Abstract

The wavelength dependence and the structural dependence of leakage loss and group velocity dispersion (GVD) in air-core photonic bandgap fibers (PBGFs) are numerically investigated by using a full-vector finite element method. It is shown that at least seventeen rings of arrays of air holes are required in the cladding region to reduce the leakage losses to a level of 0.1 dB/km in 1.55-µm wavelength range even if using large air holes of the diameter to pitch ratio of 0.9 and that the leakage losses in air-core PBGFs decrease drastically with increasing the hole diameter to pitch ratio. Moreover, it is shown that the waveguide GVD and dispersion slope of air-core PBGFs are much larger than those of conventional silica fibers and that the shape of air-core region greatly affects the leakage losses and the dispersion properties.

© 2003 Optical Society of America

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Appl. Opt.

European Conf. Opt. Commun. 2001

J.A. Weat, N. Venkataraman, C.M. Smith, and M.T. Gallagher, �??Photonic crystal fibers,�?? Proc. European Conf. Opt. Commun., Th.A.2.2 (2001).

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]

K. Saitoh and M. Koshiba, �??Confinement losses in air-guiding photonic bandgap fibers,�?? IEEE Photon. Technol. Lett. 15, 236-238 (2003).
[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.

Opt. Express

S.G. Johnson, M. Ibanescu, M. Skorobogatiy, O. Weisberg, T.D. Engeness, M. Soljacic, S.A. Jacobs, J.D. Joannopoulos, and Y. Fink, �??Low-loss asymptotically single-mode propagation in large-core OmniGuide fibers,�?? Opt. Express 9, 748-779 (2001), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-9-13-748"> http://www.opticsexpress.org/abstract.cfm?URI=OPEX-9-13-748</a>
[CrossRef] [PubMed]

M. Skorobogatiy, S.A. Jacobs, S.G. Johnson, and Y. Fink, �??Geometric variations in high index-contrast waveguides, coupled mode theory in curvilinear coordinates,�?? Opt. Express 10, 1227-1243 (2002), <a href= " http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-21-1227">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-21-1227</a>
[CrossRef] [PubMed]

B.T. Kuhlmey, R.C. McPhedran, C.M. de Sterke, P.A. Robinson, G. Renversez, and D. Maystre, �??Microstructured optical fibers: where�??s the edge?,�?? Opt. Express 10, 1285-1290 (2002),<a href=" http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-22-1285"> http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-22-1285</a>
[CrossRef] [PubMed]

D. Ferrarini, L. Vincetti, M. Zoboli, A. Cucinotta, and S. Selleri, �??Leakage properties of photonic crystal fibers,�?? Opt. Express 10, 1314-1319 (2002), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-23-1314">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-23-1314</a>.
[CrossRef] [PubMed]

N.A. Issa, A. Argyros, M.A. van Eijkelenborg, and J. Zagari, �??Identifying hollow waveguide guidance in air-cored microstructured optical fibers,�?? Opt. Express 9, 996-1001 (2003),<a href=" http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-9-996"> http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-9-996</a>
[CrossRef]

K. Saitoh, M. Koshiba, T. Hasegawa, and E. Sasaoka, �??Chromatic dispersion control in photonic crystal fibers: application to ultra-flattened dispersion,�?? Opt. Express 11, 843-852 (2003),<a href=" http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-8-843"> http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-8-843</a>
[CrossRef] [PubMed]

T.D. Engeness, M. Ibanescu, S.G. Johnson, O. Weisberg, M. Skorobogatiy, S. Jacobs, and Y. Fink, �??Dispersion tailoring and compensation by modal interactions in OmniGuide fibers,�?? Opt. Express 11, 1175-1196 (2003), <a href=" http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-10-1175">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-10-1175</a>
[CrossRef] [PubMed]

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.

