Abstract

In order to control the dispersion and the dispersion slope of index-guiding photonic crystal fibers (PCFs), a new controlling technique of chromatic dispersion in PCF is reported. Moreover, our technique is applied to design PCF with both ultra-low dispersion and ultra-flattened dispersion in a wide wavelength range. A full-vector finite element method with anisotropic perfectly matched layers is used to analyze the dispersion properties and the confinement losses in a PCF with a finite number of air holes. It is shown from numerical results that it is possible to design a fourring PCF with flattened dispersion of 0±0.5 ps/(km·nm) from a wavelength of 1.19 µm to 1.69 µm and a five-ring PCF with flattened dispersion of 0 ±0.4 ps/(km·nm) from a wavelength 1.23 µm to 1.72 µm.

©2003 Optical Society of America

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References

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  1. J. Broeng, D. Mogilevstev, S.E. Barkou, and A. Bjarklev, “Photonic crystal fibers: A new class of optical waveguides,” Opt. Fiber Technol. 5, 305–330, (1999).
    [Crossref]
  2. T.A. Birks, J.C. Knight, B.J. Mangan, and P.St.J. Russell, “Photonic crystal fibers: An endless variety,” IEICE Trans. Electron. E84-C, 585–592, (2001).
  3. 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]
  4. 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]
  5. J.C. Knight, J. Broeng, T.A. Birks, and P.St.J. Russell, “Photonic band gap guidance in optical fiber,” Science 282, 1476–1478, (1998).
    [Crossref] [PubMed]
  6. R.F. Cregan, B.J. Mangan, J.C. Knight, T.A. Birks, P.St.J. Russell, P.J. Roberts, and D.C. Allan, “Singlemode photonic band gap guidance of light in air,” Science 285, 1537–1539, (1999).
    [Crossref] [PubMed]
  7. M.J. Gander, R. McBride, J.D.C. Jones, D. Mogilevtsev, T.A. Birks, J.C. Knight, and P.St.J. Russell, “Experimantal measurement of group velocity dispersion in photonic crystal fibre,” Electron. Lett. 35, 63–64, (1999).
    [Crossref]
  8. J.C. Knight, J. Arriaga, T.A. Birks, A. Ortigosa-Blanch, W.J. Wadsworth, and P.St.J. Russell, “Anomalous dispersion in photonic crystal fiber,” IEEE Photon. Technol. Lett. 12, 807–809, (2000).
    [Crossref]
  9. A. Ferrando, E. Silvestre, J.J. Miret, and P. Andrés, “Nearly zero ultraflattened dispersion in photonic crystal fibers,” Opt. Lett. 25, 790–792, (2000).
    [Crossref]
  10. A. Ferrando, E. Silvestre, P. Andrés, J.J. Miret, and M.V. Andrés, “Desinging the properties of dispersionflattened photonic crystal fibers,” Opt. Express 9, 687–697, (2001), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-9-13-687
    [Crossref] [PubMed]
  11. W.H. Reeves, J.C. Knight, P.St.J. Russell, and P.J. Roberts, “Demonstration of ultra-flattened dispersion in photonic crystal fibers,” Opt. Express,  10, 609–613 (2002), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-14-609
    [Crossref] [PubMed]
  12. T. Hasegawa, E. Sasaoka, M. Onishi, M. Nishimura, Y. Tsuji, and M. Koshiba, “Hole-assisted lightguide fiber - A practical derivative of photonic crystal fiber,” Proc. Mater. Res. Soc. Spring Meeting L4.2. (2002).
  13. K. Saitoh and M. Koshiba, “Full-vectorial imaginary-distance beam propagation method based on finite element scheme: Application to photonic crystal fibers,” IEEE J. Quantum Electron. 38, 927–933, (2002).
    [Crossref]
  14. 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]
  15. M. Koshiba and K. Saitoh, “Numerical verification of degeneracy in hexagonal photonic crystal fibers,” IEEE Photon. Technol. Lett. 13, 1313–1315, (2001).
    [Crossref]
  16. J.W.H. Liu, “The multifrontal method for sparse matrix solutions: theory and practice,” SIAM Rev. 34, 82–109,(1992).
    [Crossref]
  17. T.P. White, B.T. Kuhlmey, R.C. McPhedran, D. Maystre, G. Renversez, C. Martijn de Sterke, and L.C. Botten, “Multipole method for microstructured optical fibers. I. Formulation,” J. Opt. Soc. Am. B 19, 2322–2330, (2002).
    [Crossref]

