Abstract

The modal cutoff of square-lattice photonic crystal fibers with a finite number of air-hole rings has been accurately investigated to our knowledge for the first time. By analyzing the leaky behavior of the second-order mode, we have obtained a phase diagram that describes the regions of single-mode and multimode operation as well as the endlessly single-mode regime. Furthermore, starting from these results, we have obtained the cutoff normalized frequency according to two different formulations of the V parameter previously adopted for fibers with a triangular lattice. A final comparison of the cutoff properties of fibers characterized by a square lattice and a triangular lattice has been carried out.

© 2005 Optical Society of America

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References

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  1. A. Bjarklev, “Photonic crystal fibres and their applications,” in Proceedings of the European Conference on Optical Communications (ECOC), tutorial We3.3, pp. 324–347 (ECOC, 2003).
  2. D. J. Richardson, W. Belardi, K. Furusawa, J. H.V. Price, A. Malinowski, T. M. Monro, “Holey fibers: fundamentals and applications,” in Conference on Lasers and Electro-Optics, Vol. 73 of 2002 OSA Technical Digest Series (Optical Society of America, 2002), pp. 453–454.
  3. B. J. Eggleton, “Microstructured optical fibre devices,” in Proceedings of the European Conference on Optical Communications (ECOC), tutorial We3.2, pp. 200–233 (ECOC, 2004).
  4. J. C. Knight, T. A. Birks, P. St.J. Russell, D. M. Atkin, “All-silica single-mode optical fiber with photonic crystal cladding,” Opt. Lett. 21, 1547–1549 (1996).
    [CrossRef] [PubMed]
  5. T. A. Birks, J. C. Knight, P. St.J. Russell, “Endlessly single-mode photonic crystal fiber,” Opt. Lett. 22, 961–963 (1997).
    [CrossRef] [PubMed]
  6. D. Ferrarini, L. Vincetti, M. Zoboli, A. Cucinotta, S. Selleri, “Leakage properties of photonic crystal fibers,” Opt. Express 10, 1314–1319 (2002), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-23-1314.
    [CrossRef] [PubMed]
  7. B. Kuhlmey, G. Renversez, D. Maystre, “Chromatic dispersion and losses of microstructured optical fibers,” Appl. Opt. 42, 634–639 (2003).
    [CrossRef] [PubMed]
  8. L. Vincetti, “Confinement losses in honeycomb fibers,” IEEE Photon. Technol. Lett. 16, 2048–2050 (2004).
    [CrossRef]
  9. B. T. Kuhlmey, R. C. McPhedran, C. Martijn de Sterke, “Modal cutoff in microstructured optical fibers,” Opt. Lett. 27, 1684–1686 (2002).
    [CrossRef]
  10. B. T. Kuhlmey, R. C. McPhedran, C. M. de Sterke, P. A. Robinson, G. Renversez, D. Maystre, “Microstructured optical fibers: where’s the edge?” Opt. Express 10, 1285–1290 (2002), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-22-1285.
    [CrossRef] [PubMed]
  11. N. A. Mortensen, J. R. Folkenberg, M. D. Nielsen, K. P. Hansen, “Modal cutoff and the V parameter in photonic crystal fibers,” Opt. Lett. 28, 1879–1881 (2003).
    [CrossRef] [PubMed]
  12. P. St.J. Russell, E. Marin, A. Diez, S. Guenneau, A. B. Movchan, “Sonic band gaps in PCF preforms: enhancing the interaction of sound and light,” Opt. Express 11, 2555–2560 (2003), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-20-2555.
    [CrossRef] [PubMed]
  13. M. G. Franczyk, J. C. Knight, T. A. Birks, P. St.J. Russell, A. Ferrando, “Birefringent photonic crystal fiber with square lattice,” in Lightguides and Their Applications II, J. Wojcik and W. Wojcik, eds., Proc. SPIE5576, 25–28 (2004).
