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Birefringence induced by irregular structure in photonic crystal fiber

In-Kag Hwang, Yong-Jae Lee , and Yong-Hee Lee

Open Access Open Access

Abstract

The unintentional birefringence induced by the irregular structure in photonic crystal fibers is analyzed numerically using the plane wave expansion method. The statistical correlations between the birefringence and the various irregularities are obtained. The birefringence is found to be largely dependent on the fiber design parameters as well as the degree of the irregularity. And the large pitch and the small air hole make the fiber less sensitive to the structural irregularity, which is successfully explained by the simple perturbation theory. The accuracy of our analyses is confirmed by the detailed investigation of computational errors. This study provides the essential information for the characterization and the design of low birefringence photonic crystal fibers.

©2003 Optical Society of America

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Figures (6)
Fig. 1.
Fig. 1. Photonic crystal fiber structure.

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Fig. 2.
Fig. 2. (a) The mode indices for two polarizations versus grid resolution. (b) Numerical birefringence error versus grid resolution at various Λ/λ.

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Fig. 3.
Fig. 3. Numerical birefringence error versus grid resolution at various Λ/λ, calculated with the rectangular supercell.

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Fig. 4.
Fig. 4. Birefringence due to variation of hole diameters. (a) Probability distribution of each hole diameter, d: d 0, original hole diameter; δd, standard deviation of d. (b) Birefringence of 20 PCF samples with δd/d 0=0.2. Two insets are the structures of two PCFs with the largest and the smallest birefringence. (c) Birefringence of PCFs at various degrees of hole diameter variation. The marker and error bar denote the mean and the standard deviation, respectively, of birefringence distribution. The dotted lines are obtained by linear fitting of mean values.

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Fig. 5.
Fig. 5. Birefringence due to variation of hole positions. (a) Probability distribution of offset q in each hole: δq, standard deviation of q. (b) Birefringence of PCFs at various degrees of hole position variation. The marker and error bar denote the mean and the standard deviation, respectively, of birefringence distribution. The dotted lines were obtained by linear fitting of mean values.

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Fig. 6.
Fig. 6. Optical intensity profile as a function of x at y=0, for (a) d/Λ=0.46 and (b) d/Λ=0.36. The dotted vertical lines denote the boundary of air holes. The solid and broken curves are intensity profiles for Λ/λ=2.09 and 10.35, respectively.

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Tables (2)

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Table 1. The fitting coefficients A and B of Eq. (1), obtained from the data in Fig. 4 (c)

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Table 2. The fitting coefficients A and B of Eq. (1), obtained from the data in Fig. 5 (b)

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Equations (5)

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log 10 ( Δ n ) = A · log 10 ( δ d d · 100 ) + B
Δ n = ( δ d d · 100 ) A · 10 B
S = π ( d 2 ) 2
δ S d ≈ π 2 d · δ d = π 2 d 2 · ( δ d d )
δ S q ≈ 2 d · δ q = 2 d Λ · ( δ q Λ )
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