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Chromatic dispersion control in photonic crystal fibers: application to ultra-flattened dispersion

K. Saitoh, M. Koshiba, T. Hasegawa, and E. Sasaoka

Open Access Open Access

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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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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