Abstract

Modal birefringence introduced by lateral stress resulting from bending is evaluated experimentally as a function of bending curvature in wide region of bending radius from 2.2 to 30 mm by a technique utilizing birefringent-matching stimulated four-photon mixing at pump wavelengths of 1.06 and 1.34μm. Wavelength dependence of polarization mode dispersion is also measured in the 0.8–1.6-μm wavelength region by an improved spatial technique based on optical heterodyne detection. The results obtained experimentally on these quantities are compared with those calculated theoretically. It is found that the birefringence evaluated experimentally agrees well with that calculated theoretically, even for a bending radius as small as 2 mm. As for polarization mode dispersion, the theoretical evaluation of the normalized frequency dependence of the modal dispersion agrees well with that obtained experimentally with respect to curve tendency against the V value and the magnitude of the dispersion far from the cutoff V value. However, it is observed that the modal dispersion drastically decreases with the V value in the region of 1.6 < V < 1.8 in the experiment, whereas the theory predicts that the dispersion becomes constant over the V-value region of V > 1.2. This discrepancy is considered to be due to difference between the actual stress distribution resulting from bending and the calculated one obtained by using the slab approximation to evaluate bending-induced birefringence.

© 1986 Optical Society of America

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References

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  1. S. Ezekiel, H. J. Arditty, in Fiber-Optic Rotation Sensors and Related Technologies, S. Ezekiel, H. J. Arditty, eds., Vol. 32 of Springer Series in Optical Sciences (Springer-Verlag, Berlin, 1982).
    [Crossref]
  2. H. C. Lefevre, “Single-mode fiber fractional wave devices and polarization controller,” Electron. Lett. 16, 778–780 (1980).
    [Crossref]
  3. Y. Yen, R. Ulrich, “Birefringent optical filters in single-mode fiber,” Opt. Lett. 6, 278–280 (1981).
    [Crossref] [PubMed]
  4. K. Okamoto, J. Noda, H. Miyazawa, “Fiber-optic Solc filter for use in Raman amplification of light,” Electron. Lett. 21, 90–91 (1985).
    [Crossref]
  5. G. W. Day, D. N. Payne, A. J. Barlow, J. J. Ramoskov-Hansen, “Design and performance of tuned fiber coil isolator,” IEEE J. Lightwave Technol. LT-2, 56–60 (1984).
    [Crossref]
  6. R. Ulrich, A. Simon, “Polarization optics of twisted single-mode fibers,” Appl. Opt. 18, 2241–2251 (1979).
    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  12. N. Shibata, M. Tateda, S. Seikai, N. Uchida, “Spatial technique for measuring modal delay differences in a dual mode optical fiber,” Appl. Opt. 19, 1489–1492 (1980).
    [Crossref] [PubMed]
  13. N. Shibata, M. Tsubokawa, S. Seikai, “Measurements of polarisation mode dispersion by optical heterodyne detection,” Electron. Lett. 20, 1055–1057 (1984).
    [Crossref]
  14. N. Shibata, M. Tsubokawa, S. Seikai, “Polarization mode dispersion in a coil of single-mode fiber,” Opt. Lett. 10, 92–94 (1985).
    [Crossref] [PubMed]
  15. N. Shibata, N. Uchida, M. Tateda, S. Seikai, “Normalised frequency dependence of polarisation mode dispersion due to thermal-stress-induced birefringence in an elliptical core single-mode fibre,” Electron. Lett. 18, 563–564 (1982).
    [Crossref]
  16. K. Okamoto, T. Edahiro, N. Shibata, “Polarization properties of single-polarization fibers,” Opt. Lett. 7, 569–571 (1982).
    [Crossref] [PubMed]
  17. J. Sakai, T. Kimura, “Birefringence caused by thermal stress in elliptically deformed core optical fibers,” IEEE J. Quantum Electron. QE-18, 1899–1895 (1982).
    [Crossref]
  18. N. Shibata, K. Okamoto, K. Suzuki, Y. Ishida, “Polarization mode properties of elliptical-core fibers and stress-induced birefringent fibers,” J. Opt. Soc. Am. 73, 1792–1798 (1983).
    [Crossref]
  19. D. Marcuse, “Curvature loss formula for optical fibers,” J. Opt. Soc. Am. 66, 216–220 (1976).
    [Crossref]
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    [Crossref]
  21. N. K. Sinha, “Normalized dispersion of birefringence of quartz and stress-optical coefficient of fused silica and plate glass,” Phys. Chem. Glasses 19, 67–77 (1978).