2002 (3)

2001 (3)

T.A. Birks, J.C. Knight, B.J. Mangan, and P.St.J. Russell, “Photonic crystal fibers: An endless variety,” IEICE Trans. Electron. E84-C, 585–592, (2001).

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

A. Ferrando, E. Silvestre, P. Andrés, J.J. Miret, and M.V. Andrés, “Desinging the properties of dispersionflattened photonic crystal fibers,” Opt. Express 9, 687–697, (2001), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-9-13-687
[Crossref] [PubMed]

2000 (3)

1999 (3)

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

J. Broeng, D. Mogilevstev, S.E. Barkou, and A. Bjarklev, “Photonic crystal fibers: A new class of optical waveguides,” Opt. Fiber Technol. 5, 305–330, (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, “Singlemode photonic band gap guidance of light in air,” Science 285, 1537–1539, (1999).
[Crossref] [PubMed]

1998 (1)

J.C. Knight, J. Broeng, T.A. Birks, and P.St.J. Russell, “Photonic band gap guidance in optical fiber,” Science 282, 1476–1478, (1998).
[Crossref] [PubMed]

1997 (1)

1996 (1)

1992 (1)

J.W.H. Liu, “The multifrontal method for sparse matrix solutions: theory and practice,” SIAM Rev. 34, 82–109,(1992).
[Crossref]

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, “Singlemode photonic band gap guidance of light in air,” Science 285, 1537–1539, (1999).
[Crossref] [PubMed]

Andrés, M.V.

Andrés, P.

Arriaga, J.

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

Atkin, D.M.

Barkou, S.E.

J. Broeng, D. Mogilevstev, S.E. Barkou, and A. Bjarklev, “Photonic crystal fibers: A new class of optical waveguides,” Opt. Fiber Technol. 5, 305–330, (1999).
[Crossref]

Birks, T.A.

T.A. Birks, J.C. Knight, B.J. Mangan, and P.St.J. Russell, “Photonic crystal fibers: An endless variety,” IEICE Trans. Electron. E84-C, 585–592, (2001).

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

M.J. Gander, R. McBride, J.D.C. Jones, D. Mogilevtsev, T.A. Birks, J.C. Knight, and P.St.J. Russell, “Experimantal measurement of group velocity dispersion in photonic crystal fibre,” Electron. Lett. 35, 63–64, (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, “Singlemode photonic band gap guidance of light in air,” Science 285, 1537–1539, (1999).
[Crossref] [PubMed]

J.C. Knight, J. Broeng, T.A. Birks, and P.St.J. Russell, “Photonic band gap guidance in optical fiber,” Science 282, 1476–1478, (1998).
[Crossref] [PubMed]

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]

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]

Bjarklev, A.

J. Broeng, D. Mogilevstev, S.E. Barkou, and A. Bjarklev, “Photonic crystal fibers: A new class of optical waveguides,” Opt. Fiber Technol. 5, 305–330, (1999).
[Crossref]

Botten, L.C.

Broeng, J.

J. Broeng, D. Mogilevstev, S.E. Barkou, and A. Bjarklev, “Photonic crystal fibers: A new class of optical waveguides,” Opt. Fiber Technol. 5, 305–330, (1999).
[Crossref]

J.C. Knight, J. Broeng, T.A. Birks, and P.St.J. Russell, “Photonic band gap guidance in optical fiber,” Science 282, 1476–1478, (1998).
[Crossref] [PubMed]

Cregan, R.F.

