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Leakage loss and group velocity dispersion in air-core photonic bandgap fibers

Kunimasa Saitoh and Masanori Koshiba

Open Access Open Access

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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Figures (14)
Fig. 1.
Fig. 1. Photonic crystal fiber with finite cross section.

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Fig.2.
Fig.2. Air-core PBGF with ten rings of arrays of air holes.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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Fig. 11.
Fig. 11. Schematics of air-core PBGF cross sections for (a) type-1, (b) type-2, and (c) type-3 PBGFs.

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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.

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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.

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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.

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Equations (7)

Equations on this page are rendered with MathJax. Learn more.

∇ × ( [ 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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