Abstract

Using a rigorous and vector multipole method, we compute both losses and dispersion properties of microstructured optical fibers with finite cross sections. We restrict our study to triangular lattices of air-hole inclusions in a silica matrix, taking into account material dispersion. The fiber core is modeled by a missing inclusion. The influence of pitch, hole diameter, and number of hole rings on chromatic dispersion is described, and physical insights are given to explain the behavior observed. It is shown that flattened dispersion curves obtained for certain microstructured fiber configurations are unsuitable for applications because of the fibers’ high losses and that they cannot be improved by a simple increase of the number of air-hole rings.

© 2003 Optical Society of America

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References

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  1. D. Mogilevstev, T. A. Birks, P. St. J. Russell, “Group-velocity dispersion in photonic crystal fibers,” Opt. Lett. 23, 1662–1664 (1998).
    [CrossRef]
  2. J. C. Knight, J. Arriaga, T. A. Birks, A. Ortisaga-Blanch, W. J. Wadsworth, P. St. J. Russell, “Anomalous dispersion in photonic crystal fibers,” IEEE Photon. Technol. Lett. 12, 807–809 (2000).
    [CrossRef]
  3. T. P. White, B. 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]
  4. B. Kuhlmey, T. P. White, G. Renversez, D. Maystre, L. C. Botten, C. M. de Sterke, R. C. McPhedran, “Multipole method for microstructured optical fibers. II. Implementation and results,” J. Opt. Soc. Am. B 19, 2331–2340 (2002).
    [CrossRef]
  5. R. C. McPhedran, L. C. Botten, Department of Mathematical Sciences, University of Technology, Sydney, New South Wales 2007, Australia.
  6. M. J. Steel, T. P. White, C. M. de Sterke, R. C. McPhedran, L. C. Botten, “Symmetry and degeneracy in microstrutured optical fibers,” Opt. Lett. 26, 488–490 (2001).
    [CrossRef]
  7. J. W. Fleming, “Material dispersion in lightguide glasses,” Electron. Lett. 14, 326–328 (1978).
    [CrossRef]
  8. G. P. Agrawal, Nonlinear Fiber Optics (Academic, San Diego, Calif., 1989).
  9. T. P. White, R. C. McPhedran, C. M. de Sterke, L. C. Botten, M. J. Steel, “Confinement losses in microstructured optical fibers,” Opt. Lett. 26, 1660–1662 (2001).
    [CrossRef]
  10. A. Ferrando, E. Silvestre, J.-J. Miret, P. Andrés, M. V. Andrés, “Vector description of higher-order modes in photonic crystal fibers,” J. Opt. Soc. Am. A 17, 1333–1340 (2000).
    [CrossRef]
  11. A. Ferrando, E. Silvestre, J.-J. Miret, P. Andrés, “Nearly zero ultraflattened dispersion in photonic crystal fibers,” Opt. Lett. 25, 790–792 (2000).
    [CrossRef]
  12. F. Zolla, R. Petit, “Method of fictitious sources as applied to the electromagnetic diffraction of a plane wave by a grating in conical mounts,” J. Opt. Soc. Am. A 13, 1087–1096 (1996).
    [CrossRef]
  13. D. Felbacq, G. Tayeb, D. Maystre, “Scattering by a random set of parallel cylinders,” J. Opt. Soc. Am. A 9, 2526–2538 (1994).
    [CrossRef]
  14. E. Centeno, D. Felbacq, “Scattering by a random set of parallel cylinders,” J. Opt. Soc. Am. A 17, 320–327 (2000).
    [CrossRef]
  15. P. R. Mc Issac, “Symmetry-induced modal characteristics of uniform waveguides. I. Summary of results,” IEEE Trans. Microwave Theory Tech. 23, 421–433 (1975).
    [CrossRef]
  16. M. J. Gander, R. McBride, J. C. D. Jones, D. Mogilevtsev, T. A. Birks, J. C. Knight, P. St. J. Russell, “Experimental measurement of group velocity dispersion in photonic crystal fibre, Electron. Lett. 35, 63–64 (1999).
    [CrossRef]
  17. 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]
  18. H. Kubota, S. Suzuki, S. Kawanishi, M. Nakazawa, M. Takana. “Low-loss, 2 km-long photonic crystal fiber with zero GVD in the near IR suitable for picosecond pulse propagation at 800 nm band,” in Conference on Lasers and Electro-Optics (CLEO), Vol. 56 of OSP Trends in Optics and Photonics (Optical Society of America, Washington, D. C., 2001), pp. CPD3-1–CPD3-2.
  19. G. Renversez, B. Kuhlmey, R. C. McPhedran are preparing the following paper for publication, “Dispersion management with microstructured optical fibers: ultra-flattened chromatic dispersion with low losses.”