R.F. Cregan, B.J. Mangan, J.C. Knight, T.A. Birks, P.St.J. Russell, P.J. Roberts, and D.C. Allan, “Singlemode photonic band gap guidance of light in air,” Science 285, 1537–1539, (1999).
[Crossref] [PubMed]

de Sterke, C. Martijn

Ferrando, A.

Gander, M.J.

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

Hasegawa, T.

T. Hasegawa, E. Sasaoka, M. Onishi, M. Nishimura, Y. Tsuji, and M. Koshiba, “Hole-assisted lightguide fiber - A practical derivative of photonic crystal fiber,” Proc. Mater. Res. Soc. Spring Meeting L4.2. (2002).

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, “Experimantal measurement of group velocity dispersion in photonic crystal fibre,” Electron. Lett. 35, 63–64, (1999).
[Crossref]

Knight, J.C.

W.H. Reeves, J.C. Knight, P.St.J. Russell, and P.J. Roberts, “Demonstration of ultra-flattened dispersion in photonic crystal fibers,” Opt. Express,  10, 609–613 (2002), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-14-609
[Crossref] [PubMed]

T.A. Birks, J.C. Knight, B.J. Mangan, and P.St.J. Russell, “Photonic crystal fibers: An endless variety,” IEICE Trans. Electron. E84-C, 585–592, (2001).

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

M.J. Gander, R. McBride, J.D.C. Jones, D. Mogilevtsev, T.A. Birks, J.C. Knight, and P.St.J. Russell, “Experimantal measurement of group velocity dispersion in photonic crystal fibre,” Electron. Lett. 35, 63–64, (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, “Singlemode photonic band gap guidance of light in air,” Science 285, 1537–1539, (1999).
[Crossref] [PubMed]

J.C. Knight, J. Broeng, T.A. Birks, and P.St.J. Russell, “Photonic band gap guidance in optical fiber,” Science 282, 1476–1478, (1998).
[Crossref] [PubMed]

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]

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]

Koshiba, M.

K. Saitoh and M. Koshiba, “Full-vectorial imaginary-distance beam propagation method based on 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]

T. Hasegawa, E. Sasaoka, M. Onishi, M. Nishimura, Y. Tsuji, and M. Koshiba, “Hole-assisted lightguide fiber - A practical derivative of photonic crystal fiber,” Proc. Mater. Res. Soc. Spring Meeting L4.2. (2002).

Kuhlmey, B.T.

Liu, J.W.H.

J.W.H. Liu, “The multifrontal method for sparse matrix solutions: theory and practice,” SIAM Rev. 34, 82–109,(1992).
[Crossref]

Mangan, B.J.

T.A. Birks, J.C. Knight, B.J. Mangan, and P.St.J. Russell, “Photonic crystal fibers: An endless variety,” IEICE Trans. Electron. E84-C, 585–592, (2001).

R.F. Cregan, B.J. Mangan, J.C. Knight, T.A. Birks, P.St.J. Russell, P.J. Roberts, and D.C. Allan, “Singlemode photonic band gap guidance of light in air,” Science 285, 1537–1539, (1999).
[Crossref] [PubMed]

Maystre, D.

McBride, R.

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

McPhedran, R.C.

Miret, J.J.

Mogilevstev, D.

J. Broeng, D. Mogilevstev, S.E. Barkou, and A. Bjarklev, “Photonic crystal fibers: A new class of optical waveguides,” Opt. Fiber Technol. 5, 305–330, (1999).
[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, “Experimantal measurement of group velocity dispersion in photonic crystal fibre,” Electron. Lett. 35, 63–64, (1999).
[Crossref]

Nishimura, M.

T. Hasegawa, E. Sasaoka, M. Onishi, M. Nishimura, Y. Tsuji, and M. Koshiba, “Hole-assisted lightguide fiber - A practical derivative of photonic crystal fiber,” Proc. Mater. Res. Soc. Spring Meeting L4.2. (2002).

