Abstract

Birefringence induced by thermal stress in bow-tie optical fibers is studied in detail by the use of the finite-element method. Results of computer modeling show that a higher degree of birefringence can be obtained with the use of a larger cladding and larger stress-applying zones in the fiber.

© 1994 Optical Society of America

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References

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  1. J. Noda, K. Okamoto, Y. Sasaki, “Polarization-maintaining fibers and their applications,” J. Lightwave Technol. LT-4, 1071–1089 (1986).
    [CrossRef]
  2. Y. Yamamoto, T. Kimura, “Coherent optical fiber transmission systems,” IEEE J. Quantum Electron. QE-17, 919–935 (1981).
    [CrossRef]
  3. R. Griffiths, “Recent and current developments in distributed fiber optics sensing for structral monitoring,” in Fiber Optic and Laser Sensors VI, R. P. DePaula, E. Udd, eds., Proc. Soc. Photo-Opt. Instrum. Eng.985, 69–76 (1988).
  4. K. Okamoto, T. Hosaka, T. Edahiro, “Stress analysis of optical fibers by a finite element method,” IEEE J. Quantum Electron. QE-17, 2123–2129 (1981).
    [CrossRef]
  5. K. Tajima, M. Ohashi, Y. Sasaki, “A new single-polarization optical fiber,” J. Lightwave Technol. 7, 1499–1503 (1989).
    [CrossRef]
  6. Y. Liu, B. M. A. Rahman, K. T. V. Grattan, “Finite element analysis of the stress distribution in “bow-tie” optical fibres with sensor application,” in Sensors VI Technology, Systems and Applications, K. T. V. Grattan, ed. (Hilger, Bristol, UK, 1993), pp. 299–304.
  7. K. Hayata, M. Koshiba, M. Suzuki, “Stress-induced birefringence of side-tunnel type polarization-maintaing fibers,” J. Lightwave Technol. LT-4, 601–607 (1986).
    [CrossRef]
  8. K. Tsai, K. Kim, T. F. Morse, “General solutions for stress-induced polarization in optical fibers,” J. Lightwave Technol. 9, 7–17 (1991).
    [CrossRef]
  9. B. M. A. Rahman, F. A. Fernandez, J. B. Davies, “Review of finite element methods for microwave and optical waveguides,” Proc. IEEE 79, 1442–1448 (1991).
    [CrossRef]
  10. M. P. Varnham, D. N. Payne, A. J. Barlow, R. D. Birch, “Analytical solution for the birefringence produced by thermal stress in polarization-maintaining optical fibers,” J. Lightwave Technol. LT-1, 332–339 (1983).
    [CrossRef]

1991 (2)

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

B. M. A. Rahman, F. A. Fernandez, J. B. Davies, “Review of finite element methods for microwave and optical waveguides,” Proc. IEEE 79, 1442–1448 (1991).
[CrossRef]

1989 (1)

K. Tajima, M. Ohashi, Y. Sasaki, “A new single-polarization optical fiber,” J. Lightwave Technol. 7, 1499–1503 (1989).
[CrossRef]

1986 (2)

K. Hayata, M. Koshiba, M. Suzuki, “Stress-induced birefringence of side-tunnel type polarization-maintaing fibers,” J. Lightwave Technol. LT-4, 601–607 (1986).
[CrossRef]

J. Noda, K. Okamoto, Y. Sasaki, “Polarization-maintaining fibers and their applications,” J. Lightwave Technol. LT-4, 1071–1089 (1986).
[CrossRef]

1983 (1)

M. P. Varnham, D. N. Payne, A. J. Barlow, R. D. Birch, “Analytical solution for the birefringence produced by thermal stress in polarization-maintaining optical fibers,” J. Lightwave Technol. LT-1, 332–339 (1983).
[CrossRef]

1981 (2)

Y. Yamamoto, T. Kimura, “Coherent optical fiber transmission systems,” IEEE J. Quantum Electron. QE-17, 919–935 (1981).
[CrossRef]

K. Okamoto, T. Hosaka, T. Edahiro, “Stress analysis of optical fibers by a finite element method,” IEEE J. Quantum Electron. QE-17, 2123–2129 (1981).
[CrossRef]

Barlow, A. J.

