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Finite element characterization of chromatic dispersion in nonlinear holey fibers

Takeshi Fujisawa and Masanori Koshiba

Open Access Open Access

Abstract

Chromatic dispersion characteristics of nonlinear photonic crystal fibers are, for the first time to our knowledge, theoretically investigated. A self-consistent numerical approach based on the full-vector finite-element method in terms of all the components of electric fields is described for the steady-state analysis of axially-nonsymmetrical nonlinear optical fibers. Electric fields obtained with this approach can be directly utilized for evaluating nonlinear refractive index distributions. To eliminate nonphysical, spurious solutions and to accurately model curved boundaries of circular air holes, curvilinear hybrid edge/nodal elements are introduced. It is found from the numerical results that under high optical intensity, chromatic dispersion characteristics become different from those of the linear state due to optical Kerr-effect nonlinearity, especially in short wavelength region.

©2003 Optical Society of America

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References

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  • Publication
  1. K. Okamoto and E.A.J. Marcatili, “Chromatic dispersion characteristics of fibers with optical Kerr-effect,” J. Lightwave Technol. 7, 1988–1994 (1989).
    [Crossref]
  2. R.A. Sammut and C. Pask, “Group velocity and dispersion in nonlinear-optical fibers,” Opt. Lett. 16, 70–72 (1991).
    [Crossref] [PubMed]
  3. H.Y. Lin and H.-C. Chang, “An efficient method for determining the chromatic dispersion characteristics of nonlinear single-mode optical fibers,” J. Lightwave Technol. 10, 1188–1195 (1992).
    [Crossref]
  4. J.C. Knight, T.A. Birks, P.St.J. Russell, and 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, and P.St.J. Russell, “Endlessly single-mode photonic crystal fiber,” Opt. Lett. 22, 961–963 (1997).
    [Crossref] [PubMed]
  6. J.C. Knight, T.A. Birks, R.F. Cregan, P.St.J. Russell, and J.-P. de Sandro, “Large mode area photonic crystal fiber,” Electron. Lett. 34, 1347–1348 (1998).
    [Crossref]
  7. N.G.R. Broderick, T.M. Monro, P.J. Bennett, and D.J. Richardson, “Nonlinearity in holey optical fibers: measurement and future opportunities,” Opt. Lett. 24, 1395–1397 (1999).
    [Crossref]
  8. M.J. Gander, R. McBride, J.D.C. Jones, D. Mogilevtsev, T.A. Birks, J.C. Knight, and P.St.J. Russell, “Experimental measurement of group velocity in photonic crystal fiber,” Electron. Lett. 35, 63–64 (1999).
    [Crossref]
  9. M.J. Gander, R. McBride, J.D.C. Jones, T.A. Birks, J.C. Knight, P.St.J. Russell, P.M. Blanchard, J.G. Burnett, and A.H. Greenaway, “Measurement of the wavelength dependence of beam divergence for photonic crystal fiber,” Opt. Lett. 24, 1017–1019 (1999).
    [Crossref]
  10. W.J. Wadsworth, J.C. Knight, A. Ortigosa-Blanch, J. Arriaga, E. Silvestre, and P.St.J. Russell, “Soliton effects in photonic crystal fibres at 850 nm,” Electron. Lett. 36, 53–55 (2000).
    [Crossref]
  11. W.J. Wadsworth, A. Ortigosa-Blanch, J.C. Knight, T.A. Birks, T.-P. Martin Man, and P.St.J. Russell, “Supercontinuum generation in photonic crystal fibers and optical fiber tapers: a novel light source,” J. Opt. Soc. Am. B 19, 2148–2155 (2002).
    [Crossref]
  12. A.W. Snyder, Y. Chen, L. Poladian, and D.J. Mitchell, “Fundamental mode of highly nonlinear fibers,” Electron. Lett. 26, 643–644 (1990).
    [Crossref]
  13. R.A. Sammut and C. Pask, “Variational approach to nonlinear waveguides-gaussian approximations,” Electron. Lett. 26, 1131–1132 (1990).
