter for holey fibers,” Opt. Exp., 11, 1746–1756 (2003), http://www.opticsexpress.org.
[CrossRef]

Shevchenko, V. V.

V. V. Shevchenko, “Spectral expansion eigen and attached functions of an non-self-adjoint problem on an entire axis,” Diffirencialnye Uravnenia 15, 2004–2020 (1979) (in Russian).

Silvestre, E.

Simonsen, H. R.

Sotskaya, L. I.

A. B. Sotsky and L. I. Sotskaya, “Modes of capillary optical fibers,” Opt. Commun. 230, 67–79 (2004).
[CrossRef]

A. B. Sotsky and L. I. Sotskaya, “The properties of modes of microstructures optical fibers in the vicinity of critical conditions,” Tech. Phys. Lett. 29, 764–767 (2003).
[CrossRef]

Sotsky, A. B.

A. B. Sotsky and L. I. Sotskaya, “Modes of capillary optical fibers,” Opt. Commun. 230, 67–79 (2004).
[CrossRef]

A. B. Sotsky and L. I. Sotskaya, “The properties of modes of microstructures optical fibers in the vicinity of critical conditions,” Tech. Phys. Lett. 29, 764–767 (2003).
[CrossRef]

A. B. Sotsky, “To computing complex zeros of transcendental equations,” Dokl. NASB 45, 19–22 (2001) (in Russian).

A. B. Sotsky and L. I. Sotskya, “Leaky modes in optical fibers with transverse anisotropy,” Opt. Spectrosc. 88, 415–422 (2000).
[CrossRef]

Sotskya, L. I.

A. B. Sotsky and L. I. Sotskya, “Leaky modes in optical fibers with transverse anisotropy,” Opt. Spectrosc. 88, 415–422 (2000).
[CrossRef]

Steel, M. J.

van Eijkelenborg, M. A.

M. A. van Eijkelenborg, M. C. J. Large, A. Argyros, J. Zagari, S. Manos, N. A. Issa, I. Bassett, S. Fleming, R. C. McPhedran, C. M. de Sterke, and A. P. Nicorovici, “Microstructured polymer optical fiber,” Opt. Exp. 9, 319–327 (2001), http://www.opticsexpress.org.
[CrossRef]

Wadsworth, W. J.

W. J. Wadsworth, R. M. Persival, G. Bouwmans, J. C. Knight, and P. St. J. Russell, “High power air-clad photonic crystal fiber laser,” Opt. Exp. 11, 48–53 (2003), http://www.opticsexpress.org.
[CrossRef]

White, T. P.

Zagari, J.

M. A. van Eijkelenborg, M. C. J. Large, A. Argyros, J. Zagari, S. Manos, N. A. Issa, I. Bassett, S. Fleming, R. C. McPhedran, C. M. de Sterke, and A. P. Nicorovici, “Microstructured polymer optical fiber,” Opt. Exp. 9, 319–327 (2001), http://www.opticsexpress.org.
[CrossRef]

Zhu, Z.

Z. Zhu and T. G. Brown, “Full-vectorial finite-difference analysis of microstructured optical fibers,” Opt. Exp. 10, 853–864 (2002), http://www.opticsexpress.org.
[CrossRef]

Diffirencialnye Uravnenia (1)

V. V. Shevchenko, “Spectral expansion eigen and attached functions of an non-self-adjoint problem on an entire axis,” Diffirencialnye Uravnenia 15, 2004–2020 (1979) (in Russian).

Dokl. NASB (1)

A. B. Sotsky, “To computing complex zeros of transcendental equations,” Dokl. NASB 45, 19–22 (2001) (in Russian).

Electron. Lett. (1)

M. D. Nielsen, J. R. Folkenberg, and N. A. Mortensen, “Single-mode photonic crystal fiber with an effective area of 600 μm2 and low bending loss,” Electron. Lett. 39, 1802–1803 (2003), www:arxiv.org./abs/physics/0311065.
[CrossRef]

J. Lightwave Technol. (4)

J. Opt. A. Pure Appl. Opt. (1)

N. A. Mortensen and J. R. Folkenberg, “Low-loss criterion and effective area considerations for photonic crystal fibers,” J. Opt. A. Pure Appl. Opt. 5, 163–167 (2003).
[CrossRef]

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

J. Opt. Soc. Am. B (2)

Laser Phys. (1)

V. P. Minkovich, A. V. Kir’yanov, and S. Calixto, “Large-hole-large-spacing holey fibers with a few air holes—fabrication and measurements of light-delivering properties and optical losses,” Laser Phys. 14, 000–000 (2004).