  14. Y. Ni, Z. Lei, J. Shu, P. Jiangde, “Dispersion of square solid-core photonic bandgap fibers,” Opt. Express 12, 2825–2830 (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-13-2825.
    [CrossRef] [PubMed]
  15. A. H. Bouk, A. Cucinotta, F. Poli, S. Selleri, “Dispersion properties of square-lattice photonic crystal fibers,” Opt. Express 12, 941–946 (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-5-941.
    [CrossRef] [PubMed]
  16. Y. C. Liu, Y. Lai, “Optical birefringence and polarization dependent loss of square- and rectangular-lattice holey fibers with elliptical air holes: numerical analysis,” Opt. Express 13, 225–235 (2005), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-1-225.
    [CrossRef] [PubMed]
  17. T. A. Birks, D. Mogilevstev, J. C. Knight, P. St.J. Russell, J. Broeng, P. J. Roberts, J. A. West, D. J. Allan, J. C. Fajardo, “The analogy between photonic crystal fibres and step index fibres,” in Optical Fiber Communication Conference (Optical Society of America, 1999), pp. 114–116.
  18. N. A. Mortensen, “Effective area of photonic crystal fiber,” Opt. Express 10, 341–348 (2002), http://www.opticsexpress.org/abstract.cfm?URI =OPEX-10-7-341.
    [CrossRef] [PubMed]
  19. F. Brechet, J. Marcou, D. Pagnoux, P. Roy, “Complete analysis of the characteristics of propagation into photonic crystal fibers, by the finite element method,” Opt. Fiber Technol. 6, 181–191 (2000).
    [CrossRef]
  20. M. Koshiba, “Full-vector analysis of photonic crystal fibers using the finite element method,” IEICE Trans. Electron. E85-C, 881–888 (2002).
  21. M. Koshiba, K. Saitoh, “Applicability of classical optical fiber theories to holey fibers,” Opt. Lett. 29, 1739–1741 (2004).
    [CrossRef] [PubMed]
  22. M. D. Nielsen, N. A Mortensen, “Photonic crystal fiber design based on the V-parameter,” Opt. Express 11, 2762–2767 (2003), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-21-2762.
    [CrossRef] [PubMed]
  23. A. Ferrando, E. Silvestre, J. J. Miret, P. Andrés, “Full-vector analysis of a realistic photonic crystal fiber,” J. Opt. Soc. Am. A 17, 1333–1340 (2000).
    [CrossRef]
  24. A. Cucinotta, S. Selleri, L. Vincetti, M. Zoboli, “Perturbation analysis of dispersion properties in photonic crystal fibers through the finite element method,” J. Lightwave Technol. 20, 1433–1442 (2002)
    [CrossRef]
  25. T. P. White, B. T. Kuhlmey, R. C. McPhedran, D. Maystre, G. Renversez, C. M. de Sterke, L. C. Botten, “Multipole method for microstructured optical fibers I. Formulation,” J. Opt. Soc. Am. B 19, 2322–2330 (2002).
    [CrossRef]
  26. T. P. White, B. T. Kuhlmey, R. C. McPhedran, D. Maystre, G. Renversez, C. M. de Sterke, L. C. Botten, “Multipole method for microstructured optical fibers II. Implementation and results,” J. Opt. Soc. Am. B 19, 2331–2340 (2002).
    [CrossRef]
  27. S. G. Johnson, J. D. Joannopoulos, “Block-iterative frequency-domain methods for Maxwell’s equations in a planewave basis,” Opt. Express 8, 173–179 (2001), http://www.opticsexpress.org/abstract.cfm?URI =OPEX-8-3-173.
    [CrossRef] [PubMed]

2005 (1)

2004 (4)

2003 (4)

2002 (8)

D. Ferrarini, L. Vincetti, M. Zoboli, A. Cucinotta, S. Selleri, “Leakage properties of photonic crystal fibers,” Opt. Express 10, 1314–1319 (2002), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-23-1314.
[CrossRef] [PubMed]

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

B. T. Kuhlmey, R. C. McPhedran, C. M. de Sterke, P. A. Robinson, G. Renversez, D. Maystre, “Microstructured optical fibers: where’s the edge?” Opt. Express 10, 1285–1290 (2002), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-22-1285.
[CrossRef] [PubMed]