    [Crossref]
  14. R.A. Sammut and C. Pask, “Gaussian and equivalent-step-index approximations for nonlinear waveguides,” J. Opt. Soc. Am. B 8, 395–402 (1991).
    [Crossref]
  15. Y. Chen, “Nonlinear fibers with arbitrary nonlinearity,” J. Opt. Soc. Am. B 8, 2338–2341 (1991).
    [Crossref]
  16. M.J. Holmes, D.M. Spirit, and F.P. Payne, “New gaussian-based approximation for modeling non-linear effects in optical fibers,” J. Lightwave Technol. 12, 193–201 (1994).
    [Crossref]
  17. F. Brechet, J. Marcou, D. Pagnoux, and P. Roy, “Complete analysis of the characteristics of propagation into photonic crystal fibers,” Opt. Fiber Technol. 6, 181- (2000).
    [Crossref]
  18. M. Koshiba and K. Saitoh, “Numerical verification of degeneracy in hexagonal photonic crystal fibers,” IEEE Photon. Technol. Lett. 13, 1313–1315 (2001).
    [Crossref]
  19. M. Koshiba, “Full-vector analysis of photonic crystal fibers using the finite element method,” IEICE Trans. Electron. E85-C, 881–888 (2002).
  20. 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]
  21. A. Cucinotta, S. Selleri, L. Vincetti, and M. Zoboli, “Holey fiber analysis through the finite element method,” IEEE Photon. Technol. Lett. 14, 1530–1532 (2002).
    [Crossref]
  22. K. Hayata and M. Koshiba, “Full vectorial analysis of nonlinear-optical waveguides,” J. Opt. Soc. Am. B 5, 2494–2501 (1988).
    [Crossref]
  23. R.D. Ettinger, F.A. Fernandez, B.M.A. Rahman, and J.B. Davies, “Vector finite element solution of saturable nonlinear strip-loaded optical waveguides,” IEEE Photon. Technol. Lett. 3, 147–149 (1991).
    [Crossref]
  24. X.H. Wang and G.K. Cambrell, “Full vectorial simulation of bistability phenomena in nonlinear-optical channel waveguides,” J. Opt. Soc. Am. B 10, 1090–1095 (1993).
    [Crossref]
  25. X.H. Wang and G.K. Cambrell, “Simulation of strong nonlinear effects in optical waveguides,” J. Opt. Soc. Am. B 10, 2048–2055 (1993).
    [Crossref]
  26. S. Selleri and M. Zoboli, “An improved finite element method formulation for the analysis of nonlinear anisotropic dielectric waveguides,” IEEE Trans. Micorwave Theory Tech. 43, 887–892 (1995).
    [Crossref]
  27. M. Zoboli, F.Di Pasquale, and S. Selleri, “Full-vectorial and scalar solutions of nonlinear optical fibers,” Opt. Comuun. 97, 11–15 (1993).
    [Crossref]
  28. X.H. Wang and G.K. Cambrell, “Vectorial simulation and power-parameter characterization of nonlinear planar optical waveguides,” J. Opt. Soc. Am. B 12, 265–274 (1995).
    [Crossref]
  29. S.S.A. Obayya, B.M.A. Rahman, K.T.V. Grattan, and H.A. El-Mikati, “Full-vectorial finite-element solution of nonlinear bistable optical waveguides,” IEEE J. Quantum Electron. 38, 1120–1125 (2002).
    [Crossref]
  30. M. Koshiba and Y. Tsuji, “Curvilinear hybrid edge/nodal elements with triangular shape for guided-wave problems,” J. Lightwave Technol. 18, 737–743 (2000).
    [Crossref]

2002 (5)

W.J. Wadsworth, A. Ortigosa-Blanch, J.C. Knight, T.A. Birks, T.-P. Martin Man, and P.St.J. Russell, “Supercontinuum generation in photonic crystal fibers and optical fiber tapers: a novel light source,” J. Opt. Soc. Am. B 19, 2148–2155 (2002).
[Crossref]

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

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, “Holey fiber analysis through the finite element method,” IEEE Photon. Technol. Lett. 14, 1530–1532 (2002).
[Crossref]

S.S.A. Obayya, B.M.A. Rahman, K.T.V. Grattan, and H.A. El-Mikati, “Full-vectorial finite-element solution of nonlinear bistable optical waveguides,” IEEE J. Quantum Electron. 38, 1120–1125 (2002).
[Crossref]

