Abstract

An analysis of the confinement losses in photonic crystal fibers due to the finite numbers of air holes is performed by means of the finite element method. The high flexibility of the numerical method allows to consider fibers with regular lattices, like the triangular and the honeycomb ones, and circular holes, but also fibers with more complicated cross sections like the cobweb fiber. Numerical results show that by increasing the number of air hole rings the attenuation constant decreases. This dependence is very strong for triangular and cobweb fibers, whereas it is very weak for the honeycomb one.

© 2002 Optical Society of America

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References

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  1. T. P. White, R. C. McPhedram, C. M. de Sterke, L. C. Botten, and M. J. Steel, “Confinement losses in microstructured optical fibers,” Opt. Lett. 26, 1660–1662 (2001).
    [Crossref]
  2. V. Finazzi, T. M. Monro, and D. J. Richardson, “Confinement losses in highly nonlinear holey optical fibers,” in Optical Fiber Communication 2002, vol. 70 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C.2002), paper ThS4.
  3. K. Saitoh and M. Koshiba, “Full-vectorial imaginary-distance beam propagation method based on a finite element scheme: application to photonic crystal fibers,” IEEE J. Quantum Electron. 38, 927–933 (2002).
    [Crossref]
  4. A. Cucinotta, S. Selleri, L. Vincetti, and M. Zoboli, “Perturbation analysis of dispersion properties in photonic crystal fibers through the finite element method,” J. Lightwave Technol. 20,(2002).
    [Crossref]
  5. A. Cucinotta, S. Selleri, L. Vincetti, and M. Zoboli, “Holey fiber analysis through the finite element method,” IEEE Photon. Technol. Lett. 14, 1530–15322002.
    [Crossref]
  6. S. Selleri, L. Vincetti, A. Cucinotta, and M. Zoboli, “Complex FEM modal solver of optical waveguides with PML boundary conditions,” Opt. Quantum Electron. 33, 359–371(2001).
    [Crossref]
  7. J.C. Knight, J. Arriaga, T.A. Birks, A. Ortigosa-Blanch, W.J. Wadsworth, and P. St. Russell, “Anomalous dispersion in photonic crystal fiber,” IEEE Photon. Technol. Lett.,  12, 807–809 (2000).
    [Crossref]
  8. S. E. Barkou, J. Broeng, and A. Bjarklev, “Dispersion properties of photonic bandgap guiding fibers,” in Optical Fiber Communication Conference , OSA Technical Digest (Optical Society of America, Washington DC, 1998), FG5.
  9. A. Ferrando, E. Silvestre, P. Andrés, J. J. Miret, and M. V. Andrés, “Designing the properties of dispersion-flattend photonic crystal fibers,” Opt. Express 9, 687–697 (2001). http: //www.opticsexpress.org/abstract.cfm?URI=OPEX-9-13-687
    [Crossref] [PubMed]

2002 (3)

K. Saitoh and M. Koshiba, “Full-vectorial imaginary-distance beam propagation method based on a finite element scheme: application to photonic crystal fibers,” IEEE J. Quantum Electron. 38, 927–933 (2002).
[Crossref]

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

A. Cucinotta, S. Selleri, L. Vincetti, and M. Zoboli, “Holey fiber analysis through the finite element method,” IEEE Photon. Technol. Lett. 14, 1530–15322002.
[Crossref]

2001 (3)

2000 (1)

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

Andrés, M. V.

Andrés, P.

Arriaga, J.

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

Barkou, S. E.

S. E. Barkou, J. Broeng, and A. Bjarklev, “Dispersion properties of photonic bandgap guiding fibers,” in Optical Fiber Communication Conference , OSA Technical Digest (Optical Society of America, Washington DC, 1998), FG5.

Birks, T.A.

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

Bjarklev, A.

S. E. Barkou, J. Broeng, and A. Bjarklev, “Dispersion properties of photonic bandgap guiding fibers,” in Optical Fiber Communication Conference , OSA Technical Digest (Optical Society of America, Washington DC, 1998), FG5.

Botten, L. C.

Broeng, J.

S. E. Barkou, J. Broeng, and A. Bjarklev, “Dispersion properties of photonic bandgap guiding fibers,” in Optical Fiber Communication Conference , OSA Technical Digest (Optical Society of America, Washington DC, 1998), FG5.

Cucinotta, A.

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

A. Cucinotta, S. Selleri, L. Vincetti, and M. Zoboli, “Holey fiber analysis through the finite element method,” IEEE Photon. Technol. Lett. 14, 1530–15322002.
[Crossref]

S. Selleri, L. Vincetti, A. Cucinotta, and M. Zoboli, “Complex FEM modal solver of optical waveguides with PML boundary conditions,” Opt. Quantum Electron. 33, 359–371(2001).
[Crossref]

de Sterke, C. M.

Ferrando, A.

Finazzi, V.

V. Finazzi, T. M. Monro, and D. J. Richardson, “Confinement losses in highly nonlinear holey optical fibers,” in Optical Fiber Communication 2002, vol. 70 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C.2002), paper ThS4.

Knight, J.C.

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

Koshiba, M.

K. Saitoh and M. Koshiba, “Full-vectorial imaginary-distance beam propagation method based on a finite element scheme: application to photonic crystal fibers,” IEEE J. Quantum Electron. 38, 927–933 (2002).
[Crossref]

McPhedram, R. C.

Miret, J. J.

Monro, T. M.

V. Finazzi, T. M. Monro, and D. J. Richardson, “Confinement losses in highly nonlinear holey optical fibers,” in Optical Fiber Communication 2002, vol. 70 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C.2002), paper ThS4.