N. A. Mortensen, “Effective area of photonic crystal fiber,” Opt. Express 10, 341–348 (2002), http://www.opticsexpress.org/abstract.cfm?URI =OPEX-10-7-341.
[CrossRef] [PubMed]

A. Cucinotta, S. Selleri, L. Vincetti, M. Zoboli, “Perturbation analysis of dispersion properties in photonic crystal fibers through the finite element method,” J. Lightwave Technol. 20, 1433–1442 (2002)
[CrossRef]

T. P. White, B. T. Kuhlmey, R. C. McPhedran, D. Maystre, G. Renversez, C. M. de Sterke, L. C. Botten, “Multipole method for microstructured optical fibers I. Formulation,” J. Opt. Soc. Am. B 19, 2322–2330 (2002).
[CrossRef]

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

M. Koshiba, “Full-vector analysis of photonic crystal fibers using the finite element method,” IEICE Trans. Electron. E85-C, 881–888 (2002).

2001 (1)

2000 (2)

F. Brechet, J. Marcou, D. Pagnoux, P. Roy, “Complete analysis of the characteristics of propagation into photonic crystal fibers, by the finite element method,” Opt. Fiber Technol. 6, 181–191 (2000).
[CrossRef]

A. Ferrando, E. Silvestre, J. J. Miret, P. Andrés, “Full-vector analysis of a realistic photonic crystal fiber,” J. Opt. Soc. Am. A 17, 1333–1340 (2000).
[CrossRef]

1997 (1)

1996 (1)

Allan, D. J.

T. A. Birks, D. Mogilevstev, J. C. Knight, P. St.J. Russell, J. Broeng, P. J. Roberts, J. A. West, D. J. Allan, J. C. Fajardo, “The analogy between photonic crystal fibres and step index fibres,” in Optical Fiber Communication Conference (Optical Society of America, 1999), pp. 114–116.

Andrés, P.

Atkin, D. M.

Belardi, W.

D. J. Richardson, W. Belardi, K. Furusawa, J. H.V. Price, A. Malinowski, T. M. Monro, “Holey fibers: fundamentals and applications,” in Conference on Lasers and Electro-Optics, Vol. 73 of 2002 OSA Technical Digest Series (Optical Society of America, 2002), pp. 453–454.

Birks, T. A.

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

J. C. Knight, T. A. Birks, P. St.J. Russell, D. M. Atkin, “All-silica single-mode optical fiber with photonic crystal cladding,” Opt. Lett. 21, 1547–1549 (1996).
[CrossRef] [PubMed]

T. A. Birks, D. Mogilevstev, J. C. Knight, P. St.J. Russell, J. Broeng, P. J. Roberts, J. A. West, D. J. Allan, J. C. Fajardo, “The analogy between photonic crystal fibres and step index fibres,” in Optical Fiber Communication Conference (Optical Society of America, 1999), pp. 114–116.

M. G. Franczyk, J. C. Knight, T. A. Birks, P. St.J. Russell, A. Ferrando, “Birefringent photonic crystal fiber with square lattice,” in Lightguides and Their Applications II, J. Wojcik and W. Wojcik, eds., Proc. SPIE5576, 25–28 (2004).

Bjarklev, A.

A. Bjarklev, “Photonic crystal fibres and their applications,” in Proceedings of the European Conference on Optical Communications (ECOC), tutorial We3.3, pp. 324–347 (ECOC, 2003).

Botten, L. C.

Bouk, A. H.

Brechet, F.

F. Brechet, J. Marcou, D. Pagnoux, P. Roy, “Complete analysis of the characteristics of propagation into photonic crystal fibers, by the finite element method,” Opt. Fiber Technol. 6, 181–191 (2000).
[CrossRef]

Broeng, J.