1985 (3)

1984 (2)

N. Shibata, M. Tsubokawa, S. Seikai, “Measurements of polarisation mode dispersion by optical heterodyne detection,” Electron. Lett. 20, 1055–1057 (1984).
[Crossref]

G. W. Day, D. N. Payne, A. J. Barlow, J. J. Ramoskov-Hansen, “Design and performance of tuned fiber coil isolator,” IEEE J. Lightwave Technol. LT-2, 56–60 (1984).
[Crossref]

1983 (1)

1982 (3)

N. Shibata, N. Uchida, M. Tateda, S. Seikai, “Normalised frequency dependence of polarisation mode dispersion due to thermal-stress-induced birefringence in an elliptical core single-mode fibre,” Electron. Lett. 18, 563–564 (1982).
[Crossref]

K. Okamoto, T. Edahiro, N. Shibata, “Polarization properties of single-polarization fibers,” Opt. Lett. 7, 569–571 (1982).
[Crossref] [PubMed]

J. Sakai, T. Kimura, “Birefringence caused by thermal stress in elliptically deformed core optical fibers,” IEEE J. Quantum Electron. QE-18, 1899–1895 (1982).
[Crossref]

1981 (2)

1980 (4)

1979 (1)

1978 (2)

D. Marcuse, “Gaussian approximation of the fundamental modes of graded-index fibers,” J. Opt. Soc. Am. 68, 103–109 (1978).
[Crossref]

N. K. Sinha, “Normalized dispersion of birefringence of quartz and stress-optical coefficient of fused silica and plate glass,” Phys. Chem. Glasses 19, 67–77 (1978).

1976 (1)

Arditty, H. J.

S. Ezekiel, H. J. Arditty, in Fiber-Optic Rotation Sensors and Related Technologies, S. Ezekiel, H. J. Arditty, eds., Vol. 32 of Springer Series in Optical Sciences (Springer-Verlag, Berlin, 1982).
[Crossref]

Barlow, A. J.

G. W. Day, D. N. Payne, A. J. Barlow, J. J. Ramoskov-Hansen, “Design and performance of tuned fiber coil isolator,” IEEE J. Lightwave Technol. LT-2, 56–60 (1984).
[Crossref]

Bosch, M. A.

Day, G. W.

G. W. Day, D. N. Payne, A. J. Barlow, J. J. Ramoskov-Hansen, “Design and performance of tuned fiber coil isolator,” IEEE J. Lightwave Technol. LT-2, 56–60 (1984).
[Crossref]

Edahiro, T.

Eickhoff, W.

Ezekiel, S.

S. Ezekiel, H. J. Arditty, in Fiber-Optic Rotation Sensors and Related Technologies, S. Ezekiel, H. J. Arditty, eds., Vol. 32 of Springer Series in Optical Sciences (Springer-Verlag, Berlin, 1982).
[Crossref]

Ihashi, M.

Ishida, Y.

Kimura, T.

J. Sakai, T. Kimura, “Birefringence caused by thermal stress in elliptically deformed core optical fibers,” IEEE J. Quantum Electron. QE-18, 1899–1895 (1982).
[Crossref]

Kitayama, K.

Lefevre, H. C.

H. C. Lefevre, “Single-mode fiber fractional wave devices and polarization controller,” Electron. Lett. 16, 778–780 (1980).
[Crossref]

Lin, C.

Marcuse, D.

Miyazawa, H.

K. Okamoto, J. Noda, H. Miyazawa, “Fiber-optic Solc filter for use in Raman amplification of light,” Electron. Lett. 21, 90–91 (1985).
[Crossref]

Noda, J.

K. Okamoto, J. Noda, H. Miyazawa, “Fiber-optic Solc filter for use in Raman amplification of light,” Electron. Lett. 21, 90–91 (1985).
[Crossref]

Okamoto, K.

Payne, D. N.

G. W. Day, D. N. Payne, A. J. Barlow, J. J. Ramoskov-Hansen, “Design and performance of tuned fiber coil isolator,” IEEE J. Lightwave Technol. LT-2, 56–60 (1984).
[Crossref]

Ramoskov-Hansen, J. J.

