Abstract

We report on two types of polarization maintaining solid photonic crystal fibers that guide light by a combination of a photonic bandgap and total internal reflection. Group and phase birefringence are studied experimentally and numerically for stress-applying parts made from B-doped and F-doped silica. The stress field originating from Ge-doped cladding rods is shown to interfere with the stress field from the B-doped and F-doped rods. Since the differential expansion coefficients of B-doped and F-doped silica have opposite signs this interference is either destructive or constructive. Consequently, we found that the fiber with F-doped stress applying parts has the highest modal phase birefringence, and polarization cross talk is characterized by an h-parameter below 3⋅10−5 m−1.

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]

2009 (1)

2008 (1)

2006 (3)

2005 (3)

1993 (1)

M. Kyoto, Y. Ohoga, S. Ishikawa, and Y. Ishiguro, “Characterization of fluorine-doped silica glasses,” J. Mater. Sci. 28(10), 2738–2744 (1993).
[CrossRef]

1991 (1)

K. Tsai, K. Kim, and T. Morse, “General solutions for stress-induced polarization in optical fibers,” J. Lightwave Technol. 9(1), 7–17 (1991).
[CrossRef]

1988 (1)

P. K. Bachmann, D. U. Wiechert, and T. P. M. Meeuwsen, “Thermal expansion coefficients of doped and undoped silica prepared by means of PCVD,” J. Mater. Sci. 23(7), 2584–2588 (1988).
[CrossRef]

1987 (1)

1986 (2)

1985 (1)

1984 (1)

P. Chu and R. Sammut, “Analytical method for calculation of stresses and material birefringence in polarization-maintaining optical fiber,” J. Lightwave Technol. 2(5), 650–662 (1984).
[CrossRef]

1983 (2)

R. Stolen, “Calculation of stress birefringence in fibers by an infinitesimal element method,” J. Lightwave Technol. 1(2), 297–301 (1983).
[CrossRef]

S. C. Rashleigh, “Measurement of fiber birefringence by wavelength scanning: effect of dispersion,” Opt. Lett. 8(6), 336–338 (1983).
[CrossRef] [PubMed]

1982 (1)

J. Sakai and T. Kimura, “Birefringence caused by thermal stress in elliptically deformed core optical fibers,” IEEE J. Quantum Electron. 18(11), 1899–1909 (1982).
[CrossRef]

1980 (1)

G. W. Scherer, “Stress-optical effects in optical waveguides,” J. Non-Cryst. Solids 38–39, 201–204 (1980).
[CrossRef]

1979 (1)

S. Takahashi and S. Shibata, “Thermal variation of attenuation for optical fibers,” J. Non-Cryst. Solids 30(3), 359–370 (1979).
[CrossRef]

1978 (1)

Y. Huang, A. Sarkar, and P. Schultz, “Relationship between composition, density and refractive index for germania silica glasses,” J. Non-Cryst. Solids 27(1), 29–37 (1978).
[CrossRef]

1975 (1)

P. McIsaac, “Symmetry-Induced Modal Characteristics of Uniform Waveguides — I: Summary of Results,” IEEE T. Microw. Theory 23(5), 421–429 (1975).
[CrossRef]

Bachmann, P. K.

Bigot, L.

Bird, D. M.

Birks, T. A.

Bouwmans, G.

Broeng, J.

Cerqueira S, A.

Chu, P.

P. Chu and R. Sammut, “Analytical method for calculation of stresses and material birefringence in polarization-maintaining optical fiber,” J. Lightwave Technol. 2(5), 650–662 (1984).
[CrossRef]

Cordeiro, C. M. B.

Douay, M.

Eggleton, B. J.

Fleming, S.

Gan, Z.

R. Guan, F. Zhu, Z. Gan, D. Huang, and S. Liu, “Stress birefringence analysis of polarization maintaining optical fibers,” Opt. Fiber Technol. 11(3), 240–254 (2005).
[CrossRef]

George, A. K.

Goto, R.

Guan, R.

