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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References

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    [CrossRef]
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ECOC 2002 (1)

T. Niemi, H. Ludvigsen, F. Scholder, M. Legré, M. Wegmuller, N. Gisin, J. R. Jensen, A. Petersson, and P. M. W. Skovgaard, �??Polarization properties of single-moded, large-mode area photonic crystal fibers,�?? in Proc. European Conference on Optical Communication 2002, paper M.S1.09.

Electron. Lett. (1)

J. C. Knight, T. A. Birks, R. F. Cregan, P. St. J. Russell, and J. �??P. de Sandro, �??Large mode area photonic crystal fiber,�?? Electron. Lett. 34, 1347-1348 (1998).
[CrossRef]

IEEE J. Quantum Electron. (1)

Se-Heon Kim and Yong-Hee Lee, �??Symmetry Relations of Two-Dimensional Photonic Crystal Cavity Modes,�?? IEEE J. Quantum Electron. 39, 1081-1086 (2003).
[CrossRef]

IEEE Photon. Technol. Lett. (3)

J. C. Knight, J. Arriaga, T. A. Birks, A. Ortigosa-Blanch, W. J. Wadsworth, and P. St. J. Russell, �??Anomalous dispersion in photonic crystal fiber,�?? IEEE Photon. Technol. Lett. 12, 807-809 (2000).
[CrossRef]

Theis P. Hansen, Jes Broeng, Stig E. B. Libori, Erik Knudsen, Anders Bjarklev, Jacob Riis Jensen, and Harald Simonsen, �??Highly birefringent index-guiding photonic crystal fibers,�?? IEEE Photon. Technol. Lett. 13, 588-590 (2001).
[CrossRef]

Masanori Koshiba, and Kunimasa Saitoh, �??Numerical verification of degeneracy in hexagonal photonic crystal fibers,�?? IEEE Photon. Technol. Lett. 13, 1313-1315 (2001).
[CrossRef]

J. Lightwave Technol. (1)

J. Opt. Soc. Korea (1)

OFC 2001 (1)

S. B. Libori, J. Broeng, E. Knudsen, A. Bjarklev, and H. R. Simonsen, �??High-birefringent photonic crystal fiber,�?? in Proc. Optical Fiber Communication Conference 2001, Vol. 54 of OSA Proceedings Series (Optical Society of America, Washington, D.C., 1900), pp. TuM2-1 -TuM2-3.

Opt. Express (1)

Opt. Lett. (3)

Other (1)

A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman & Hall, New York, 1983), Chap. 18.

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Figures (6)

Fig. 1.
Fig. 1.

Photonic crystal fiber structure.

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.

Fig. 3.
Fig. 3.

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

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.

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.

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.

Tables (2)

Tables Icon

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

Tables Icon

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

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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