G. W. Day, D. N. Payne, A. J. Barlow, J. J. Ramoskov-Hansen, “Design and performance of tuned fiber coil isolator,” IEEE J. Lightwave Technol. LT-2, 56–60 (1984).
[Crossref]

Rashleigh, S. C.

Sakai, J.

J. Sakai, T. Kimura, “Birefringence caused by thermal stress in elliptically deformed core optical fibers,” IEEE J. Quantum Electron. QE-18, 1899–1895 (1982).
[Crossref]

Seikai, S.

N. Shibata, M. Ihashi, K. Kitayama, S. Seikai, “Evaluation of bending-induced birefringence based on stimulated four-photon mixing,” Opt. Lett. 10, 154–156 (1985).
[Crossref] [PubMed]

N. Shibata, M. Tsubokawa, S. Seikai, “Polarization mode dispersion in a coil of single-mode fiber,” Opt. Lett. 10, 92–94 (1985).
[Crossref] [PubMed]

N. Shibata, M. Tsubokawa, S. Seikai, “Measurements of polarisation mode dispersion by optical heterodyne detection,” Electron. Lett. 20, 1055–1057 (1984).
[Crossref]

N. Shibata, N. Uchida, M. Tateda, S. Seikai, “Normalised frequency dependence of polarisation mode dispersion due to thermal-stress-induced birefringence in an elliptical core single-mode fibre,” Electron. Lett. 18, 563–564 (1982).
[Crossref]

N. Shibata, M. Tateda, S. Seikai, N. Uchida, “Spatial technique for measuring modal delay differences in a dual mode optical fiber,” Appl. Opt. 19, 1489–1492 (1980).
[Crossref] [PubMed]

Shibata, N.

Simon, A.

Sinha, N. K.

N. K. Sinha, “Normalized dispersion of birefringence of quartz and stress-optical coefficient of fused silica and plate glass,” Phys. Chem. Glasses 19, 67–77 (1978).

Smith, A. M.

A. M. Smith, “Bend induced birefringence in single-mode optical fibre,” presented at the Optical Communication Conference, Amsterdam, The Netherlands, September1979, paper 10.2.

Stolen, R. H.

Suzuki, K.

Tateda, M.

N. Shibata, N. Uchida, M. Tateda, S. Seikai, “Normalised frequency dependence of polarisation mode dispersion due to thermal-stress-induced birefringence in an elliptical core single-mode fibre,” Electron. Lett. 18, 563–564 (1982).
[Crossref]

N. Shibata, M. Tateda, S. Seikai, N. Uchida, “Spatial technique for measuring modal delay differences in a dual mode optical fiber,” Appl. Opt. 19, 1489–1492 (1980).
[Crossref] [PubMed]

Tsubokawa, M.

N. Shibata, M. Tsubokawa, S. Seikai, “Polarization mode dispersion in a coil of single-mode fiber,” Opt. Lett. 10, 92–94 (1985).
[Crossref] [PubMed]

N. Shibata, M. Tsubokawa, S. Seikai, “Measurements of polarisation mode dispersion by optical heterodyne detection,” Electron. Lett. 20, 1055–1057 (1984).
[Crossref]

Uchida, N.

N. Shibata, N. Uchida, M. Tateda, S. Seikai, “Normalised frequency dependence of polarisation mode dispersion due to thermal-stress-induced birefringence in an elliptical core single-mode fibre,” Electron. Lett. 18, 563–564 (1982).
[Crossref]

N. Shibata, M. Tateda, S. Seikai, N. Uchida, “Spatial technique for measuring modal delay differences in a dual mode optical fiber,” Appl. Opt. 19, 1489–1492 (1980).
[Crossref] [PubMed]

Ulrich, R.

Yen, Y.

Appl. Opt. (2)

Electron. Lett. (4)

N. Shibata, M. Tsubokawa, S. Seikai, “Measurements of polarisation mode dispersion by optical heterodyne detection,” Electron. Lett. 20, 1055–1057 (1984).
[Crossref]

H. C. Lefevre, “Single-mode fiber fractional wave devices and polarization controller,” Electron. Lett. 16, 778–780 (1980).
[Crossref]

K. Okamoto, J. Noda, H. Miyazawa, “Fiber-optic Solc filter for use in Raman amplification of light,” Electron. Lett. 21, 90–91 (1985).
[Crossref]