Ortigosa-Blanch, A.

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

Richardson, D. J.

V. Finazzi, T. M. Monro, and D. J. Richardson, “Confinement losses in highly nonlinear holey optical fibers,” in Optical Fiber Communication 2002, vol. 70 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C.2002), paper ThS4.

Russell, P. St.

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

Saitoh, K.

K. Saitoh and M. Koshiba, “Full-vectorial imaginary-distance beam propagation method based on a finite element scheme: application to photonic crystal fibers,” IEEE J. Quantum Electron. 38, 927–933 (2002).
[Crossref]

Selleri, S.

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

A. Cucinotta, S. Selleri, L. Vincetti, and M. Zoboli, “Holey fiber analysis through the finite element method,” IEEE Photon. Technol. Lett. 14, 1530–15322002.
[Crossref]

S. Selleri, L. Vincetti, A. Cucinotta, and M. Zoboli, “Complex FEM modal solver of optical waveguides with PML boundary conditions,” Opt. Quantum Electron. 33, 359–371(2001).
[Crossref]

Silvestre, E.

Steel, M. J.

Vincetti, L.

A. Cucinotta, S. Selleri, L. Vincetti, and M. Zoboli, “Holey fiber analysis through the finite element method,” IEEE Photon. Technol. Lett. 14, 1530–15322002.
[Crossref]

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

S. Selleri, L. Vincetti, A. Cucinotta, and M. Zoboli, “Complex FEM modal solver of optical waveguides with PML boundary conditions,” Opt. Quantum Electron. 33, 359–371(2001).
[Crossref]

Wadsworth, W.J.

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

White, T. P.

Zoboli, M.

A. Cucinotta, S. Selleri, L. Vincetti, and M. Zoboli, “Holey fiber analysis through the finite element method,” IEEE Photon. Technol. Lett. 14, 1530–15322002.
[Crossref]

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

S. Selleri, L. Vincetti, A. Cucinotta, and M. Zoboli, “Complex FEM modal solver of optical waveguides with PML boundary conditions,” Opt. Quantum Electron. 33, 359–371(2001).
[Crossref]

IEEE J. Quantum Electron. (1)

K. Saitoh and M. Koshiba, “Full-vectorial imaginary-distance beam propagation method based on a finite element scheme: application to photonic crystal fibers,” IEEE J. Quantum Electron. 38, 927–933 (2002).
[Crossref]

IEEE Photon. Technol. Lett. (2)

A. Cucinotta, S. Selleri, L. Vincetti, and M. Zoboli, “Holey fiber analysis through the finite element method,” IEEE Photon. Technol. Lett. 14, 1530–15322002.
[Crossref]

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

J. Lightwave Technol. (1)

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

Opt. Express (1)

Opt. Lett. (1)

Opt. Quantum Electron. (1)

S. Selleri, L. Vincetti, A. Cucinotta, and M. Zoboli, “Complex FEM modal solver of optical waveguides with PML boundary conditions,” Opt. Quantum Electron. 33, 359–371(2001).
[Crossref]

Other (2)

S. E. Barkou, J. Broeng, and A. Bjarklev, “Dispersion properties of photonic bandgap guiding fibers,” in Optical Fiber Communication Conference , OSA Technical Digest (Optical Society of America, Washington DC, 1998), FG5.

V. Finazzi, T. M. Monro, and D. J. Richardson, “Confinement losses in highly nonlinear holey optical fibers,” in Optical Fiber Communication 2002, vol. 70 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C.2002), paper ThS4.

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Figures (6)

Fig. 1.
Fig. 1.

(a): triangular fiber with four hole rings. The lines with different colors show different rings: black first ring, red second one, yellow third one, and blue fourth one. The dashed lines shows the quarter of the structure considered in the analysis. (b): main component of the magnetic field for a fiber having two rings, d/Λ = 0.3 and Λ = 2.3μm.

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Fig. 2.
Fig. 2.

(a): confinement loss as a function of hole diameter d normalized to pitch Λ = 2.3μm for different numbers of rings. (b): confinement loss as a function of pitch Λ for different ratios d/Λ. In both cases a wavelength λ = 1.55μm is assumed

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Fig. 3.
Fig. 3.

Confinement loss as a function of the wavelength λ for different numbers of rings and d/Λ = 0.5. (a) Λ = 2.3μm; (b) Λ = 4.6μm,

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Fig. 4.
Fig. 4.

(a): honeycomb fiber with three hole rings. The circles with different colors show different rings: red first ring and black second one. The dashed lines shows the quarter of the structure considered in the analysis. (b): fundamental mode profile of a honeycomb fiber having three rings and d/Λ = 0.41 at the wavelength λ = 1.55μm.

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Fig. 5.
Fig. 5.

(a): confinement loss as a function of numbers of rings at the wavelength λ = 1.55μm and for d/Λ = 0.41 red line and for d/Λ = 0.55 green line. (b): confinement loss as a function of the wavelength λ for different numbers of rings and d/Λ = 0.41. In both cases Λ = 1.62μm is assumed.

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Fig. 6.
Fig. 6.

(a): cross sections of the cobweb fiber with one (top) and three (bottom) rings. (b): confinement loss as a function of the wavelength for different ring numbers.

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Equations (2)

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∇ ¯ × ( ε ̿ r − 1 ∇ ¯ × h ¯ ) − k 0 2 μ ̿ r h ¯ = 0
( [ A ] − ( γ k 0 ) 2 [ B ] ) { H } = 0

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