Abstract

We address the long-standing unresolved problem concerning the V parameter in a photonic crystal fiber. In formulating the parameter appropriate for a core defect in a periodic structure, we argue that the multimode cutoff occurs at a wavelength λ* that satisfies VPCFλ*=π. By comparing this approach with numerics and recent cutoff calculations we confirm this result.

© 2003 Optical Society of America

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  1. J. C. Knight, T. A. Birks, P. St. J. Russell, and D. M. Atkin, Opt. Lett. 21, 1547 (1996).
    [CrossRef] [PubMed]
  2. J. C. Knight, J. Broeng, T. A. Birks, and P. St. J. Russell, Science 282, 1476 (1998).
    [CrossRef] [PubMed]
  3. F. Benabid, J. C. Knight, G. Antonopoulos, and P. St. J. Russell, Science 298, 399 (2002).
    [CrossRef] [PubMed]
  4. M. Mekata, Phys. Today 56, 12 (2003).
    [CrossRef]
  5. R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. St. J. Russell, P. J. Roberts, and D. C. Allan, Science 285, 1537 (1999).
    [CrossRef] [PubMed]
  6. P. Russell, Science 299, 358 (2003).
    [CrossRef] [PubMed]
  7. T. A. Birks, J. C. Knight, and P. St. J. Russell, Opt. Lett. 22, 961 (1997).
    [CrossRef] [PubMed]
  8. J. C. Knight, T. A. Birks, R. F. Cregan, P. St. J. Russell, and J.-P. De Sandro, Electron. Lett. 34, 1347 (1998).
    [CrossRef]
  9. D. Mogilevtsev, T. A. Birks, and P. St. J. Russell, Opt. Lett. 23, 1662 (1998).
    [CrossRef]
  10. A. Ferrando, E. Silvestre, J. J. Miret, and P. Andrés, Opt. Lett. 25, 790 (2000).
    [CrossRef]
  11. J. C. Knight, J. Arriaga, T. A. Birks, A. Ortigosa-Blanch, W. J. Wadsworth, and P. St. J. Russell, IEEE Photon. Technol. Lett. 12, 807 (2000).
    [CrossRef]
  12. A. K. Ghatak and K. Thyagarajan, Introduction to Fiber Optics (Cambridge U. Press, Cambridge, 1998).
    [CrossRef]
  13. A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman & Hall, New York, 1983).
  14. J. C. Knight, T. A. Birks, and P. St. J. Russell, J. Opt. Soc. Am. A 15, 748 (1998).
    [CrossRef]
  15. J. Broeng, D. Mogilevstev, S. E. Barkou, and A. Bjarklev, Opt. Fiber Technol. 5, 305 (1999).
    [CrossRef]
  16. J. C. Knight, T. A. Birks, R. F. Cregan, P. St. J. Russell, and J. P. de Sandro, Opt. Mater. 11, 143 (1999).
    [CrossRef]
  17. N. A. Mortensen, Opt. Express 10, 341 (2002), http://www.opticsexpress.org.
    [CrossRef] [PubMed]
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    [CrossRef]
  19. E. A. Montie, E. C. Cosman, G. W. 't Hooft, M. B. van der Mark, and C. W. J. Beenakker, Nature 350, 594 (1991).
    [CrossRef]
  20. A. Szafer and A. D. Stone, Phys. Rev. Lett. 62, 300 (1989).
    [CrossRef] [PubMed]
  21. S. G. Johnson and J. D. Joannopoulos, Opt. Express 8, 173 (2001), http://www.opticsexpress.org.
    [CrossRef] [PubMed]
  22. J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton U. Press, Princeton, N.J., 1995).
  23. J. R. Folkenberg, N. A. Mortensen, K. P. Hansen, T. P. Hansen, H. R. Simonsen, and C. Jakobsen, Opt. Lett. 28, 1882 (2003).
    [CrossRef] [PubMed]

2003 (3)

M. Mekata, Phys. Today 56, 12 (2003).
[CrossRef]

P. Russell, Science 299, 358 (2003).
[CrossRef] [PubMed]

J. R. Folkenberg, N. A. Mortensen, K. P. Hansen, T. P. Hansen, H. R. Simonsen, and C. Jakobsen, Opt. Lett. 28, 1882 (2003).
[CrossRef] [PubMed]

2002 (3)

2001 (1)

2000 (2)

J. C. Knight, J. Arriaga, T. A. Birks, A. Ortigosa-Blanch, W. J. Wadsworth, and P. St. J. Russell, IEEE Photon. Technol. Lett. 12, 807 (2000).
[CrossRef]