R. Guan, F. Zhu, Z. Gan, D. Huang, and S. Liu, “Stress birefringence analysis of polarization maintaining optical fibers,” Opt. Fiber Technol. 11(3), 240–254 (2005).
[CrossRef]

Hermann, W.

Hermann, W. G.

Himeno, K.

Huang, D.

R. Guan, F. Zhu, Z. Gan, D. Huang, and S. Liu, “Stress birefringence analysis of polarization maintaining optical fibers,” Opt. Fiber Technol. 11(3), 240–254 (2005).
[CrossRef]

Huang, Y.

Y. Huang, A. Sarkar, and P. Schultz, “Relationship between composition, density and refractive index for germania silica glasses,” J. Non-Cryst. Solids 27(1), 29–37 (1978).
[CrossRef]

Ishiguro, Y.

M. Kyoto, Y. Ohoga, S. Ishikawa, and Y. Ishiguro, “Characterization of fluorine-doped silica glasses,” J. Mater. Sci. 28(10), 2738–2744 (1993).
[CrossRef]

Ishikawa, S.

M. Kyoto, Y. Ohoga, S. Ishikawa, and Y. Ishiguro, “Characterization of fluorine-doped silica glasses,” J. Mater. Sci. 28(10), 2738–2744 (1993).
[CrossRef]

Isomäki, A.

Jackson, S. D.

Kim, K.

K. Tsai, K. Kim, and T. Morse, “General solutions for stress-induced polarization in optical fibers,” J. Lightwave Technol. 9(1), 7–17 (1991).
[CrossRef]

Kimura, T.

J. Sakai and T. Kimura, “Birefringence caused by thermal stress in elliptically deformed core optical fibers,” IEEE J. Quantum Electron. 18(11), 1899–1909 (1982).
[CrossRef]

Kitayama, K.-

Knight, J. C.

Kuhlmey, B. T.

Kyoto, M.

M. Kyoto, Y. Ohoga, S. Ishikawa, and Y. Ishiguro, “Characterization of fluorine-doped silica glasses,” J. Mater. Sci. 28(10), 2738–2744 (1993).
[CrossRef]

Liu, S.

R. Guan, F. Zhu, Z. Gan, D. Huang, and S. Liu, “Stress birefringence analysis of polarization maintaining optical fibers,” Opt. Fiber Technol. 11(3), 240–254 (2005).
[CrossRef]

Lopez, F.

Luan, F.

Lyngsø, J. K.

Maruyama, H.

McIsaac, P.

P. McIsaac, “Symmetry-Induced Modal Characteristics of Uniform Waveguides — I: Summary of Results,” IEEE T. Microw. Theory 23(5), 421–429 (1975).
[CrossRef]

Meeuwsen, T. P. M.

P. K. Bachmann, D. U. Wiechert, and T. P. M. Meeuwsen, “Thermal expansion coefficients of doped and undoped silica prepared by means of PCVD,” J. Mater. Sci. 23(7), 2584–2588 (1988).
[CrossRef]

Morse, T.

K. Tsai, K. Kim, and T. Morse, “General solutions for stress-induced polarization in optical fibers,” J. Lightwave Technol. 9(1), 7–17 (1991).
[CrossRef]

Noda, J.

Ohashi, M.

Ohoga, Y.

M. Kyoto, Y. Ohoga, S. Ishikawa, and Y. Ishiguro, “Characterization of fluorine-doped silica glasses,” J. Mater. Sci. 28(10), 2738–2744 (1993).
[CrossRef]

Okhotnikov, O. G.

Olausson, C. B.

Pearce, G. J.

Provino, L.

Quiquempois, Y.

Ramachandran, S.

Rashleigh, S. C.

Sakai, J.

J. Sakai and T. Kimura, “Birefringence caused by thermal stress in elliptically deformed core optical fibers,” IEEE J. Quantum Electron. 18(11), 1899–1909 (1982).
[CrossRef]

Sammut, R.