T. A. Birks, D. Mogilevstev, J. C. Knight, P. St.J. Russell, J. Broeng, P. J. Roberts, J. A. West, D. J. Allan, J. C. Fajardo, “The analogy between photonic crystal fibres and step index fibres,” in Optical Fiber Communication Conference (Optical Society of America, 1999), pp. 114–116.

Cucinotta, A.

de Sterke, C. M.

de Sterke, C. Martijn

Diez, A.

Eggleton, B. J.

B. J. Eggleton, “Microstructured optical fibre devices,” in Proceedings of the European Conference on Optical Communications (ECOC), tutorial We3.2, pp. 200–233 (ECOC, 2004).

Fajardo, J. C.

T. A. Birks, D. Mogilevstev, J. C. Knight, P. St.J. Russell, J. Broeng, P. J. Roberts, J. A. West, D. J. Allan, J. C. Fajardo, “The analogy between photonic crystal fibres and step index fibres,” in Optical Fiber Communication Conference (Optical Society of America, 1999), pp. 114–116.

Ferrando, A.

A. Ferrando, E. Silvestre, J. J. Miret, P. Andrés, “Full-vector analysis of a realistic photonic crystal fiber,” J. Opt. Soc. Am. A 17, 1333–1340 (2000).
[CrossRef]

M. G. Franczyk, J. C. Knight, T. A. Birks, P. St.J. Russell, A. Ferrando, “Birefringent photonic crystal fiber with square lattice,” in Lightguides and Their Applications II, J. Wojcik and W. Wojcik, eds., Proc. SPIE5576, 25–28 (2004).

Ferrarini, D.

Folkenberg, J. R.

Franczyk, M. G.

M. G. Franczyk, J. C. Knight, T. A. Birks, P. St.J. Russell, A. Ferrando, “Birefringent photonic crystal fiber with square lattice,” in Lightguides and Their Applications II, J. Wojcik and W. Wojcik, eds., Proc. SPIE5576, 25–28 (2004).

Furusawa, K.

D. J. Richardson, W. Belardi, K. Furusawa, J. H.V. Price, A. Malinowski, T. M. Monro, “Holey fibers: fundamentals and applications,” in Conference on Lasers and Electro-Optics, Vol. 73 of 2002 OSA Technical Digest Series (Optical Society of America, 2002), pp. 453–454.

Guenneau, S.

Hansen, K. P.

Jiangde, P.

Joannopoulos, J. D.

Johnson, S. G.

Knight, J. C.

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

J. C. Knight, T. A. Birks, P. St.J. Russell, D. M. Atkin, “All-silica single-mode optical fiber with photonic crystal cladding,” Opt. Lett. 21, 1547–1549 (1996).
[CrossRef] [PubMed]

T. A. Birks, D. Mogilevstev, J. C. Knight, P. St.J. Russell, J. Broeng, P. J. Roberts, J. A. West, D. J. Allan, J. C. Fajardo, “The analogy between photonic crystal fibres and step index fibres,” in Optical Fiber Communication Conference (Optical Society of America, 1999), pp. 114–116.

M. G. Franczyk, J. C. Knight, T. A. Birks, P. St.J. Russell, A. Ferrando, “Birefringent photonic crystal fiber with square lattice,” in Lightguides and Their Applications II, J. Wojcik and W. Wojcik, eds., Proc. SPIE5576, 25–28 (2004).

Koshiba, M.

M. Koshiba, K. Saitoh, “Applicability of classical optical fiber theories to holey fibers,” Opt. Lett. 29, 1739–1741 (2004).
[CrossRef] [PubMed]

M. Koshiba, “Full-vector analysis of photonic crystal fibers using the finite element method,” IEICE Trans. Electron. E85-C, 881–888 (2002).

Kuhlmey, B.

Kuhlmey, B. T.

Lai, Y.

Lei, Z.

Liu, Y. C.

Malinowski, A.

D. J. Richardson, W. Belardi, K. Furusawa, J. H.V. Price, A. Malinowski, T. M. Monro, “Holey fibers: fundamentals and applications,” in Conference on Lasers and Electro-Optics, Vol. 73 of 2002 OSA Technical Digest Series (Optical Society of America, 2002), pp. 453–454.