2001 (1)

M. Koshiba and K. Saitoh, “Numerical verification of degeneracy in hexagonal photonic crystal fibers,” IEEE Photon. Technol. Lett. 13, 1313–1315 (2001).
[Crossref]

2000 (3)

F. Brechet, J. Marcou, D. Pagnoux, and P. Roy, “Complete analysis of the characteristics of propagation into photonic crystal fibers,” Opt. Fiber Technol. 6, 181- (2000).
[Crossref]

W.J. Wadsworth, J.C. Knight, A. Ortigosa-Blanch, J. Arriaga, E. Silvestre, and P.St.J. Russell, “Soliton effects in photonic crystal fibres at 850 nm,” Electron. Lett. 36, 53–55 (2000).
[Crossref]

M. Koshiba and Y. Tsuji, “Curvilinear hybrid edge/nodal elements with triangular shape for guided-wave problems,” J. Lightwave Technol. 18, 737–743 (2000).
[Crossref]

1999 (3)

1998 (1)

J.C. Knight, T.A. Birks, R.F. Cregan, P.St.J. Russell, and J.-P. de Sandro, “Large mode area photonic crystal fiber,” Electron. Lett. 34, 1347–1348 (1998).
[Crossref]

1997 (1)

1996 (1)

1995 (2)

X.H. Wang and G.K. Cambrell, “Vectorial simulation and power-parameter characterization of nonlinear planar optical waveguides,” J. Opt. Soc. Am. B 12, 265–274 (1995).
[Crossref]

S. Selleri and M. Zoboli, “An improved finite element method formulation for the analysis of nonlinear anisotropic dielectric waveguides,” IEEE Trans. Micorwave Theory Tech. 43, 887–892 (1995).
[Crossref]

1994 (1)

M.J. Holmes, D.M. Spirit, and F.P. Payne, “New gaussian-based approximation for modeling non-linear effects in optical fibers,” J. Lightwave Technol. 12, 193–201 (1994).
[Crossref]

1993 (3)

1992 (1)

H.Y. Lin and H.-C. Chang, “An efficient method for determining the chromatic dispersion characteristics of nonlinear single-mode optical fibers,” J. Lightwave Technol. 10, 1188–1195 (1992).
[Crossref]

1991 (4)

1990 (2)

A.W. Snyder, Y. Chen, L. Poladian, and D.J. Mitchell, “Fundamental mode of highly nonlinear fibers,” Electron. Lett. 26, 643–644 (1990).
[Crossref]

R.A. Sammut and C. Pask, “Variational approach to nonlinear waveguides-gaussian approximations,” Electron. Lett. 26, 1131–1132 (1990).
[Crossref]

1989 (1)

K. Okamoto and E.A.J. Marcatili, “Chromatic dispersion characteristics of fibers with optical Kerr-effect,” J. Lightwave Technol. 7, 1988–1994 (1989).
[Crossref]

1988 (1)

Arriaga, J.

W.J. Wadsworth, J.C. Knight, A. Ortigosa-Blanch, J. Arriaga, E. Silvestre, and P.St.J. Russell, “Soliton effects in photonic crystal fibres at 850 nm,” Electron. Lett. 36, 53–55 (2000).
[Crossref]

Atkin, D.M

Bennett, P.J.

Birks, T.A.

Blanchard, P.M.

Brechet, F.

F. Brechet, J. Marcou, D. Pagnoux, and P. Roy, “Complete analysis of the characteristics of propagation into photonic crystal fibers,” Opt. Fiber Technol. 6, 181- (2000).
[Crossref]

Broderick, N.G.R.

Burnett, J.G.

Cambrell, G.K.

Chang, H.-C.

H.Y. Lin and H.-C. Chang, “An efficient method for determining the chromatic dispersion characteristics of nonlinear single-mode optical fibers,” J. Lightwave Technol. 10, 1188–1195 (1992).
[Crossref]

Chen, Y.