P. Chu and R. Sammut, “Analytical method for calculation of stresses and material birefringence in polarization-maintaining optical fiber,” J. Lightwave Technol. 2(5), 650–662 (1984).
[CrossRef]

Sarkar, A.

Y. Huang, A. Sarkar, and P. Schultz, “Relationship between composition, density and refractive index for germania silica glasses,” J. Non-Cryst. Solids 27(1), 29–37 (1978).
[CrossRef]

Scherer, G. W.

G. W. Scherer, “Stress-optical effects in optical waveguides,” J. Non-Cryst. Solids 38–39, 201–204 (1980).
[CrossRef]

Schultz, P.

Y. Huang, A. Sarkar, and P. Schultz, “Relationship between composition, density and refractive index for germania silica glasses,” J. Non-Cryst. Solids 27(1), 29–37 (1978).
[CrossRef]

Seikai, S.

Shibata, N.

Shibata, S.

S. Takahashi and S. Shibata, “Thermal variation of attenuation for optical fibers,” J. Non-Cryst. Solids 30(3), 359–370 (1979).
[CrossRef]

Shirakawa, A.

Stolen, R.

R. Stolen, “Calculation of stress birefringence in fibers by an infinitesimal element method,” J. Lightwave Technol. 1(2), 297–301 (1983).
[CrossRef]

Takada, K.

Takahashi, S.

S. Takahashi and S. Shibata, “Thermal variation of attenuation for optical fibers,” J. Non-Cryst. Solids 30(3), 359–370 (1979).
[CrossRef]

Tsai, K.

K. Tsai, K. Kim, and T. Morse, “General solutions for stress-induced polarization in optical fibers,” J. Lightwave Technol. 9(1), 7–17 (1991).
[CrossRef]

Tsubokawa, M.

Ueda, K.

Ulrich, R.

Wang, A.

Wehr, H.

Wiechert, D. U.

Zhu, F.

R. Guan, F. Zhu, Z. Gan, D. Huang, and S. Liu, “Stress birefringence analysis of polarization maintaining optical fibers,” Opt. Fiber Technol. 11(3), 240–254 (2005).
[CrossRef]

Appl. Opt. (3)

IEEE J. Quantum Electron. (1)

J. Sakai and T. Kimura, “Birefringence caused by thermal stress in elliptically deformed core optical fibers,” IEEE J. Quantum Electron. 18(11), 1899–1909 (1982).
[CrossRef]

IEEE T. Microw. Theory (1)

P. McIsaac, “Symmetry-Induced Modal Characteristics of Uniform Waveguides — I: Summary of Results,” IEEE T. Microw. Theory 23(5), 421–429 (1975).
[CrossRef]

J. Lightwave Technol. (4)

R. Stolen, “Calculation of stress birefringence in fibers by an infinitesimal element method,” J. Lightwave Technol. 1(2), 297–301 (1983).
[CrossRef]

P. Chu and R. Sammut, “Analytical method for calculation of stresses and material birefringence in polarization-maintaining optical fiber,” J. Lightwave Technol. 2(5), 650–662 (1984).
[CrossRef]

K. Tsai, K. Kim, and T. Morse, “General solutions for stress-induced polarization in optical fibers,” J. Lightwave Technol. 9(1), 7–17 (1991).
[CrossRef]

S. Ramachandran, “Dispersion-Tailored Few-Mode Fibers: A Versatile Platform for In-Fiber Photonic Devices,” J. Lightwave Technol. 23(11), 3426–3443 (2005).
[CrossRef]

J. Mater. Sci. (2)

P. K. Bachmann, D. U. Wiechert, and T. P. M. Meeuwsen, “Thermal expansion coefficients of doped and undoped silica prepared by means of PCVD,” J. Mater. Sci. 23(7), 2584–2588 (1988).
[CrossRef]

M. Kyoto, Y. Ohoga, S. Ishikawa, and Y. Ishiguro, “Characterization of fluorine-doped silica glasses,” J. Mater. Sci. 28(10), 2738–2744 (1993).
[CrossRef]