M. P. Varnham, D. N. Payne, A. J. Barlow, R. D. Birch, “Analytical solution for the birefringence produced by thermal stress in polarization-maintaining optical fibers,” J. Lightwave Technol. LT-1, 332–339 (1983).
[CrossRef]

Birch, R. D.

M. P. Varnham, D. N. Payne, A. J. Barlow, R. D. Birch, “Analytical solution for the birefringence produced by thermal stress in polarization-maintaining optical fibers,” J. Lightwave Technol. LT-1, 332–339 (1983).
[CrossRef]

Davies, J. B.

B. M. A. Rahman, F. A. Fernandez, J. B. Davies, “Review of finite element methods for microwave and optical waveguides,” Proc. IEEE 79, 1442–1448 (1991).
[CrossRef]

Edahiro, T.

K. Okamoto, T. Hosaka, T. Edahiro, “Stress analysis of optical fibers by a finite element method,” IEEE J. Quantum Electron. QE-17, 2123–2129 (1981).
[CrossRef]

Fernandez, F. A.

B. M. A. Rahman, F. A. Fernandez, J. B. Davies, “Review of finite element methods for microwave and optical waveguides,” Proc. IEEE 79, 1442–1448 (1991).
[CrossRef]

Grattan, K. T. V.

Y. Liu, B. M. A. Rahman, K. T. V. Grattan, “Finite element analysis of the stress distribution in “bow-tie” optical fibres with sensor application,” in Sensors VI Technology, Systems and Applications, K. T. V. Grattan, ed. (Hilger, Bristol, UK, 1993), pp. 299–304.

Griffiths, R.

R. Griffiths, “Recent and current developments in distributed fiber optics sensing for structral monitoring,” in Fiber Optic and Laser Sensors VI, R. P. DePaula, E. Udd, eds., Proc. Soc. Photo-Opt. Instrum. Eng.985, 69–76 (1988).

Hayata, K.

K. Hayata, M. Koshiba, M. Suzuki, “Stress-induced birefringence of side-tunnel type polarization-maintaing fibers,” J. Lightwave Technol. LT-4, 601–607 (1986).
[CrossRef]

Hosaka, T.

K. Okamoto, T. Hosaka, T. Edahiro, “Stress analysis of optical fibers by a finite element method,” IEEE J. Quantum Electron. QE-17, 2123–2129 (1981).
[CrossRef]

Kim, K.

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

Kimura, T.

Y. Yamamoto, T. Kimura, “Coherent optical fiber transmission systems,” IEEE J. Quantum Electron. QE-17, 919–935 (1981).
[CrossRef]

Koshiba, M.

K. Hayata, M. Koshiba, M. Suzuki, “Stress-induced birefringence of side-tunnel type polarization-maintaing fibers,” J. Lightwave Technol. LT-4, 601–607 (1986).
[CrossRef]

Liu, Y.

Y. Liu, B. M. A. Rahman, K. T. V. Grattan, “Finite element analysis of the stress distribution in “bow-tie” optical fibres with sensor application,” in Sensors VI Technology, Systems and Applications, K. T. V. Grattan, ed. (Hilger, Bristol, UK, 1993), pp. 299–304.

Morse, T. F.

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

Noda, J.

J. Noda, K. Okamoto, Y. Sasaki, “Polarization-maintaining fibers and their applications,” J. Lightwave Technol. LT-4, 1071–1089 (1986).
[CrossRef]

Ohashi, M.

K. Tajima, M. Ohashi, Y. Sasaki, “A new single-polarization optical fiber,” J. Lightwave Technol. 7, 1499–1503 (1989).
[CrossRef]

Okamoto, K.