Y. Chen, “Nonlinear fibers with arbitrary nonlinearity,” J. Opt. Soc. Am. B 8, 2338–2341 (1991).
[Crossref]

A.W. Snyder, Y. Chen, L. Poladian, and D.J. Mitchell, “Fundamental mode of highly nonlinear fibers,” Electron. Lett. 26, 643–644 (1990).
[Crossref]

Cregan, R.F.

J.C. Knight, T.A. Birks, R.F. Cregan, P.St.J. Russell, and J.-P. de Sandro, “Large mode area photonic crystal fiber,” Electron. Lett. 34, 1347–1348 (1998).
[Crossref]

Cucinotta, A.

A. Cucinotta, S. Selleri, L. Vincetti, and M. Zoboli, “Holey fiber analysis through the finite element method,” IEEE Photon. Technol. Lett. 14, 1530–1532 (2002).
[Crossref]

Davies, J.B.

R.D. Ettinger, F.A. Fernandez, B.M.A. Rahman, and J.B. Davies, “Vector finite element solution of saturable nonlinear strip-loaded optical waveguides,” IEEE Photon. Technol. Lett. 3, 147–149 (1991).
[Crossref]

de Sandro, J.-P.

J.C. Knight, T.A. Birks, R.F. Cregan, P.St.J. Russell, and J.-P. de Sandro, “Large mode area photonic crystal fiber,” Electron. Lett. 34, 1347–1348 (1998).
[Crossref]

El-Mikati, H.A.

S.S.A. Obayya, B.M.A. Rahman, K.T.V. Grattan, and H.A. El-Mikati, “Full-vectorial finite-element solution of nonlinear bistable optical waveguides,” IEEE J. Quantum Electron. 38, 1120–1125 (2002).
[Crossref]

Ettinger, R.D.

R.D. Ettinger, F.A. Fernandez, B.M.A. Rahman, and J.B. Davies, “Vector finite element solution of saturable nonlinear strip-loaded optical waveguides,” IEEE Photon. Technol. Lett. 3, 147–149 (1991).
[Crossref]

Fernandez, F.A.

R.D. Ettinger, F.A. Fernandez, B.M.A. Rahman, and J.B. Davies, “Vector finite element solution of saturable nonlinear strip-loaded optical waveguides,” IEEE Photon. Technol. Lett. 3, 147–149 (1991).
[Crossref]

Gander, M.J.

M.J. Gander, R. McBride, J.D.C. Jones, T.A. Birks, J.C. Knight, P.St.J. Russell, P.M. Blanchard, J.G. Burnett, and A.H. Greenaway, “Measurement of the wavelength dependence of beam divergence for photonic crystal fiber,” Opt. Lett. 24, 1017–1019 (1999).
[Crossref]

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

Grattan, K.T.V.

S.S.A. Obayya, B.M.A. Rahman, K.T.V. Grattan, and H.A. El-Mikati, “Full-vectorial finite-element solution of nonlinear bistable optical waveguides,” IEEE J. Quantum Electron. 38, 1120–1125 (2002).
[Crossref]

Greenaway, A.H.

Hayata, K.

Holmes, M.J.

M.J. Holmes, D.M. Spirit, and F.P. Payne, “New gaussian-based approximation for modeling non-linear effects in optical fibers,” J. Lightwave Technol. 12, 193–201 (1994).
[Crossref]

Jones, J.D.C.

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

M.J. Gander, R. McBride, J.D.C. Jones, T.A. Birks, J.C. Knight, P.St.J. Russell, P.M. Blanchard, J.G. Burnett, and A.H. Greenaway, “Measurement of the wavelength dependence of beam divergence for photonic crystal fiber,” Opt. Lett. 24, 1017–1019 (1999).
[Crossref]

Knight, J.C.

Koshiba, M.

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

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]

M. Koshiba and K. Saitoh, “Numerical verification of degeneracy in hexagonal photonic crystal fibers,” IEEE Photon. Technol. Lett. 13, 1313–1315 (2001).
[Crossref]

M. Koshiba and Y. Tsuji, “Curvilinear hybrid edge/nodal elements with triangular shape for guided-wave problems,” J. Lightwave Technol. 18, 737–743 (2000).
[Crossref]

K. Hayata and M. Koshiba, “Full vectorial analysis of nonlinear-optical waveguides,” J. Opt. Soc. Am. B 5, 2494–2501 (1988).
[Crossref]

Lin, H.Y.