J. Non-Cryst. Solids (3)

Y. Huang, A. Sarkar, and P. Schultz, “Relationship between composition, density and refractive index for germania silica glasses,” J. Non-Cryst. Solids 27(1), 29–37 (1978).
[CrossRef]

S. Takahashi and S. Shibata, “Thermal variation of attenuation for optical fibers,” J. Non-Cryst. Solids 30(3), 359–370 (1979).
[CrossRef]

G. W. Scherer, “Stress-optical effects in optical waveguides,” J. Non-Cryst. Solids 38–39, 201–204 (1980).
[CrossRef]

J. Opt. Soc. Am. A (1)

Opt. Express (6)

Opt. Fiber Technol. (1)

R. Guan, F. Zhu, Z. Gan, D. Huang, and S. Liu, “Stress birefringence analysis of polarization maintaining optical fibers,” Opt. Fiber Technol. 11(3), 240–254 (2005).
[CrossRef]

Opt. Lett. (1)

Other (1)

S. Ramachandran, S. Ghalmi, J. Nicholson, M. F. Yan, P. Wisk, E. Monberg, and F. V. Dimarcello, “Demonstration of Anomalous Dispersion in a Solid, Silica-Based Fiber at λ < 1300 nm,” In Optical Fiber Communication Conference and Exposition and The National Fiber Optic Engineers Conference, Technical Digest (CD) p. PDP3 (Optical Society of America, 2006).

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Figures (9)

Fig. 1
Fig. 1

(a) Schematic drawing of the fiber preform. (b) Scanning electron microscope image of the end face of fiber I.

Fig. 2
Fig. 2

(a) Transmission measurement on a 3 m section of fiber I. (b) Transmission measurement together with group velocity dispersion of the 3rd order bandgap.

Fig. 3
Fig. 3

Measured birefringence of fiber I, Solid circles show the measured group birefringence. The open triangles display the group birefringence calculated from the DGD measurement. The open square is the measured modal phase birefringence calculated from the periodic lateral force measurement displayed in the inset. A representation of the fiber and the adopted coordinate system are also shown.

Fig. 4
Fig. 4

As in Fig. 3, but for fiber II.

Fig. 5
Fig. 5

(a) Measured polarization cross talk. The power difference at 1060 nm was caused by the supercontinuum pump. (b) Measured polarization cross talk at 1060 nm over 90 m. Results are given for five different PM aligned splices to a 1 m pigtail

Fig. 6
Fig. 6

(a-c) Contour plots of the calculated mode field intensity distributions at the short wavelength edge, center and long wavelength edge of the 3rd order bandgap. (d) Calculated effective index as function of wavelength.

Fig. 7
Fig. 7

Differential stress field (σxy) in the core region, where white and black regions correspond to positive and negative differential stress, respectively. (a) B-doped inclusions only, resulting in a positive differential stress field in the fiber center. (b) Full B-doped structure, where the stress field from the Ge-doped rods destructively interferes with the stress field from the B-doped rods. (c) F-doped inclusions only, with a negative differential stress field in the center. (d) Full F-doped structure where the stress field from the Ge-doped rods constructively interferes with the stress field from the F-doped rods.

Fig. 8
Fig. 8

Calculated group and modal phase birefringence for a fiber with B-doped stress applying parts

Fig. 9
Fig. 9

Calculated group and modal phase birefringence for a fiber with F-doped stress applying parts

Tables (2)

Tables Icon

Table 1 Fabricated fiber properties

Tables Icon

Table 2 Various calculated differential stress fields at the fiber center.

Equations (5)

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

| B g ( λ ) | = λ 2 Δ λ L ,
B ( λ + Δ λ ) B ( λ ) + d B d λ Δ λ = B ( λ ) + B ( λ ) B g ( λ ) λ Δ λ .
B = n e f f x - n e f f y B g = n g x - n g y ,
h = 10 P C T / 10 L ,
B = C [ σ x ( x , y ) σ y ( x , y ) ] | E ( x , y ) | 2 d x d y | E ( x , y ) | 2 d x d y .

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