2002 (2)

2001 (2)

2000 (5)

J. C. Knight, J. Arriaga, T. A. Birks, A. Ortisaga-Blanch, W. J. Wadsworth, P. St. J. Russell, “Anomalous dispersion in photonic crystal fibers,” IEEE Photon. Technol. Lett. 12, 807–809 (2000).
[CrossRef]

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]

E. Centeno, D. Felbacq, “Scattering by a random set of parallel cylinders,” J. Opt. Soc. Am. A 17, 320–327 (2000).
[CrossRef]

A. Ferrando, E. Silvestre, J.-J. Miret, P. Andrés, M. V. Andrés, “Vector description of higher-order modes in photonic crystal fibers,” J. Opt. Soc. Am. A 17, 1333–1340 (2000).
[CrossRef]

A. Ferrando, E. Silvestre, J.-J. Miret, P. Andrés, “Nearly zero ultraflattened dispersion in photonic crystal fibers,” Opt. Lett. 25, 790–792 (2000).
[CrossRef]

1999 (1)

M. J. Gander, R. McBride, J. C. D. Jones, D. Mogilevtsev, T. A. Birks, J. C. Knight, P. St. J. Russell, “Experimental measurement of group velocity dispersion in photonic crystal fibre, Electron. Lett. 35, 63–64 (1999).
[CrossRef]

1998 (1)

1996 (1)

F. Zolla, R. Petit, “Method of fictitious sources as applied to the electromagnetic diffraction of a plane wave by a grating in conical mounts,” J. Opt. Soc. Am. A 13, 1087–1096 (1996).
[CrossRef]

1994 (1)

D. Felbacq, G. Tayeb, D. Maystre, “Scattering by a random set of parallel cylinders,” J. Opt. Soc. Am. A 9, 2526–2538 (1994).
[CrossRef]

1978 (1)

J. W. Fleming, “Material dispersion in lightguide glasses,” Electron. Lett. 14, 326–328 (1978).
[CrossRef]

1975 (1)

P. R. Mc Issac, “Symmetry-induced modal characteristics of uniform waveguides. I. Summary of results,” IEEE Trans. Microwave Theory Tech. 23, 421–433 (1975).
[CrossRef]

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics (Academic, San Diego, Calif., 1989).

Andrés, M. V.

Andrés, P.

Arriaga, J.

J. C. Knight, J. Arriaga, T. A. Birks, A. Ortisaga-Blanch, W. J. Wadsworth, P. St. J. Russell, “Anomalous dispersion in photonic crystal fibers,” IEEE Photon. Technol. Lett. 12, 807–809 (2000).
[CrossRef]

Birks, T. A.

J. C. Knight, J. Arriaga, T. A. Birks, A. Ortisaga-Blanch, W. J. Wadsworth, P. St. J. Russell, “Anomalous dispersion in photonic crystal fibers,” IEEE Photon. Technol. Lett. 12, 807–809 (2000).
[CrossRef]

M. J. Gander, R. McBride, J. C. D. Jones, D. Mogilevtsev, T. A. Birks, J. C. Knight, P. St. J. Russell, “Experimental measurement of group velocity dispersion in photonic crystal fibre, Electron. Lett. 35, 63–64 (1999).
[CrossRef]

D. Mogilevstev, T. A. Birks, P. St. J. Russell, “Group-velocity dispersion in photonic crystal fibers,” Opt. Lett. 23, 1662–1664 (1998).
[CrossRef]

Botten, L. C.