J. Noda, K. Okamoto, Y. Sasaki, “Polarization-maintaining fibers and their applications,” J. Lightwave Technol. LT-4, 1071–1089 (1986).
[CrossRef]

K. Okamoto, T. Hosaka, T. Edahiro, “Stress analysis of optical fibers by a finite element method,” IEEE J. Quantum Electron. QE-17, 2123–2129 (1981).
[CrossRef]

Payne, D. N.

M. P. Varnham, D. N. Payne, A. J. Barlow, R. D. Birch, “Analytical solution for the birefringence produced by thermal stress in polarization-maintaining optical fibers,” J. Lightwave Technol. LT-1, 332–339 (1983).
[CrossRef]

Rahman, B. M. A.

B. M. A. Rahman, F. A. Fernandez, J. B. Davies, “Review of finite element methods for microwave and optical waveguides,” Proc. IEEE 79, 1442–1448 (1991).
[CrossRef]

Y. Liu, B. M. A. Rahman, K. T. V. Grattan, “Finite element analysis of the stress distribution in “bow-tie” optical fibres with sensor application,” in Sensors VI Technology, Systems and Applications, K. T. V. Grattan, ed. (Hilger, Bristol, UK, 1993), pp. 299–304.

Sasaki, Y.

K. Tajima, M. Ohashi, Y. Sasaki, “A new single-polarization optical fiber,” J. Lightwave Technol. 7, 1499–1503 (1989).
[CrossRef]

J. Noda, K. Okamoto, Y. Sasaki, “Polarization-maintaining fibers and their applications,” J. Lightwave Technol. LT-4, 1071–1089 (1986).
[CrossRef]

Suzuki, M.

K. Hayata, M. Koshiba, M. Suzuki, “Stress-induced birefringence of side-tunnel type polarization-maintaing fibers,” J. Lightwave Technol. LT-4, 601–607 (1986).
[CrossRef]

Tajima, K.

K. Tajima, M. Ohashi, Y. Sasaki, “A new single-polarization optical fiber,” J. Lightwave Technol. 7, 1499–1503 (1989).
[CrossRef]

Tsai, K.

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

Varnham, M. P.

M. P. Varnham, D. N. Payne, A. J. Barlow, R. D. Birch, “Analytical solution for the birefringence produced by thermal stress in polarization-maintaining optical fibers,” J. Lightwave Technol. LT-1, 332–339 (1983).
[CrossRef]

Yamamoto, Y.

Y. Yamamoto, T. Kimura, “Coherent optical fiber transmission systems,” IEEE J. Quantum Electron. QE-17, 919–935 (1981).
[CrossRef]

IEEE J. Quantum Electron. (2)

Y. Yamamoto, T. Kimura, “Coherent optical fiber transmission systems,” IEEE J. Quantum Electron. QE-17, 919–935 (1981).
[CrossRef]

K. Okamoto, T. Hosaka, T. Edahiro, “Stress analysis of optical fibers by a finite element method,” IEEE J. Quantum Electron. QE-17, 2123–2129 (1981).
[CrossRef]

J. Lightwave Technol. (5)

K. Tajima, M. Ohashi, Y. Sasaki, “A new single-polarization optical fiber,” J. Lightwave Technol. 7, 1499–1503 (1989).
[CrossRef]

K. Hayata, M. Koshiba, M. Suzuki, “Stress-induced birefringence of side-tunnel type polarization-maintaing fibers,” J. Lightwave Technol. LT-4, 601–607 (1986).
[CrossRef]

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

J. Noda, K. Okamoto, Y. Sasaki, “Polarization-maintaining fibers and their applications,” J. Lightwave Technol. LT-4, 1071–1089 (1986).
[CrossRef]

M. P. Varnham, D. N. Payne, A. J. Barlow, R. D. Birch, “Analytical solution for the birefringence produced by thermal stress in polarization-maintaining optical fibers,” J. Lightwave Technol. LT-1, 332–339 (1983).
[CrossRef]

