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Empirical relations for simple design of photonic crystal fibers

Kunimasa Saitoh and Masanori Koshiba

Open Access Open Access

Abstract

In order to simply design a photonic crystal fiber (PCF), we provide numerically based empirical relations for V parameter and W parameter of PCFs only dependent on the two structural parameters — the air hole diameter and the hole pitch. We demonstrate the accuracy of these expressions by comparing the proposed empirical relations with the results of full-vector finite element method. Through the empirical relations we can easily evaluate the fundamental properties of PCFs without the need for numerical computations.

©2005 Optical Society of America

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Figures (6)
Fig. 1.
Fig. 1. Index-guiding photonic crystal fiber.

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Fig. 2.
Fig. 2. Effective V parameter as a function of λ/Λ.

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Fig. 3.
Fig. 3. Effective cladding index as a function of λ/Λ.

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Fig. 4.
Fig. 4. Effective W parameter as a function of λ/Λ.

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Fig. 5.
Fig. 5. Effective index of the fundamental mode neff as a function of λ/Λ.

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Fig. 6.
Fig. 6. Chromatic dispersion as a function of wavelength for (a) Λ=2.0 µm, (b) Λ=2.5 µm, and (c) Λ=3.0 µm. Solid curves, results of empirical relations; dashed curves, results of vector FEM.

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Tables (2)

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Table 1. Fitting coefficients in Eq. (6).

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Table 2. Fitting coefficients in Eq. (8).

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Equations (9)

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V = 2 π λ a eff n co 2 − n FSM 2 = U 2 + W 2
U = 2 π λ a eff n co 2 − n eff 2
W = 2 π λ a eff n eff 2 − n FSM 2
V eff = 2 π λ Λ n eff 2 − n FSM 2
V ( λ Λ , d Λ ) = A 1 + A 2 1 + A 3 exp ( A 4 λ ⁄ Λ )
A i = a i 0 + a i 1 ( d Λ ) b i 1 + a i 2 ( d Λ ) b i 2 + a i 3 ( d Λ ) b i 3
W ( λ Λ , d Λ ) = B 1 + B 2 1 + B 3 exp ( B 4 λ ⁄ Λ )
B i = c i 0 + c i 1 ( d Λ ) d i 1 + c i 2 ( d Λ ) d i 2 + c i 3 ( d Λ ) d i 3
D = − λ c d 2 n eff d λ 2 + D m

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