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]

Centeno, E.

de Sterke, C. M.

Felbacq, D.

E. Centeno, D. Felbacq, “Scattering by a random set of parallel cylinders,” J. Opt. Soc. Am. A 17, 320–327 (2000).
[CrossRef]

D. Felbacq, G. Tayeb, D. Maystre, “Scattering by a random set of parallel cylinders,” J. Opt. Soc. Am. A 9, 2526–2538 (1994).
[CrossRef]

Ferrando, A.

Fleming, J. W.

J. W. Fleming, “Material dispersion in lightguide glasses,” Electron. Lett. 14, 326–328 (1978).
[CrossRef]

Gander, M. J.

M. J. Gander, R. McBride, J. C. D. Jones, D. Mogilevtsev, T. A. Birks, J. C. Knight, P. St. J. Russell, “Experimental measurement of group velocity dispersion in photonic crystal fibre, Electron. Lett. 35, 63–64 (1999).
[CrossRef]

Jones, J. C. D.

M. J. Gander, R. McBride, J. C. D. Jones, D. Mogilevtsev, T. A. Birks, J. C. Knight, P. St. J. Russell, “Experimental measurement of group velocity dispersion in photonic crystal fibre, Electron. Lett. 35, 63–64 (1999).
[CrossRef]

Kawanishi, S.

H. Kubota, S. Suzuki, S. Kawanishi, M. Nakazawa, M. Takana. “Low-loss, 2 km-long photonic crystal fiber with zero GVD in the near IR suitable for picosecond pulse propagation at 800 nm band,” in Conference on Lasers and Electro-Optics (CLEO), Vol. 56 of OSP Trends in Optics and Photonics (Optical Society of America, Washington, D. C., 2001), pp. CPD3-1–CPD3-2.

Knight, J. C.

J. C. Knight, J. Arriaga, T. A. Birks, A. Ortisaga-Blanch, W. J. Wadsworth, P. St. J. Russell, “Anomalous dispersion in photonic crystal fibers,” IEEE Photon. Technol. Lett. 12, 807–809 (2000).
[CrossRef]

M. J. Gander, R. McBride, J. C. D. Jones, D. Mogilevtsev, T. A. Birks, J. C. Knight, P. St. J. Russell, “Experimental measurement of group velocity dispersion in photonic crystal fibre, Electron. Lett. 35, 63–64 (1999).
[CrossRef]

Kubota, H.

H. Kubota, S. Suzuki, S. Kawanishi, M. Nakazawa, M. Takana. “Low-loss, 2 km-long photonic crystal fiber with zero GVD in the near IR suitable for picosecond pulse propagation at 800 nm band,” in Conference on Lasers and Electro-Optics (CLEO), Vol. 56 of OSP Trends in Optics and Photonics (Optical Society of America, Washington, D. C., 2001), pp. CPD3-1–CPD3-2.

Kuhlmey, B.

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]

Maystre, D.

Mc Issac, P. R.

P. R. Mc Issac, “Symmetry-induced modal characteristics of uniform waveguides. I. Summary of results,” IEEE Trans. Microwave Theory Tech. 23, 421–433 (1975).
[CrossRef]

McBride, R.

M. J. Gander, R. McBride, J. C. D. Jones, D. Mogilevtsev, T. A. Birks, J. C. Knight, P. St. J. Russell, “Experimental measurement of group velocity dispersion in photonic crystal fibre, Electron. Lett. 35, 63–64 (1999).
[CrossRef]

McPhedran, R. C.

Miret, J.-J.

Mogilevstev, D.

Mogilevtsev, D.

M. J. Gander, R. McBride, J. C. D. Jones, D. Mogilevtsev, T. A. Birks, J. C. Knight, P. St. J. Russell, “Experimental measurement of group velocity dispersion in photonic crystal fibre, Electron. Lett. 35, 63–64 (1999).
[CrossRef]

Nakazawa, M.