Marcou, J.

F. Brechet, J. Marcou, D. Pagnoux, P. Roy, “Complete analysis of the characteristics of propagation into photonic crystal fibers, by the finite element method,” Opt. Fiber Technol. 6, 181–191 (2000).
[CrossRef]

Marin, E.

Maystre, D.

McPhedran, R. C.

Miret, J. J.

Mogilevstev, D.

T. A. Birks, D. Mogilevstev, J. C. Knight, P. St.J. Russell, J. Broeng, P. J. Roberts, J. A. West, D. J. Allan, J. C. Fajardo, “The analogy between photonic crystal fibres and step index fibres,” in Optical Fiber Communication Conference (Optical Society of America, 1999), pp. 114–116.

Monro, T. M.

D. J. Richardson, W. Belardi, K. Furusawa, J. H.V. Price, A. Malinowski, T. M. Monro, “Holey fibers: fundamentals and applications,” in Conference on Lasers and Electro-Optics, Vol. 73 of 2002 OSA Technical Digest Series (Optical Society of America, 2002), pp. 453–454.

Mortensen, N. A

Mortensen, N. A.

Movchan, A. B.

Ni, Y.

Nielsen, M. D.

Pagnoux, D.

F. Brechet, J. Marcou, D. Pagnoux, P. Roy, “Complete analysis of the characteristics of propagation into photonic crystal fibers, by the finite element method,” Opt. Fiber Technol. 6, 181–191 (2000).
[CrossRef]

Poli, F.

Price, J. H.V.

D. J. Richardson, W. Belardi, K. Furusawa, J. H.V. Price, A. Malinowski, T. M. Monro, “Holey fibers: fundamentals and applications,” in Conference on Lasers and Electro-Optics, Vol. 73 of 2002 OSA Technical Digest Series (Optical Society of America, 2002), pp. 453–454.

Renversez, G.

Richardson, D. J.

D. J. Richardson, W. Belardi, K. Furusawa, J. H.V. Price, A. Malinowski, T. M. Monro, “Holey fibers: fundamentals and applications,” in Conference on Lasers and Electro-Optics, Vol. 73 of 2002 OSA Technical Digest Series (Optical Society of America, 2002), pp. 453–454.

Roberts, P. J.

T. A. Birks, D. Mogilevstev, J. C. Knight, P. St.J. Russell, J. Broeng, P. J. Roberts, J. A. West, D. J. Allan, J. C. Fajardo, “The analogy between photonic crystal fibres and step index fibres,” in Optical Fiber Communication Conference (Optical Society of America, 1999), pp. 114–116.

Robinson, P. A.

Roy, P.

F. Brechet, J. Marcou, D. Pagnoux, P. Roy, “Complete analysis of the characteristics of propagation into photonic crystal fibers, by the finite element method,” Opt. Fiber Technol. 6, 181–191 (2000).
[CrossRef]

Russell, P. St.J.

P. St.J. Russell, E. Marin, A. Diez, S. Guenneau, A. B. Movchan, “Sonic band gaps in PCF preforms: enhancing the interaction of sound and light,” Opt. Express 11, 2555–2560 (2003), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-20-2555.
[CrossRef] [PubMed]

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

J. C. Knight, T. A. Birks, P. St.J. Russell, D. M. Atkin, “All-silica single-mode optical fiber with photonic crystal cladding,” Opt. Lett. 21, 1547–1549 (1996).
[CrossRef] [PubMed]

M. G. Franczyk, J. C. Knight, T. A. Birks, P. St.J. Russell, A. Ferrando, “Birefringent photonic crystal fiber with square lattice,” in Lightguides and Their Applications II, J. Wojcik and W. Wojcik, eds., Proc. SPIE5576, 25–28 (2004).

T. A. Birks, D. Mogilevstev, J. C. Knight, P. St.J. Russell, J. Broeng, P. J. Roberts, J. A. West, D. J. Allan, J. C. Fajardo, “The analogy between photonic crystal fibres and step index fibres,” in Optical Fiber Communication Conference (Optical Society of America, 1999), pp. 114–116.