Onishi, M.

T. Hasegawa, E. Sasaoka, M. Onishi, M. Nishimura, Y. Tsuji, and M. Koshiba, “Hole-assisted lightguide fiber - A practical derivative of photonic crystal fiber,” Proc. Mater. Res. Soc. Spring Meeting L4.2. (2002).

Ortigosa-Blanch, A.

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

Reeves, W.H.

Renversez, G.

Roberts, P.J.

W.H. Reeves, J.C. Knight, P.St.J. Russell, and P.J. Roberts, “Demonstration of ultra-flattened dispersion in photonic crystal fibers,” Opt. Express,  10, 609–613 (2002), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-14-609
[Crossref] [PubMed]

R.F. Cregan, B.J. Mangan, J.C. Knight, T.A. Birks, P.St.J. Russell, P.J. Roberts, and D.C. Allan, “Singlemode photonic band gap guidance of light in air,” Science 285, 1537–1539, (1999).
[Crossref] [PubMed]

Russell, P.St.J.

W.H. Reeves, J.C. Knight, P.St.J. Russell, and P.J. Roberts, “Demonstration of ultra-flattened dispersion in photonic crystal fibers,” Opt. Express,  10, 609–613 (2002), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-14-609
[Crossref] [PubMed]

T.A. Birks, J.C. Knight, B.J. Mangan, and P.St.J. Russell, “Photonic crystal fibers: An endless variety,” IEICE Trans. Electron. E84-C, 585–592, (2001).

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

M.J. Gander, R. McBride, J.D.C. Jones, D. Mogilevtsev, T.A. Birks, J.C. Knight, and P.St.J. Russell, “Experimantal measurement of group velocity dispersion in photonic crystal fibre,” Electron. Lett. 35, 63–64, (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, “Singlemode photonic band gap guidance of light in air,” Science 285, 1537–1539, (1999).
[Crossref] [PubMed]

J.C. Knight, J. Broeng, T.A. Birks, and P.St.J. Russell, “Photonic band gap guidance in optical fiber,” Science 282, 1476–1478, (1998).
[Crossref] [PubMed]

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]

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]

Saitoh, K.

K. Saitoh and M. Koshiba, “Full-vectorial imaginary-distance beam propagation method based on 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]

Sasaoka, E.

T. Hasegawa, E. Sasaoka, M. Onishi, M. Nishimura, Y. Tsuji, and M. Koshiba, “Hole-assisted lightguide fiber - A practical derivative of photonic crystal fiber,” Proc. Mater. Res. Soc. Spring Meeting L4.2. (2002).

Silvestre, E.

Tsuji, Y.

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]

T. Hasegawa, E. Sasaoka, M. Onishi, M. Nishimura, Y. Tsuji, and M. Koshiba, “Hole-assisted lightguide fiber - A practical derivative of photonic crystal fiber,” Proc. Mater. Res. Soc. Spring Meeting L4.2. (2002).

Wadsworth, W.J.

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

White, T.P.

Electron. Lett. (1)

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

IEEE J. Quantum Electron. (1)

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

IEEE Photon. Technol. Lett. (2)

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

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

IEICE Trans. Electron. (1)

T.A. Birks, J.C. Knight, B.J. Mangan, and P.St.J. Russell, “Photonic crystal fibers: An endless variety,” IEICE Trans. Electron. E84-C, 585–592, (2001).

J. Lightwave Technol. (1)

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

Opt. Express (2)

Opt. Fiber Technol. (1)

J. Broeng, D. Mogilevstev, S.E. Barkou, and A. Bjarklev, “Photonic crystal fibers: A new class of optical waveguides,” Opt. Fiber Technol. 5, 305–330, (1999).
[Crossref]

Opt. Lett. (3)

Science (2)

J.C. Knight, J. Broeng, T.A. Birks, and P.St.J. Russell, “Photonic band gap guidance in optical fiber,” Science 282, 1476–1478, (1998).
[Crossref] [PubMed]