A. Ferrando, E. Silvestre, J. J. Miret, and P. Andrés, Opt. Lett. 25, 790 (2000).
[CrossRef]

1999 (3)

R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. St. J. Russell, P. J. Roberts, and D. C. Allan, Science 285, 1537 (1999).
[CrossRef] [PubMed]

J. Broeng, D. Mogilevstev, S. E. Barkou, and A. Bjarklev, Opt. Fiber Technol. 5, 305 (1999).
[CrossRef]

J. C. Knight, T. A. Birks, R. F. Cregan, P. St. J. Russell, and J. P. de Sandro, Opt. Mater. 11, 143 (1999).
[CrossRef]

1998 (4)

J. C. Knight, T. A. Birks, R. F. Cregan, P. St. J. Russell, and J.-P. De Sandro, Electron. Lett. 34, 1347 (1998).
[CrossRef]

J. C. Knight, J. Broeng, T. A. Birks, and P. St. J. Russell, Science 282, 1476 (1998).
[CrossRef] [PubMed]

J. C. Knight, T. A. Birks, and P. St. J. Russell, J. Opt. Soc. Am. A 15, 748 (1998).
[CrossRef]

D. Mogilevtsev, T. A. Birks, and P. St. J. Russell, Opt. Lett. 23, 1662 (1998).
[CrossRef]

1997 (1)

1996 (1)

1991 (1)

E. A. Montie, E. C. Cosman, G. W. 't Hooft, M. B. van der Mark, and C. W. J. Beenakker, Nature 350, 594 (1991).
[CrossRef]

1989 (1)

A. Szafer and A. D. Stone, Phys. Rev. Lett. 62, 300 (1989).
[CrossRef] [PubMed]

Allan, D. C.

R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. St. J. Russell, P. J. Roberts, and D. C. Allan, Science 285, 1537 (1999).
[CrossRef] [PubMed]

Andrés, P.

Antonopoulos, G.

F. Benabid, J. C. Knight, G. Antonopoulos, and P. St. J. Russell, Science 298, 399 (2002).
[CrossRef] [PubMed]

Arriaga, J.

J. C. Knight, J. Arriaga, T. A. Birks, A. Ortigosa-Blanch, W. J. Wadsworth, and P. St. J. Russell, IEEE Photon. Technol. Lett. 12, 807 (2000).
[CrossRef]

Atkin, D. M.

Barkou, S. E.

J. Broeng, D. Mogilevstev, S. E. Barkou, and A. Bjarklev, Opt. Fiber Technol. 5, 305 (1999).
[CrossRef]

Beenakker, C. W. J.

E. A. Montie, E. C. Cosman, G. W. 't Hooft, M. B. van der Mark, and C. W. J. Beenakker, Nature 350, 594 (1991).
[CrossRef]

Benabid, F.

F. Benabid, J. C. Knight, G. Antonopoulos, and P. St. J. Russell, Science 298, 399 (2002).
[CrossRef] [PubMed]

Birks, T. A.

J. C. Knight, J. Arriaga, T. A. Birks, A. Ortigosa-Blanch, W. J. Wadsworth, and P. St. J. Russell, IEEE Photon. Technol. Lett. 12, 807 (2000).
[CrossRef]

R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. St. J. Russell, P. J. Roberts, and D. C. Allan, Science 285, 1537 (1999).
[CrossRef] [PubMed]

J. C. Knight, T. A. Birks, R. F. Cregan, P. St. J. Russell, and J. P. de Sandro, Opt. Mater. 11, 143 (1999).
[CrossRef]

J. C. Knight, T. A. Birks, and P. St. J. Russell, J. Opt. Soc. Am. A 15, 748 (1998).
[CrossRef]

J. C. Knight, J. Broeng, T. A. Birks, and P. St. J. Russell, Science 282, 1476 (1998).
[CrossRef] [PubMed]

J. C. Knight, T. A. Birks, R. F. Cregan, P. St. J. Russell, and J.-P. De Sandro, Electron. Lett. 34, 1347 (1998).
[CrossRef]

D. Mogilevtsev, T. A. Birks, and P. St. J. Russell, Opt. Lett. 23, 1662 (1998).
[CrossRef]

T. A. Birks, J. C. Knight, and P. St. J. Russell, Opt. Lett. 22, 961 (1997).
[CrossRef] [PubMed]

J. C. Knight, T. A. Birks, P. St. J. Russell, and D. M. Atkin, Opt. Lett. 21, 1547 (1996).
[CrossRef] [PubMed]

Bjarklev, A.