H. Kubota, S. Suzuki, S. Kawanishi, M. Nakazawa, M. Takana. “Low-loss, 2 km-long photonic crystal fiber with zero GVD in the near IR suitable for picosecond pulse propagation at 800 nm band,” in Conference on Lasers and Electro-Optics (CLEO), Vol. 56 of OSP Trends in Optics and Photonics (Optical Society of America, Washington, D. C., 2001), pp. CPD3-1–CPD3-2.

Ortisaga-Blanch, A.

J. C. Knight, J. Arriaga, T. A. Birks, A. Ortisaga-Blanch, W. J. Wadsworth, P. St. J. Russell, “Anomalous dispersion in photonic crystal fibers,” IEEE Photon. Technol. Lett. 12, 807–809 (2000).
[CrossRef]

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]

Petit, R.

F. Zolla, R. Petit, “Method of fictitious sources as applied to the electromagnetic diffraction of a plane wave by a grating in conical mounts,” J. Opt. Soc. Am. A 13, 1087–1096 (1996).
[CrossRef]

Renversez, G.

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.

J. C. Knight, J. Arriaga, T. A. Birks, A. Ortisaga-Blanch, W. J. Wadsworth, P. St. J. Russell, “Anomalous dispersion in photonic crystal fibers,” IEEE Photon. Technol. Lett. 12, 807–809 (2000).
[CrossRef]

M. J. Gander, R. McBride, J. C. D. Jones, D. Mogilevtsev, T. A. Birks, J. C. Knight, P. St. J. Russell, “Experimental measurement of group velocity dispersion in photonic crystal fibre, Electron. Lett. 35, 63–64 (1999).
[CrossRef]

D. Mogilevstev, T. A. Birks, P. St. J. Russell, “Group-velocity dispersion in photonic crystal fibers,” Opt. Lett. 23, 1662–1664 (1998).
[CrossRef]

Silvestre, E.

Steel, M. J.

Suzuki, S.

H. Kubota, S. Suzuki, S. Kawanishi, M. Nakazawa, M. Takana. “Low-loss, 2 km-long photonic crystal fiber with zero GVD in the near IR suitable for picosecond pulse propagation at 800 nm band,” in Conference on Lasers and Electro-Optics (CLEO), Vol. 56 of OSP Trends in Optics and Photonics (Optical Society of America, Washington, D. C., 2001), pp. CPD3-1–CPD3-2.

Takana, M.

H. Kubota, S. Suzuki, S. Kawanishi, M. Nakazawa, M. Takana. “Low-loss, 2 km-long photonic crystal fiber with zero GVD in the near IR suitable for picosecond pulse propagation at 800 nm band,” in Conference on Lasers and Electro-Optics (CLEO), Vol. 56 of OSP Trends in Optics and Photonics (Optical Society of America, Washington, D. C., 2001), pp. CPD3-1–CPD3-2.

Tayeb, G.

D. Felbacq, G. Tayeb, D. Maystre, “Scattering by a random set of parallel cylinders,” J. Opt. Soc. Am. A 9, 2526–2538 (1994).
[CrossRef]

Wadsworth, W. J.

J. C. Knight, J. Arriaga, T. A. Birks, A. Ortisaga-Blanch, W. J. Wadsworth, P. St. J. Russell, “Anomalous dispersion in photonic crystal fibers,” IEEE Photon. Technol. Lett. 12, 807–809 (2000).
[CrossRef]

White, T. P.

Zolla, F.

F. Zolla, R. Petit, “Method of fictitious sources as applied to the electromagnetic diffraction of a plane wave by a grating in conical mounts,” J. Opt. Soc. Am. A 13, 1087–1096 (1996).
[CrossRef]

Electron. Lett. (2)

J. W. Fleming, “Material dispersion in lightguide glasses,” Electron. Lett. 14, 326–328 (1978).
[CrossRef]

M. J. Gander, R. McBride, J. C. D. Jones, D. Mogilevtsev, T. A. Birks, J. C. Knight, P. St. J. Russell, “Experimental measurement of group velocity dispersion in photonic crystal fibre, Electron. Lett. 35, 63–64 (1999).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