R.F. Cregan, B.J. Mangan, J.C. Knight, T.A. Birks, P.St.J. Russell, P.J. Roberts, and D.C. Allan, “Singlemode photonic band gap guidance of light in air,” Science 285, 1537–1539, (1999).
[Crossref] [PubMed]

SIAM Rev. (1)

J.W.H. Liu, “The multifrontal method for sparse matrix solutions: theory and practice,” SIAM Rev. 34, 82–109,(1992).
[Crossref]

Other (1)

T. Hasegawa, E. Sasaoka, M. Onishi, M. Nishimura, Y. Tsuji, and M. Koshiba, “Hole-assisted lightguide fiber - A practical derivative of photonic crystal fiber,” Proc. Mater. Res. Soc. Spring Meeting L4.2. (2002).

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Figures (7)

Fig. 1.
Fig. 1. Transverse cross section of photonic crystal fiber surrounded by PMLs.

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Fig. 2.
Fig. 2. Cross section of proposed photonic crystal fiber. Λ is the hole-to-hole spacing and di (i=1 ~ n) is the hole diameter of ith air-hole ring.

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Fig. 3.
Fig. 3. Index-guiding PCFs with four rings of air holes. The air holes are shown as colored circles. The hole-to-hole spacing Λ=2.0 µm and the each air-hole diameter is (a) d 1=d 2=d 3=d 4=0.5 µm, (b) d 1=0.5 µm, d 2=d 3=d 4=0.6 µm, (c) d 1=0.5 µm, d 2=0.6 µm, d 3=d 4=0.7 µm, (d) d 1=0.5 µm, d 2=0.6 µm, d 3=0.7 µm, d 4=1.8 µm.

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Fig. 4.
Fig. 4. Chromatic dispersion curves as a function of wavelength for PCFs with four rings of air holes in Fig. 3. The hole-to-hole spacing Λ=2.0 µm and the each air-hole diameter is (a) d 1=d 2=d 3=d 4=0.5 µm, (b) d 1=0.5 µm, d 2=d 3=d 4=0.6 µm, (c) d 1=0.5 µm, d 2=0.6 µm, d 3=d 4=0.7 µm, (d) d 1=0.5 µm, d 2=0.6 µm, d 3=0.7 µm, d 4=1.8 µm.

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Fig. 5.
Fig. 5. Ultra-flattened dispersion PCFs with (a) four air-hole rings and (b) five air-hole rings. The hole-to-hole spacing and the air-hole diameters are (a) Λ=1.56 µm, d 1/Λ=0.32, d 2/Λ=0.45, d 3/Λ=0.67, d 4/Λ=0.95 and (b) Λ=1.58 µm, d 1/Λ=0.31, d 2/Λ=0.45, d 3/Λ=0.55, d 4/Λ=0.63, d 5/Λ=0.95.

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Fig. 6.
Fig. 6. (a) Chromatic dispersion curve, (b) confinement loss, and (c) effective mode area as a function of wavelength for ultra-flattened dispersion PCF with four air-hole rings in Fig. 5(a).

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Fig. 7.
Fig. 7. (a) Chromatic dispersion curve, (b) confinement loss, and (c) effective mode area as a function of wavelength for ultra-flattened dispersion PCF with five air-hole rings in Fig. 5(b).

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Tables (1)

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Table 1. PML parameters.

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Equations (7)

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∇ × ( [ s ] − 1 ∇ × E ) − k 0 2 n 2 [ s ] E = 0
[ s ] = [ s y s x 0 0 0 s x s y 0 0 0 s x s y ]
s i = 1 − j α i ( ρ t i ) 2
[ K ] { E } = k 0 2 n eff 2 [ M ] { E }
D = − λ c d 2 Re [ n eff ] d λ 2
confinement loss = 8.686 Im [ k 0 n eff ]
A eff = ( ∫ ∫ ∣ E 2 ∣ dx dy ) 2 ∫ ∫ ∣ E ∣ 4 dx dy .

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