J. Broeng, D. Mogilevstev, S. E. Barkou, and A. Bjarklev, Opt. Fiber Technol. 5, 305 (1999).
[CrossRef]

Broeng, J.

J. Broeng, D. Mogilevstev, S. E. Barkou, and A. Bjarklev, Opt. Fiber Technol. 5, 305 (1999).
[CrossRef]

J. C. Knight, J. Broeng, T. A. Birks, and P. St. J. Russell, Science 282, 1476 (1998).
[CrossRef] [PubMed]

Cosman, E. C.

E. A. Montie, E. C. Cosman, G. W. 't Hooft, M. B. van der Mark, and C. W. J. Beenakker, Nature 350, 594 (1991).
[CrossRef]

Cregan, R. F.

J. C. Knight, T. A. Birks, R. F. Cregan, P. St. J. Russell, and J. P. de Sandro, Opt. Mater. 11, 143 (1999).
[CrossRef]

R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. St. J. Russell, P. J. Roberts, and D. C. Allan, Science 285, 1537 (1999).
[CrossRef] [PubMed]

J. C. Knight, T. A. Birks, R. F. Cregan, P. St. J. Russell, and J.-P. De Sandro, Electron. Lett. 34, 1347 (1998).
[CrossRef]

de Sandro, J. P.

J. C. Knight, T. A. Birks, R. F. Cregan, P. St. J. Russell, and J. P. de Sandro, Opt. Mater. 11, 143 (1999).
[CrossRef]

De Sandro, J.-P.

J. C. Knight, T. A. Birks, R. F. Cregan, P. St. J. Russell, and J.-P. De Sandro, Electron. Lett. 34, 1347 (1998).
[CrossRef]

de Sterke, C. M.

Ferrando, A.

Folkenberg, J. R.

J. R. Folkenberg, N. A. Mortensen, K. P. Hansen, T. P. Hansen, H. R. Simonsen, and C. Jakobsen, Opt. Lett. 28, 1882 (2003).
[CrossRef] [PubMed]

Ghatak, A. K.

A. K. Ghatak and K. Thyagarajan, Introduction to Fiber Optics (Cambridge U. Press, Cambridge, 1998).
[CrossRef]

Hansen, K. P.

J. R. Folkenberg, N. A. Mortensen, K. P. Hansen, T. P. Hansen, H. R. Simonsen, and C. Jakobsen, Opt. Lett. 28, 1882 (2003).
[CrossRef] [PubMed]

Hansen, T. P.

J. R. Folkenberg, N. A. Mortensen, K. P. Hansen, T. P. Hansen, H. R. Simonsen, and C. Jakobsen, Opt. Lett. 28, 1882 (2003).
[CrossRef] [PubMed]

Jakobsen, C.

J. R. Folkenberg, N. A. Mortensen, K. P. Hansen, T. P. Hansen, H. R. Simonsen, and C. Jakobsen, Opt. Lett. 28, 1882 (2003).
[CrossRef] [PubMed]

Joannopoulos, J. D.

S. G. Johnson and J. D. Joannopoulos, Opt. Express 8, 173 (2001), http://www.opticsexpress.org.
[CrossRef] [PubMed]

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton U. Press, Princeton, N.J., 1995).

Johnson, S. G.

Knight, J. C.

F. Benabid, J. C. Knight, G. Antonopoulos, and P. St. J. Russell, Science 298, 399 (2002).
[CrossRef] [PubMed]

J. C. Knight, J. Arriaga, T. A. Birks, A. Ortigosa-Blanch, W. J. Wadsworth, and P. St. J. Russell, IEEE Photon. Technol. Lett. 12, 807 (2000).
[CrossRef]

R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. St. J. Russell, P. J. Roberts, and D. C. Allan, Science 285, 1537 (1999).
[CrossRef] [PubMed]

J. C. Knight, T. A. Birks, R. F. Cregan, P. St. J. Russell, and J. P. de Sandro, Opt. Mater. 11, 143 (1999).
[CrossRef]

J. C. Knight, T. A. Birks, and P. St. J. Russell, J. Opt. Soc. Am. A 15, 748 (1998).
[CrossRef]

J. C. Knight, J. Broeng, T. A. Birks, and P. St. J. Russell, Science 282, 1476 (1998).
[CrossRef] [PubMed]

J. C. Knight, T. A. Birks, R. F. Cregan, P. St. J. Russell, and J.-P. De Sandro, Electron. Lett. 34, 1347 (1998).
[CrossRef]

T. A. Birks, J. C. Knight, and P. St. J. Russell, Opt. Lett. 22, 961 (1997).
[CrossRef] [PubMed]

J. C. Knight, T. A. Birks, P. St. J. Russell, and D. M. Atkin, Opt. Lett. 21, 1547 (1996).
[CrossRef] [PubMed]

Kuhlmey, B. T.