J. C. Knight, J. Arriaga, T. A. Birks, A. Ortisaga-Blanch, W. J. Wadsworth, P. St. J. Russell, “Anomalous dispersion in photonic crystal fibers,” IEEE Photon. Technol. Lett. 12, 807–809 (2000).
[CrossRef]

IEEE Trans. Microwave Theory Tech. (1)

P. R. Mc Issac, “Symmetry-induced modal characteristics of uniform waveguides. I. Summary of results,” IEEE Trans. Microwave Theory Tech. 23, 421–433 (1975).
[CrossRef]

J. Opt. Soc. Am. A (4)

F. Zolla, R. Petit, “Method of fictitious sources as applied to the electromagnetic diffraction of a plane wave by a grating in conical mounts,” J. Opt. Soc. Am. A 13, 1087–1096 (1996).
[CrossRef]

D. Felbacq, G. Tayeb, D. Maystre, “Scattering by a random set of parallel cylinders,” J. Opt. Soc. Am. A 9, 2526–2538 (1994).
[CrossRef]

E. Centeno, D. Felbacq, “Scattering by a random set of parallel cylinders,” J. Opt. Soc. Am. A 17, 320–327 (2000).
[CrossRef]

A. Ferrando, E. Silvestre, J.-J. Miret, P. Andrés, M. V. Andrés, “Vector description of higher-order modes in photonic crystal fibers,” J. Opt. Soc. Am. A 17, 1333–1340 (2000).
[CrossRef]

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

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. (4)

Other (4)

H. Kubota, S. Suzuki, S. Kawanishi, M. Nakazawa, M. Takana. “Low-loss, 2 km-long photonic crystal fiber with zero GVD in the near IR suitable for picosecond pulse propagation at 800 nm band,” in Conference on Lasers and Electro-Optics (CLEO), Vol. 56 of OSP Trends in Optics and Photonics (Optical Society of America, Washington, D. C., 2001), pp. CPD3-1–CPD3-2.

G. Renversez, B. Kuhlmey, R. C. McPhedran are preparing the following paper for publication, “Dispersion management with microstructured optical fibers: ultra-flattened chromatic dispersion with low losses.”

R. C. McPhedran, L. C. Botten, Department of Mathematical Sciences, University of Technology, Sydney, New South Wales 2007, Australia.

G. P. Agrawal, Nonlinear Fiber Optics (Academic, San Diego, Calif., 1989).

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Figures (6)

Fig. 1
Fig. 1

Cross section of the model MOF with three rings of holes (the holes are shown colored gray); N r = 3. Λ is the pitch of the triangular lattice, and d is a holes diameter. The solid core consists of one missing hole in the center of the structure.

Fig. 2
Fig. 2

(a) Dispersion and (b) losses for a three-ring MOF as a function of wavelength and pitch Λ. The material dispersion is also shown. Hole diameter d, 0.8 μm.

Fig. 3
Fig. 3

Losses for a four-ring MOF as a function of wavelength and pitch Λ. Hole diameter d, 0.8 μm. The y scale is linear, unlike for Fig. 2(b).

Fig. 4
Fig. 4

(a) Dispersion and (b) losses for a three-ring MOF as a function of wavelength and hole diameter d. The material dispersion is also shown. Pitch Λ, 1.55 μm.

Fig. 5
Fig. 5

(a) Dispersion and (b) losses as a function of the wavelength, and number of rings N r [the types of curves have the same values for (a) and (b)]. Pitch Λ 2.0 μm; hole diameter d, 0.5 μm. (c) Dispersion for three wavelengths as a function of the number of rings N r for the same MOF.

Fig. 6
Fig. 6

Dispersion as a function of wavelength and number of rings N r . Pitch Λ, 1.55 μm; hole diameter d, 0.6 μm.

Tables (1)

Tables Icon

Table 1 Comparison of Dispersion D and Its Slope Measured and Calculated at λ = 0.813 μm by Gander et al. a

Equations (2)

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=20ln102πλ neff×106,
D=-λc2 neffλ2.

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