Saitoh, K.

Selleri, S.

Shu, J.

Silvestre, E.

Vincetti, L.

West, J. A.

T. A. Birks, D. Mogilevstev, J. C. Knight, P. St.J. Russell, J. Broeng, P. J. Roberts, J. A. West, D. J. Allan, J. C. Fajardo, “The analogy between photonic crystal fibres and step index fibres,” in Optical Fiber Communication Conference (Optical Society of America, 1999), pp. 114–116.

White, T. P.

Zoboli, M.

Appl. Opt. (1)

IEEE Photon. Technol. Lett. (1)

L. Vincetti, “Confinement losses in honeycomb fibers,” IEEE Photon. Technol. Lett. 16, 2048–2050 (2004).
[CrossRef]

IEICE Trans. Electron. (1)

M. Koshiba, “Full-vector analysis of photonic crystal fibers using the finite element method,” IEICE Trans. Electron. E85-C, 881–888 (2002).

J. Lightwave Technol. (1)

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

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

Opt. Express (9)

S. G. Johnson, J. D. Joannopoulos, “Block-iterative frequency-domain methods for Maxwell’s equations in a planewave basis,” Opt. Express 8, 173–179 (2001), http://www.opticsexpress.org/abstract.cfm?URI =OPEX-8-3-173.
[CrossRef] [PubMed]

D. Ferrarini, L. Vincetti, M. Zoboli, A. Cucinotta, S. Selleri, “Leakage properties of photonic crystal fibers,” Opt. Express 10, 1314–1319 (2002), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-23-1314.
[CrossRef] [PubMed]

M. D. Nielsen, N. A Mortensen, “Photonic crystal fiber design based on the V-parameter,” Opt. Express 11, 2762–2767 (2003), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-21-2762.
[CrossRef] [PubMed]

B. T. Kuhlmey, R. C. McPhedran, C. M. de Sterke, P. A. Robinson, G. Renversez, D. Maystre, “Microstructured optical fibers: where’s the edge?” Opt. Express 10, 1285–1290 (2002), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-22-1285.
[CrossRef] [PubMed]

Y. Ni, Z. Lei, J. Shu, P. Jiangde, “Dispersion of square solid-core photonic bandgap fibers,” Opt. Express 12, 2825–2830 (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-13-2825.
[CrossRef] [PubMed]

A. H. Bouk, A. Cucinotta, F. Poli, S. Selleri, “Dispersion properties of square-lattice photonic crystal fibers,” Opt. Express 12, 941–946 (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-5-941.
[CrossRef] [PubMed]

Y. C. Liu, Y. Lai, “Optical birefringence and polarization dependent loss of square- and rectangular-lattice holey fibers with elliptical air holes: numerical analysis,” Opt. Express 13, 225–235 (2005), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-1-225.
[CrossRef] [PubMed]

P. St.J. Russell, E. Marin, A. Diez, S. Guenneau, A. B. Movchan, “Sonic band gaps in PCF preforms: enhancing the interaction of sound and light,” Opt. Express 11, 2555–2560 (2003), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-20-2555.
[CrossRef] [PubMed]

N. A. Mortensen, “Effective area of photonic crystal fiber,” Opt. Express 10, 341–348 (2002), http://www.opticsexpress.org/abstract.cfm?URI =OPEX-10-7-341.
[CrossRef] [PubMed]

Opt. Fiber Technol. (1)

F. Brechet, J. Marcou, D. Pagnoux, P. Roy, “Complete analysis of the characteristics of propagation into photonic crystal fibers, by the finite element method,” Opt. Fiber Technol. 6, 181–191 (2000).
[CrossRef]

Opt. Lett. (5)

Other (5)

A. Bjarklev, “Photonic crystal fibres and their applications,” in Proceedings of the European Conference on Optical Communications (ECOC), tutorial We3.3, pp. 324–347 (ECOC, 2003).