Love, J. D.

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

Mangan, B. J.

R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. St. J. Russell, P. J. Roberts, and D. C. Allan, Science 285, 1537 (1999).
[CrossRef] [PubMed]

McPhedran, R. C.

Meade, R. D.

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton U. Press, Princeton, N.J., 1995).

Mekata, M.

M. Mekata, Phys. Today 56, 12 (2003).
[CrossRef]

Miret, J. J.

Mogilevstev, D.

J. Broeng, D. Mogilevstev, S. E. Barkou, and A. Bjarklev, Opt. Fiber Technol. 5, 305 (1999).
[CrossRef]

Mogilevtsev, D.

Montie, E. A.

E. A. Montie, E. C. Cosman, G. W. 't Hooft, M. B. van der Mark, and C. W. J. Beenakker, Nature 350, 594 (1991).
[CrossRef]

Mortensen, N. A.

J. R. Folkenberg, N. A. Mortensen, K. P. Hansen, T. P. Hansen, H. R. Simonsen, and C. Jakobsen, Opt. Lett. 28, 1882 (2003).
[CrossRef] [PubMed]

N. A. Mortensen, Opt. Express 10, 341 (2002), http://www.opticsexpress.org.
[CrossRef] [PubMed]

Ortigosa-Blanch, A.

J. C. Knight, J. Arriaga, T. A. Birks, A. Ortigosa-Blanch, W. J. Wadsworth, and P. St. J. Russell, IEEE Photon. Technol. Lett. 12, 807 (2000).
[CrossRef]

Roberts, P. J.

R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. St. J. Russell, P. J. Roberts, and D. C. Allan, Science 285, 1537 (1999).
[CrossRef] [PubMed]

Russell, P.

P. Russell, Science 299, 358 (2003).
[CrossRef] [PubMed]

Russell, P. St. J.

F. Benabid, J. C. Knight, G. Antonopoulos, and P. St. J. Russell, Science 298, 399 (2002).
[CrossRef] [PubMed]

J. C. Knight, J. Arriaga, T. A. Birks, A. Ortigosa-Blanch, W. J. Wadsworth, and P. St. J. Russell, IEEE Photon. Technol. Lett. 12, 807 (2000).
[CrossRef]

R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. St. J. Russell, P. J. Roberts, and D. C. Allan, Science 285, 1537 (1999).
[CrossRef] [PubMed]

J. C. Knight, T. A. Birks, R. F. Cregan, P. St. J. Russell, and J. P. de Sandro, Opt. Mater. 11, 143 (1999).
[CrossRef]

J. C. Knight, T. A. Birks, and P. St. J. Russell, J. Opt. Soc. Am. A 15, 748 (1998).
[CrossRef]

J. C. Knight, J. Broeng, T. A. Birks, and P. St. J. Russell, Science 282, 1476 (1998).
[CrossRef] [PubMed]

J. C. Knight, T. A. Birks, R. F. Cregan, P. St. J. Russell, and J.-P. De Sandro, Electron. Lett. 34, 1347 (1998).
[CrossRef]

D. Mogilevtsev, T. A. Birks, and P. St. J. Russell, Opt. Lett. 23, 1662 (1998).
[CrossRef]

T. A. Birks, J. C. Knight, and P. St. J. Russell, Opt. Lett. 22, 961 (1997).
[CrossRef] [PubMed]

J. C. Knight, T. A. Birks, P. St. J. Russell, and D. M. Atkin, Opt. Lett. 21, 1547 (1996).
[CrossRef] [PubMed]

Silvestre, E.

Simonsen, H. R.

J. R. Folkenberg, N. A. Mortensen, K. P. Hansen, T. P. Hansen, H. R. Simonsen, and C. Jakobsen, Opt. Lett. 28, 1882 (2003).
[CrossRef] [PubMed]

Snyder, A. W.

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

Stone, A. D.

A. Szafer and A. D. Stone, Phys. Rev. Lett. 62, 300 (1989).
[CrossRef] [PubMed]

Szafer, A.

A. Szafer and A. D. Stone, Phys. Rev. Lett. 62, 300 (1989).
[CrossRef] [PubMed]

't Hooft, G. W.