N. Shibata, N. Uchida, M. Tateda, S. Seikai, “Normalised frequency dependence of polarisation mode dispersion due to thermal-stress-induced birefringence in an elliptical core single-mode fibre,” Electron. Lett. 18, 563–564 (1982).
[Crossref]

IEEE J. Lightwave Technol. (1)

G. W. Day, D. N. Payne, A. J. Barlow, J. J. Ramoskov-Hansen, “Design and performance of tuned fiber coil isolator,” IEEE J. Lightwave Technol. LT-2, 56–60 (1984).
[Crossref]

IEEE J. Quantum Electron. (1)

J. Sakai, T. Kimura, “Birefringence caused by thermal stress in elliptically deformed core optical fibers,” IEEE J. Quantum Electron. QE-18, 1899–1895 (1982).
[Crossref]

J. Opt. Soc. Am. (3)

Opt. Lett. (7)

Phys. Chem. Glasses (1)

N. K. Sinha, “Normalized dispersion of birefringence of quartz and stress-optical coefficient of fused silica and plate glass,” Phys. Chem. Glasses 19, 67–77 (1978).

Other (2)

A. M. Smith, “Bend induced birefringence in single-mode optical fibre,” presented at the Optical Communication Conference, Amsterdam, The Netherlands, September1979, paper 10.2.

S. Ezekiel, H. J. Arditty, in Fiber-Optic Rotation Sensors and Related Technologies, S. Ezekiel, H. J. Arditty, eds., Vol. 32 of Springer Series in Optical Sciences (Springer-Verlag, Berlin, 1982).
[Crossref]

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Figures (8)

Fig. 1
Fig. 1

Calculated S(V) and T(V).

Fig. 2
Fig. 2

Calculated relationship between bulk phase mismatch Δ k ( Δ ν ¯ ) and frequency shift Δ ν ¯ for various GeO2 concentrations.

Fig. 3
Fig. 3

Anti-Stokes spectra for various bending radii at the pump wavelengths (λ) of 1.06 and 1.34 μm. (a) λp = 1.06 μm, R = 30 mm; (b) λp = 1.06 μm, R = 2.2 mm; (c) λp = 1.34 μm, R = 26 mm; (d) λp = 1.34 μm, R = 2.5 mm.

Fig. 4
Fig. 4

Evaluated bending-induced birefringence Bb as a function of the square of bending curvature.

Fig. 5
Fig. 5

Degree of cohoronco |γ| as a function of optical path difference 2d for laser diodes operated at wavelengths of (a) 1.28 μm and (b) 1.54 μm.

Fig. 6
Fig. 6

Beat amplitudes as a function of 2d for the coiled fiber with R = 6 mm and L = 12 m at the measured wavelengths of (a) 1.28 μm and (b) 1.54 μm.

Fig. 7
Fig. 7

Wavelength dependence of polarization mode dispersion for the coiled fiber with R = 6 mm and L = 12 m.

Fig. 8
Fig. 8

Calculated and measured V-value dependence of the modal dispersion Tp.

Equations (15)

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B b 0 = B b 1 + B b 2 .
B b 1 = 0.25 n 3 ( p 11 p 12 ) ( 1 + μ ) ( b / R ) 2
B b 2 = 0.5 n 3 ( p 11 p 12 ) ( 1 + μ ) ( 2 3 μ ) ( 1 μ ) 1 ( b / R ) ( Δ 1 / 1 ) ,
( σ x σ y ) e = [ σ x ( x , y ) σ y ( x , y ) ] P ( x , y ) d x d y P ( x , y ) d x d y ,
B b = C ( σ x σ y ) e ,
S ( V ) = ( σ x σ y ) e / ( σ x σ y ) 0 ,
B b = B b 0 S ( V ) ,
σ x ( x , y ) = ( E / 2 R 2 ) ( x 2 b 2 )
σ y ( x , y ) = 0 ,
P ( x , y ) = exp [ ( x 2 + y 2 ) / W 2 ] ,
W = a ( 0.65 + 1.619 V 3 / 2 + 2.879 V 6 ) ,
T p = ( 1 / c ) [ d ( k B b ) / d k ] = ( 1 / c ) ( B b + k [ d B b / d k ] ) ,
T p = ( 1 / c ) [ B b 0 T ( V ) + ( k / C ) ( d C ) ( d C / d k ) S ( V ) ] ,
B b = Δ k ( Δ ν ¯ ) / 4 π Δ ν p ¯ ,
T p = X / c L ,

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