Opt. Commun. (1)

A. B. Sotsky and L. I. Sotskaya, “Modes of capillary optical fibers,” Opt. Commun. 230, 67–79 (2004).
[CrossRef]

Opt. Exp. (7)

N. A. Mortensen, “Effective area of photonic crystal fibers,” Opt. Exp. 10, 341–348 (2002), http://www.opticsexpress.org.
[CrossRef]

B. T. Kuhlmey, R. C. McPhedran, C. M. de Sterke, D. A. Robinson, G. Renversez, and D. Mayster, “Microstructured optical fibers: where’s the edge?,” Opt. Exp. 10, 1285–1290 (2002), http://www.opticsexpress.org.
[CrossRef]

W. J. Wadsworth, R. M. Persival, G. Bouwmans, J. C. Knight, and P. St. J. Russell, “High power air-clad photonic crystal fiber laser,” Opt. Exp. 11, 48–53 (2003), http://www.opticsexpress.org.
[CrossRef]

Z. Zhu and T. G. Brown, “Full-vectorial finite-difference analysis of microstructured optical fibers,” Opt. Exp. 10, 853–864 (2002), http://www.opticsexpress.org.
[CrossRef]

M. Koshida and K. Saitoh, “Structural dependence of effec-tive area and mode field diameter for holey fibers,” Opt. Exp., 11, 1746–1756 (2003), http://www.opticsexpress.org.
[CrossRef]

M. A. van Eijkelenborg, M. C. J. Large, A. Argyros, J. Zagari, S. Manos, N. A. Issa, I. Bassett, S. Fleming, R. C. McPhedran, C. M. de Sterke, and A. P. Nicorovici, “Microstructured polymer optical fiber,” Opt. Exp. 9, 319–327 (2001), http://www.opticsexpress.org.
[CrossRef]

N. A. Mortensen and J. R. Folkenberg, “Near-field to far-field transition of photonic crystal fibers: symmetries and interference phenomena,” Opt. Exp. 10, 475–481 (2002), http://www.opticsexpress.org.
[CrossRef]

Opt. Express (1)

Opt. Lett. (8)

M. D. Nielsen, N. A. Mortensen, J. R. Folkenberg, and A. Bjarklev, “Mode-field radius of photonic crystal fibers expressed by the V parameter,” Opt. Lett. 28, 2309–2311 (2003).
[CrossRef] [PubMed]

T. A. Birks, J. C. Knight, and P. St. J. Russell, “Endlessly single-mode photonic crystal fiber,” Opt. Lett. 22, 961–963 (1997).
[CrossRef] [PubMed]

M. J. Steel, T. P. White, C. M. de Sterke, R. C. McPhedran, and L. C. Botten, “Symmetry and degeneracy in microstructured optical fibers,” Opt. Lett. 26, 488–490 (2001).
[CrossRef]

J. C. Baggett, T. M. Monro, K. Furusawa, and D. J. Richardson, “Comparative study of large-mode holey and conventional fibers,” Opt. Lett. 26, 1045–1047 (2001).
[CrossRef]

T. P. White, R. C. McPhedran, C. M. de Sterke, L. C. Botten, and M. J. Steel, “Confinement losses in microstructured optical fibers,” Opt. Lett. 26, 1660–1662 (2001).
[CrossRef]

B. T. Kuhlmey, R. C. McPhedran, and C. M. De Sterke, “Modal cutoff in microstructured optical fiber,” Opt. Lett. 27, 1684–1686 (2002).
[CrossRef]

N. A. Mortensen, M. D. Nielsen, J. R. Folkenberg, A. Petersson, and H. R. Simonsen, “Improved large-mode-area endlessly single-mode photonic crystal fibers,” Opt. Lett. 28, 393–395 (2003).
[CrossRef] [PubMed]

M. D. Nielsen, N. A. Mortensen, and J. R. Folkeberg, “Reduced microdeformation attenuation spectra in large-mode-area photonic crystal fibers for visible applications,” Opt. Lett. 28, 1645–1647 (2003).
[CrossRef] [PubMed]

Opt. Spectrosc. (1)

A. B. Sotsky and L. I. Sotskya, “Leaky modes in optical fibers with transverse anisotropy,” Opt. Spectrosc. 88, 415–422 (2000).
[CrossRef]

Tech. Phys. Lett. (1)

A. B. Sotsky and L. I. Sotskaya, “The properties of modes of microstructures optical fibers in the vicinity of critical conditions,” Tech. Phys. Lett. 29, 764–767 (2003).
[CrossRef]

Other (4)

C. A. Korn and T. M. Korn, Mathematical Handbook (McGraw-Hill, New York, 1968), p. 831.

M. Born and E. Wolf, Principles of Optics (Pergamon, Oxford, UK, 1968), p. 710.

V. I. Krylov, V. V. Bobkov, and P. I. Monasturnyi, Methods of Computing (Nauka, Moscow, 1977), p. 399 (in Russian).

M. J. Adams, An Introduction to Optical Waveguides (Wiley, New York, 1981), p. 512.

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 (12)

Fig. 1
Fig. 1

One-quarter part of a fundamental-mode intensity distribution for the case of a HF with dΛ-1=0.52. The number 1–8 are isolines ln(Sz maxSz-1)=0.5, 1, 1.5,, 4. The inset is an overview of a HF three-ring air-hole structure.