H.Y. Lin and H.-C. Chang, “An efficient method for determining the chromatic dispersion characteristics of nonlinear single-mode optical fibers,” J. Lightwave Technol. 10, 1188–1195 (1992).
[Crossref]

Man, T.-P. Martin

Marcatili, E.A.J.

K. Okamoto and E.A.J. Marcatili, “Chromatic dispersion characteristics of fibers with optical Kerr-effect,” J. Lightwave Technol. 7, 1988–1994 (1989).
[Crossref]

Marcou, J.

F. Brechet, J. Marcou, D. Pagnoux, and P. Roy, “Complete analysis of the characteristics of propagation into photonic crystal fibers,” Opt. Fiber Technol. 6, 181- (2000).
[Crossref]

McBride, R.

M.J. Gander, R. McBride, J.D.C. Jones, T.A. Birks, J.C. Knight, P.St.J. Russell, P.M. Blanchard, J.G. Burnett, and A.H. Greenaway, “Measurement of the wavelength dependence of beam divergence for photonic crystal fiber,” Opt. Lett. 24, 1017–1019 (1999).
[Crossref]

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

Mitchell, D.J.

A.W. Snyder, Y. Chen, L. Poladian, and D.J. Mitchell, “Fundamental mode of highly nonlinear fibers,” Electron. Lett. 26, 643–644 (1990).
[Crossref]

Mogilevtsev, D.

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

Monro, T.M.

Obayya, S.S.A.

S.S.A. Obayya, B.M.A. Rahman, K.T.V. Grattan, and H.A. El-Mikati, “Full-vectorial finite-element solution of nonlinear bistable optical waveguides,” IEEE J. Quantum Electron. 38, 1120–1125 (2002).
[Crossref]

Okamoto, K.

K. Okamoto and E.A.J. Marcatili, “Chromatic dispersion characteristics of fibers with optical Kerr-effect,” J. Lightwave Technol. 7, 1988–1994 (1989).
[Crossref]

Ortigosa-Blanch, A.

W.J. Wadsworth, A. Ortigosa-Blanch, J.C. Knight, T.A. Birks, T.-P. Martin Man, and P.St.J. Russell, “Supercontinuum generation in photonic crystal fibers and optical fiber tapers: a novel light source,” J. Opt. Soc. Am. B 19, 2148–2155 (2002).
[Crossref]

W.J. Wadsworth, J.C. Knight, A. Ortigosa-Blanch, J. Arriaga, E. Silvestre, and P.St.J. Russell, “Soliton effects in photonic crystal fibres at 850 nm,” Electron. Lett. 36, 53–55 (2000).
[Crossref]

Pagnoux, D.

F. Brechet, J. Marcou, D. Pagnoux, and P. Roy, “Complete analysis of the characteristics of propagation into photonic crystal fibers,” Opt. Fiber Technol. 6, 181- (2000).
[Crossref]

Pask, C.

Pasquale, F.Di

M. Zoboli, F.Di Pasquale, and S. Selleri, “Full-vectorial and scalar solutions of nonlinear optical fibers,” Opt. Comuun. 97, 11–15 (1993).
[Crossref]

Payne, F.P.

M.J. Holmes, D.M. Spirit, and F.P. Payne, “New gaussian-based approximation for modeling non-linear effects in optical fibers,” J. Lightwave Technol. 12, 193–201 (1994).
[Crossref]

Poladian, L.

A.W. Snyder, Y. Chen, L. Poladian, and D.J. Mitchell, “Fundamental mode of highly nonlinear fibers,” Electron. Lett. 26, 643–644 (1990).
[Crossref]

Rahman, B.M.A.

S.S.A. Obayya, B.M.A. Rahman, K.T.V. Grattan, and H.A. El-Mikati, “Full-vectorial finite-element solution of nonlinear bistable optical waveguides,” IEEE J. Quantum Electron. 38, 1120–1125 (2002).
[Crossref]

R.D. Ettinger, F.A. Fernandez, B.M.A. Rahman, and J.B. Davies, “Vector finite element solution of saturable nonlinear strip-loaded optical waveguides,” IEEE Photon. Technol. Lett. 3, 147–149 (1991).
[Crossref]

Richardson, D.J.