D. J. Richardson, W. Belardi, K. Furusawa, J. H.V. Price, A. Malinowski, T. M. Monro, “Holey fibers: fundamentals and applications,” in Conference on Lasers and Electro-Optics, Vol. 73 of 2002 OSA Technical Digest Series (Optical Society of America, 2002), pp. 453–454.

B. J. Eggleton, “Microstructured optical fibre devices,” in Proceedings of the European Conference on Optical Communications (ECOC), tutorial We3.2, pp. 200–233 (ECOC, 2004).

M. G. Franczyk, J. C. Knight, T. A. Birks, P. St.J. Russell, A. Ferrando, “Birefringent photonic crystal fiber with square lattice,” in Lightguides and Their Applications II, J. Wojcik and W. Wojcik, eds., Proc. SPIE5576, 25–28 (2004).

T. A. Birks, D. Mogilevstev, J. C. Knight, P. St.J. Russell, J. Broeng, P. J. Roberts, J. A. West, D. J. Allan, J. C. Fajardo, “The analogy between photonic crystal fibres and step index fibres,” in Optical Fiber Communication Conference (Optical Society of America, 1999), pp. 114–116.

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Figures (14)

Fig. 1
Fig. 1

Cross section of a four-air-hole-ring square-lattice PCF with air-hole diameter d and pitch Λ.

Fig. 2
Fig. 2

Second-order mode α k 0 as a function of the normalized wavelength λ Λ for eight-ring square-lattice PCFs with d Λ in the range of 0.45–0.57.

Fig. 3
Fig. 3

Second-order mode α k 0 versus the normalized wavelength λ Λ as a function of the air-hole ring number, which is four, six, or eight, for a square-lattice PCF with d Λ = 0.57 .

Fig. 4
Fig. 4

Q-parameter values as a function of the normalized wavelength λ Λ for eight-ring square-lattice PCFs with d Λ in the range of 0.45–0.57.

Fig. 5
Fig. 5

Q-parameter values versus the normalized wavelength λ Λ as a function of the air-hole ring number, which is four, six, or eight, for a square-lattice PCF with d Λ = 0.57 .

Fig. 6
Fig. 6

Normalized cutoff wavelength λ * Λ as a function of the d Λ ratio for square-lattice PCFs with four, six, and eight air-hole rings.

Fig. 7
Fig. 7

Second-order-mode normalized effective area A eff Λ 2 versus λ Λ for square-lattice PCFs with d Λ = 0.52 and with four, six, and eight air-hole rings.

Fig. 8
Fig. 8

Phase diagram of the second-order mode for eight-air-hole-ring PCFs characterized by the square and the triangular lattices.

Fig. 9
Fig. 9

Cutoff value V * of the normalized frequency according to the two definitions for square-lattice PCFs with eight rings. Solid lines represent the mean values of V 1 * and V 2 * .

Fig. 10
Fig. 10

V 1 behavior versus the normalized wavelength λ Λ for square-lattice PCFs with d Λ between 0.43 and 0.57. A solid horizontal line is drawn at the fixed value V 1 * .

Fig. 11
Fig. 11

V 2 behavior versus the normalized wavelength λ Λ for square-lattice PCFs with d Λ between 0.43 and 0.57. A solid horizontal line is drawn at the fixed value V 2 * .

Fig. 12
Fig. 12

H x (top), H y (middle), and intensity (bottom) distributions of the second-order guided mode at λ Λ 0.127 for a four-ring square-lattice PCF with d Λ = 0.57 .

Fig. 13
Fig. 13

Section of the square-lattice PCF cross section (solid curve) and of the H x field component (dotted curve) along the x axis.

Fig. 14
Fig. 14

Section of the square-lattice PCF cross section (solid curve) and of the H x field component (dotted curve) along the 45° direction.

Equations (4)

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Q = d 2 log [ α k 0 ] d 2 log ( Λ ) ,
V 1 = 2 π λ Λ n eff 2 n FSM 2 ,
V 2 = 2 π λ ρ n co 2 n FSM 2 ,
λ * Λ α ( d Λ d * Λ ) γ ,

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