Fig. 2
Fig. 2

Relative beat length ζλ0-1 versus Λλ0-1 for the fundamental modes of HFs with dΛ-1=(1) 0.38, (2) 0.48, (3) 0.52, (4) 0.6.

Fig. 3
Fig. 3

Relative area of the fundamental-mode spot versus Λλ0-1 for HFs with dΛ-1=(1) 0.38, (2) 0.48, (3) 0.52, (4) 0.6.

Fig. 4
Fig. 4

Phase diagrams for fundamental modes of HFs with dΛ-1=(1) 0.38, (2) 0.48, (3) 0.52, (4) 0.6.

Fig. 5
Fig. 5

Dependencies of k0-1 Im β on Λλ0-1 for the modes of HFs with dΛ-1=(a) 0.38, (b) 0.48, (c) 0.52, (d) 0.6 and for different numbers of hexagonal rings of air holes: nr=2 (curves 1, 4), 3 (curves 2, 5), 4 (curves 3, 6), 5 (curves 7, 8). Curves 1, 2, 3, and 7 refer to the fundamental mode and curves 4, 5, 6, and 8 refer to first higher mode. The dashed curves indicate confinement losses of 1 dB m-1 and 0.2 dB km-1, corresponding to Λ=6.8 µm.

Fig. 6
Fig. 6

Group-velocity dispersion for HFs with dΛ-1=(1) 0.38, (2) 0.48, (3) 0.52, (4) 0.6. The dashed line refers to silica dispersion.

Fig. 7
Fig. 7

Dependencies of Im β versus Im εc for the (1) fundamental and (2) first higher modes of HFs with dΛ-1=0.52, Re εc=2.1025, Λλ0-1=10 and nr=2, 3, 4.

Fig. 8
Fig. 8

(a) Endface image (atomic force microscope) of a HF with dΛ-1=0.48 (overall view). Procedure of the measurements of hole (b) spacing Λ and (c) diameter d.

Fig. 9
Fig. 9

(a) and (b) Microphotographs (30 µm×30 µm) of endface images (HF, dΛ-1=0.48) at (a) white-light illumination and (b) illumination with the Gaussian beam of a He–Ne laser. (c) Photograph of a far-field image of the same fiber (He–Ne laser, wavelength of 633 nm).

Fig. 10
Fig. 10

Dependence of HF transmission loss versus dΛ-1 measured with probe signals (OTDR) at wavelengths of 1550 nm (filled circles) and 1310 nm (open circles).

Fig. 11
Fig. 11

(a) Experimental transversal scans of a He–Ne laser beam that is passed a 2-m distance of the HF with dΛ-1=0.52 recorded at a 5-cm distance from the fiber endface. (b) Theoretical distribution for dΛ-1=0.52 calculated for the same conditions.

Fig. 12
Fig. 12

(a) Experimental dependences of width (curve 1) and normalized intensity (curve 2) of transversal distributions [Fig. 11(a)] versus dΛ-1. (b) Theoretical dependence of the width of transversal distributions [Fig. 11(b)] versus dΛ-1.

Tables (2)

Tables Icon

Table 1 Convergence of β and Im βc with m

Tables Icon

Table 2 Modal Characteristics of a HF with Λ=6.8 µm, nr=3

Equations (11)

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

Hj(x, y)=i4 -dx-H0(2)(kcr)fj(x, y)dy.
fj(x, y)=1ε(xHy-yHx) εξj-k02ΔεHj
ξx=-y,ξy=x,Δε=ε(x, y)-εc,
Hj=ν=-Clν(j)Jν(κlρ)exp(iνϕ),
MX=0,
Hz=(iβ)-1(xHx+yHy),E=(iωε)-1×H,
Im βc=2(x2+y2)1/2<RSzdxdy-1×k0(2Z)-1(x2+y2)1/2<R|E|2 Im εdxdy-R-1Sρdτ.
A=(x2+y2)1/2<RdxdySz2(x2+y2)1/2<RdxdySz2-1,
βcl=k0{n¯+(εc-n¯)cosh-2[α(λ0Λ-1)λ0Λ-1]},
n¯=f+(1-f)ε2,f=(dΛ-1)2π(23)-1,
D=dυg-1dλ0=-λ022πc d2 Re βdλ02,

Metrics