Roy, P.

F. Brechet, J. Marcou, D. Pagnoux, and P. Roy, “Complete analysis of the characteristics of propagation into photonic crystal fibers,” Opt. Fiber Technol. 6, 181- (2000).
[Crossref]

Russell, P.St.J.

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]

M. Koshiba and K. Saitoh, “Numerical verification of degeneracy in hexagonal photonic crystal fibers,” IEEE Photon. Technol. Lett. 13, 1313–1315 (2001).
[Crossref]

Sammut, R.A.

Selleri, S.

A. Cucinotta, S. Selleri, L. Vincetti, and M. Zoboli, “Holey fiber analysis through the finite element method,” IEEE Photon. Technol. Lett. 14, 1530–1532 (2002).
[Crossref]

S. Selleri and M. Zoboli, “An improved finite element method formulation for the analysis of nonlinear anisotropic dielectric waveguides,” IEEE Trans. Micorwave Theory Tech. 43, 887–892 (1995).
[Crossref]

M. Zoboli, F.Di Pasquale, and S. Selleri, “Full-vectorial and scalar solutions of nonlinear optical fibers,” Opt. Comuun. 97, 11–15 (1993).
[Crossref]

Silvestre, E.

W.J. Wadsworth, J.C. Knight, A. Ortigosa-Blanch, J. Arriaga, E. Silvestre, and P.St.J. Russell, “Soliton effects in photonic crystal fibres at 850 nm,” Electron. Lett. 36, 53–55 (2000).
[Crossref]

Snyder, A.W.

A.W. Snyder, Y. Chen, L. Poladian, and D.J. Mitchell, “Fundamental mode of highly nonlinear fibers,” Electron. Lett. 26, 643–644 (1990).
[Crossref]

Spirit, D.M.

M.J. Holmes, D.M. Spirit, and F.P. Payne, “New gaussian-based approximation for modeling non-linear effects in optical fibers,” J. Lightwave Technol. 12, 193–201 (1994).
[Crossref]

Tsuji, Y.

Vincetti, L.

A. Cucinotta, S. Selleri, L. Vincetti, and M. Zoboli, “Holey fiber analysis through the finite element method,” IEEE Photon. Technol. Lett. 14, 1530–1532 (2002).
[Crossref]

Wadsworth, W.J.

W.J. Wadsworth, A. Ortigosa-Blanch, J.C. Knight, T.A. Birks, T.-P. Martin Man, and P.St.J. Russell, “Supercontinuum generation in photonic crystal fibers and optical fiber tapers: a novel light source,” J. Opt. Soc. Am. B 19, 2148–2155 (2002).
[Crossref]

W.J. Wadsworth, J.C. Knight, A. Ortigosa-Blanch, J. Arriaga, E. Silvestre, and P.St.J. Russell, “Soliton effects in photonic crystal fibres at 850 nm,” Electron. Lett. 36, 53–55 (2000).
[Crossref]

Wang, X.H.

Zoboli, M.

A. Cucinotta, S. Selleri, L. Vincetti, and M. Zoboli, “Holey fiber analysis through the finite element method,” IEEE Photon. Technol. Lett. 14, 1530–1532 (2002).
[Crossref]

S. Selleri and M. Zoboli, “An improved finite element method formulation for the analysis of nonlinear anisotropic dielectric waveguides,” IEEE Trans. Micorwave Theory Tech. 43, 887–892 (1995).
[Crossref]

M. Zoboli, F.Di Pasquale, and S. Selleri, “Full-vectorial and scalar solutions of nonlinear optical fibers,” Opt. Comuun. 97, 11–15 (1993).
[Crossref]

Electron. Lett. (5)

J.C. Knight, T.A. Birks, R.F. Cregan, P.St.J. Russell, and J.-P. de Sandro, “Large mode area photonic crystal fiber,” Electron. Lett. 34, 1347–1348 (1998).
[Crossref]

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

A.W. Snyder, Y. Chen, L. Poladian, and D.J. Mitchell, “Fundamental mode of highly nonlinear fibers,” Electron. Lett. 26, 643–644 (1990).
[Crossref]

R.A. Sammut and C. Pask, “Variational approach to nonlinear waveguides-gaussian approximations,” Electron. Lett. 26, 1131–1132 (1990).
[Crossref]

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Figures (7)
Fig. 1.
Fig. 1. Curvilinear high-order hybrid edge/nodal element.