Phys. Rev. E

S.G. Johnson, M. Ibanescu, M.A. Skorobogatiy, O. Weisberg, J.D. Joannopoulos, and Y. Fink, �??Perturbation theory for Maxwell�??s equations with shifting material boundaries,�?? Phys. Rev. E 65, 066611 (2002)
[CrossRef]

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, �??Single-mode photonic band gap guidance of light in air,�?? Science 285, 1537-1539 (1999).
[CrossRef] [PubMed]

F. Benabid, J.C. Knight, G. Antonopoulos, and P.St.J. Russell, �??Stimulated Raman scattering in hydrogen-filled hollow-core photonic crystal fiber,�?? Science 298, 399-402 (2002).
[CrossRef] [PubMed]

D.G. Ouzouno, F.R. Ahmad, D. Müller, N. Venkataraman, M.T. Gallagher, M.G. Thomas, J. Silcox, K.W. Koch, A.L. Gaeta, �??Generation of megawatt optical solitons in hollow-core photonic bang-gap fibers,�?? Science 301, 1702-1704 (2003).
[CrossRef]

Other

G. Agrawal, Nonlinear Fiber Optics, Academic Press (San Diego, CA), 2dn Edition (1995).

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Figures (14)

Fig. 1.
Fig. 1.

Photonic crystal fiber with finite cross section.

Fig.2.
Fig.2.

Air-core PBGF with ten rings of arrays of air holes.

Fig. 3.
Fig. 3.

Modal dispersion curve as a function of normalized wavelength for the air-core PBGF with ten rings of air holes in Fig. 2, where d/Λ=0.9.

Fig. 4.
Fig. 4.

Intensity profile of horizontally polarized fundamental mode in an air-core PBGF with d/Λ=0.9 and Λ=2.32 µm at λ=1.55 µm, where |Ex |2 is expressed in the intensity contours spaced by 1 dB.

Fig. 5.
Fig. 5.

Leakage loss as a function of wavelength for an air-core PBGF with a finite number of air holes. The hole pitch Λ=2.32 µm and d/Λ=0.9.

Fig. 6.
Fig. 6.

Leakage loss as a function of the number of rings. The hole pitch Λ=2.32 µm, d/Λ=0.9, and λ=1.55 µm.

Fig. 7.
Fig. 7.

Waveguide group velocity dispersion of an air-core PBGF with a finite number of air holes. The hole pitch Λ=2.32 µm and d/Λ=0.9.

Fig. 8.
Fig. 8.

PBG boundaries and modal dispersion curves of the fundamental modes for two values of d/Λ=0.9 and d/Λ=0.95 as a function of normalized wavelength.

Fig. 9.
Fig. 9.

Normalized leakage loss as a function of the normalized wavelength in an air-core PBGF with ten rings of arrays of air holes. The hole diameter to pitch ratio d/Λ is taken as a parameter.

Fig. 10.
Fig. 10.

Normalized waveguide GVD for the fundamental mode of the air-core PBGF with ten rings of air holes in Fig. 2, where the hole diameter to pitch ratio d/Λ is taken as a parameter.

Fig. 11.
Fig. 11.

Schematics of air-core PBGF cross sections for (a) type-1, (b) type-2, and (c) type-3 PBGFs.

Fig. 12.
Fig. 12.

Intensity profiles of horizontally polarized fundamental modes for air-core PBGFs in Fig. 11, where d/Λ=0.9, λ/Λ=0.67, and |Ex |2 is expressed in the intensity contours spaced by 1 dB.

Fig. 13.
Fig. 13.

(a) Modal dispersion curves and (b) normalized waveguide GVD as a function of normalized wavelength for the three types of air-core PBGFs as shown in Fig. 11, where d/Λ=0.9 and the number of air-hole rings is ten.

Fig. 14.
Fig. 14.

(a) Normalized leakage loss and (b) normalized effective mode area as a function of normalized wavelength for the three types of air-core PBGFs as shown in Fig. 11, where d/Λ=0.9 and the number of air-hole rings is ten.

Equations (7)

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× ( [ s ] 1 × E ) k 0 2 n 2 [ s ] E = 0
E ( x , y , z ) = e ( x , y ) exp ( γ z )
γ = α + j β
[ K ] { E } = γ 2 [ M ] { E }
L c = 8.686 α
D w = λ c d 2 n eff d λ 2
A eff = ( E 2 dx dy ) 2 E 4 dx dy .

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