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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Electron. Lett.

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.

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.

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.

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.

J. Opt. Soc. Am. B

Opt. Express

Opt. Fiber Technol.

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.

Proc. Mater. Res. Soc.

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).

Science

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.

J.W.H. Liu, �??The multifrontal method for sparse matrix solutions: theory and practice,�?? SIAM Rev. 34, 82-109,(1992).
[CrossRef]

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Figures (7)

Fig. 1.
Fig. 1.

Transverse cross section of photonic crystal fiber surrounded by PMLs.

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.

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.

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.

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.

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).

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).

Tables (1)

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Table 1. PML parameters.

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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