E. A. Montie, E. C. Cosman, G. W. 't Hooft, M. B. van der Mark, and C. W. J. Beenakker, Nature 350, 594 (1991).
[CrossRef]

Thyagarajan, K.

A. K. Ghatak and K. Thyagarajan, Introduction to Fiber Optics (Cambridge U. Press, Cambridge, 1998).
[CrossRef]

van der Mark, M. B.

E. A. Montie, E. C. Cosman, G. W. 't Hooft, M. B. van der Mark, and C. W. J. Beenakker, Nature 350, 594 (1991).
[CrossRef]

Wadsworth, W. J.

J. C. Knight, J. Arriaga, T. A. Birks, A. Ortigosa-Blanch, W. J. Wadsworth, and P. St. J. Russell, IEEE Photon. Technol. Lett. 12, 807 (2000).
[CrossRef]

Winn, J. N.

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton U. Press, Princeton, N.J., 1995).

Electron. Lett. (1)

J. C. Knight, T. A. Birks, R. F. Cregan, P. St. J. Russell, and J.-P. De Sandro, Electron. Lett. 34, 1347 (1998).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

J. C. Knight, J. Arriaga, T. A. Birks, A. Ortigosa-Blanch, W. J. Wadsworth, and P. St. J. Russell, IEEE Photon. Technol. Lett. 12, 807 (2000).
[CrossRef]

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

Nature (1)

E. A. Montie, E. C. Cosman, G. W. 't Hooft, M. B. van der Mark, and C. W. J. Beenakker, Nature 350, 594 (1991).
[CrossRef]

Opt. Lett. (1)

J. R. Folkenberg, N. A. Mortensen, K. P. Hansen, T. P. Hansen, H. R. Simonsen, and C. Jakobsen, Opt. Lett. 28, 1882 (2003).
[CrossRef] [PubMed]

Opt. Express (2)

Opt. Fiber Technol. (1)

J. Broeng, D. Mogilevstev, S. E. Barkou, and A. Bjarklev, Opt. Fiber Technol. 5, 305 (1999).
[CrossRef]

Opt. Lett. (5)

Opt. Mater. (1)

J. C. Knight, T. A. Birks, R. F. Cregan, P. St. J. Russell, and J. P. de Sandro, Opt. Mater. 11, 143 (1999).
[CrossRef]

Phys. Rev. Lett. (1)

A. Szafer and A. D. Stone, Phys. Rev. Lett. 62, 300 (1989).
[CrossRef] [PubMed]

Phys. Today (1)

M. Mekata, Phys. Today 56, 12 (2003).
[CrossRef]

Science (4)

R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. St. J. Russell, P. J. Roberts, and D. C. Allan, Science 285, 1537 (1999).
[CrossRef] [PubMed]

P. Russell, Science 299, 358 (2003).
[CrossRef] [PubMed]

J. C. Knight, J. Broeng, T. A. Birks, and P. St. J. Russell, Science 282, 1476 (1998).
[CrossRef] [PubMed]

F. Benabid, J. C. Knight, G. Antonopoulos, and P. St. J. Russell, Science 298, 399 (2002).
[CrossRef] [PubMed]

Other (3)

A. K. Ghatak and K. Thyagarajan, Introduction to Fiber Optics (Cambridge U. Press, Cambridge, 1998).
[CrossRef]

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

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton U. Press, Princeton, N.J., 1995).

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Figures (2)

Fig. 1
Fig. 1

(a) Single-mode–multimode phase diagram. The solid curve shows the phase boundary of Kuhlmey et al.18 [expression (6)], and the circles indicate solutions to VPCFλ*=π [Eqs. (4) and (5)]. (b) Numerical results for PCFs with varying hole diameter (from the bottom, d/Λ=0.43, 0.44, 0.45, 0.475, 0.50, 0.55, 0.60, 0.65, 0.70). The curves show results for the V parameter [Eq. (4)], the circles indicate the corresponding cutoff wavelengths [expression (6)], and the dotted line shows VPCF* [Eq. (5)].

Fig. 2
Fig. 2

Schematics of the cross section of a PCF. The dotted curve illustrates the field amplitude of a second-order mode with a single node.

Equations (6)

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

VSIFλ=2πρλnc2-ncl21/2.
NA=sin θ=nc2-ncl21/2,
VSIF=kρ.
VPCFλ=2πΛλnc2λ-ncl2λ1/2,
VPCF*=k*Λ=2πλ*Λ=π.
λ*/Λαd/Λ-d*/Λγ.

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