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Fig. 2.
Fig. 2. Group velocity dispersion of circular-core optical fiber with core nonlinearlity.

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Fig. 3.
Fig. 3. Holey fiber.

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Fig. 4.
Fig. 4. Chromatic dispersion characteristics of nonlinear holey fibers with d/Λ=0.9 for different hole pitches of (a) Λ=1.0 µm, (b) Λ=1.5 µm, (c) Λ=2.0 µm, (d) Λ=2.5 µm.

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Fig. 5.
Fig. 5. Effective core areas of nonlinear holey fibers with Λ=1.5 µm and d/Λ=0.9.

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Fig. 6.
Fig. 6. Chromatic dispersion characteristics of nonlinear holey fibers with Λ=1.5 µm for different hole pitches of (a) d/Λ=0.5, (b) d/Λ=0.6, (c) d/Λ=0.7, (d) d/Λ=0.8.

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Fig. 7.
Fig. 7. Zero-dispersion wavelength of nonlinear holey fibers as a function of (a) hole pitch Λ and (b) of ratio of diameter to hole pitch d/Λ.

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Equations (23)

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∇ × ( ∇ × E ) − k 0 2 n 2 E = 0
E ( x , y , z ) = e ( x , y ) exp ⁡ ( − j βz )
n = n ( x , y ; ∣ e ∣ 2 ) .
E = ( i x e x + i y e y + i z e z ) exp ⁡ ( − j βz )
= ( i x { U } T + i y { V } T ) { e t } e exp ⁡ ( − j βz ) + i z j β { N } T { e z } e exp ⁡ ( − j βz )
[ K ( e ) ] { e } − β 2 [ M ( e ) ] { e } = { 0 }
{ e } = [ { e t } { e z } ]
[ K ( e ) ] = [ [ K tt ( e ) ] [ 0 ] [ 0 ] [ 0 ] ]
[ K tt ( e ) ] = ∑ e ∬ e [ − ∂ { U } ∂ y ∂ { U } T ∂ y + ∂ { U } ∂ y ∂ { V } T ∂ x + ∂ { V } ∂ x ∂ { V } T ∂ y
− ∂ { V } ∂ x ∂ { V } T ∂ x + k 0 2 n 2 { U } { U } T + k 0 2 n 2 { V } { V } T ]
[ M ( e ) ] = [ [ M tt ] [ M tz ] [ M zt ] [ M zz ( e ) ] ]
[ M tt ] = ∑ e ∬ e [ { U } { U } T + { V } { V } T ] dx dy
[ M tz ] = [ M zt ]
= ∑ e ∬ e [ { U } ∂ { N } T ∂ x + { V } ∂ { N } T ∂ y ] dx dy
[ M zz ( e ) ] = ∑ e ∬ e [ ∂ { N } ∂ x ∂ { N } T ∂ x + ∂ { N } ∂ y ∂ { N } T ∂ y − k 0 2 n 2 { N } { N } T ] dx dy
P = 1 2 ∬ ( E × H * ) · i z dx dy
= β 2 k 0 Z 0 ( { e t } T [ M tt ] { e t } + { e t } T [ M tz ] { e z } )
{ e } = { e ′ } P P ′
P ′ = β 2 k 0 Z 0 ( { e ′ t } T [ M tt ] { e ' t } + { e ′ t } T [ M tz ] { e ′ z } )
g ( V ) = V d 2 ( V b ) d V 2
n 2 = n co 2 + n co 2 n 2 Z 0 ∣ e ∣ 2 .
n 2 = n L 2 + n L 2 n 2 Z 0 ∣ e ∣ 2
A eff = ( ∬ ∣ E ∣ 2 dx dy ) 2 ∬ ∣ E ∣ 4 dx dy

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