Proc. IEEE (1)

B. M. A. Rahman, F. A. Fernandez, J. B. Davies, “Review of finite element methods for microwave and optical waveguides,” Proc. IEEE 79, 1442–1448 (1991).
[CrossRef]

Other (2)

Y. Liu, B. M. A. Rahman, K. T. V. Grattan, “Finite element analysis of the stress distribution in “bow-tie” optical fibres with sensor application,” in Sensors VI Technology, Systems and Applications, K. T. V. Grattan, ed. (Hilger, Bristol, UK, 1993), pp. 299–304.

R. Griffiths, “Recent and current developments in distributed fiber optics sensing for structral monitoring,” in Fiber Optic and Laser Sensors VI, R. P. DePaula, E. Udd, eds., Proc. Soc. Photo-Opt. Instrum. Eng.985, 69–76 (1988).

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Figures (7)

Fig. 1
Fig. 1

Typical bow-tie fiber consists of a core, a cladding, and two bow-tie-shaped SAZ’s. The radii of the core, the cladding, and the inner and the outer sides of the SAZ’s are a, b, r1, and r2, respectively. The circumferential angle of the SAZ’s is Φ.

Fig. 2
Fig. 2

Relationship between the birefringence of a bow-tie optical fiber and the size of its SAZ’s. The solid curves indicate the average birefringence in the core region, and the dashed curves illustrate the central birefringence.

Fig. 3
Fig. 3

Variations of the average birefringence B ¯, the central birefringence B0, and the birefringence obtained from a vector H-field optical modeling, Bopt, with respect to r1, the inner radius of the SAZ’s. Other geometric parameters of the fiber are a = 2.5 μm, b = 25.0 μm, and r2 = 20.0 μm.

Fig. 4
Fig. 4

Contour maps of the stress distribution: (a) σx for r1 = 2.5 μm, (b) σy, for r1 = 2.5 μm, (c) σx for r1 = 1.25 μm, and (d) σy for r1 = 1.25 μm.

Fig. 5
Fig. 5

Power density contour maps of the H11y modes: (a) r1 = 0.0, (b) r1 = 1.25 μm, and (c) r1 = 2.5 μm.

Fig. 6
Fig. 6

Relationship of the birefringence and the thermal-expansion coefficients of the fiber materials.

Fig. 7
Fig. 7

Influence of the cladding diameter on the birefringence of the fiber. The solid curves show the average birefringence in the core region. The dashed curves are the central birefringence. The pairs of curves labeled A and B illustrate the birefringence with a cladding radius of 62.5 μm and for r1 = 2.5 μm and r1 = 5 μm, respectively. The pairs of curves labeled C and D illustrate the birefringence with a cladding radius of 25 μm and for r1 = 2.5 μm and r1 = 5 μm, respectively. For all four pairs of curves, a = 2.5 μm.

Equations (9)

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σ x = E ( 1 - μ ) ( 1 - 2 μ ) [ ( 1 - μ ) x + μ y ] - α E Δ T ( 1 - 2 μ ) ,
σ y = E ( 1 - μ ) ( 1 - 2 μ ) [ μ x + ( 1 - μ ) y ] - α E Δ T ( 1 - 2 μ ) ,
σ z = μ ( σ x + σ y ) - E α Δ T ,
τ x y = E 2 ( 1 + μ ) γ x y ,
n x = n 0 + C 1 σ x + C 2 ( σ y + σ z ) ,
n y = n 0 + C 1 σ y + C 2 ( σ x + σ z ) ,
B = n x - n y = ( C 2 - C 1 ) ( σ y - σ x ) .
B ¯ = ( C 2 - C 1 ) A A ( σ y - σ x ) d x d y ,
B 0 = ( C 2 - C 1 ) ( σ y - σ x ) x = 0 , y = 0 ,

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