Abstract

Stresses, microbending loss, and refractive-index changes induced simultaneously by axial strain and hydrostatic pressure in double-coated optical fibers are analyzed. The lateral pressure and normal stresses in the optical fiber, primary coating, and secondary coating are derived. Also presented are the microbending loss and refractive-index changes in the glass fiber. The normal stresses are affected by axial strain, hydrostatic pressure, material properties, and thickness of the primary and secondary coatings. It is found that microbending loss decreases with increasing thickness, the Young’s modulus, and the Poisson’s ratio of the secondary coating but increases with the increasing Young’s modulus and Poisson’s ratio of the primary coating. Similarly, changes in refractive index in the glass fiber decrease with the increasing Young’s modulus and Poisson’s ratio of the secondary coating but increase with the increasing Young’s modulus and Poisson’s ratio of the primary coating. Therefore, to minimize microbending loss induced simultaneously by axial strain and hydrostatic pressure in the glass fiber, the polymeric coatings should be suitably selected. An optimal design procedure is also indicated.

© 2002 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. C. R. Kurkjian, J. T. Krause, M. J. Matthewson, “Strength and fatigue of silica optical fibers,” J. Lightwave Technol. 12, 1360–1370 (1989).
    [CrossRef]
  2. D. Gloge, “Optical-fiber packaging and its influence on fiber straightness and loss,” Bell Syst. Tech. J. 54, 245–262 (1975).
    [CrossRef]
  3. W. B. Gardner, “Microbending loss in optical fibers,” Bell Syst. Tech. J. 54, 457–465 (1975).
    [CrossRef]
  4. T. Yabuta, N. Yoshizawa, K. Ishihara, “Excess loss of single-mode jacketed optical fiber at low temperature,” Appl. Opt. 22, 2356–2362 (1983).
    [CrossRef] [PubMed]
  5. S. T. Shiue, “The spring constant in the buckling of tightly jacketed double-coated optical fibers,” J. Appl. Phys. 81, 3363–3368 (1997).
    [CrossRef]
  6. E. Suhir, “Effect of initial curvature on low temperature microbending in optical fibers,” J. Lightwave Technol. 6, 1321–1327 (1988).
    [CrossRef]
  7. W. W. King, C. J. Aloisio, “Thermomechanical mechanism for delamination of polymer coatings from optical fibers,” J. Electron. Packaging 119, 133–137 (1997).
    [CrossRef]
  8. Y. C. Yang, W. J. Chang, H. L. Lee, “Transient thermal loading induced microbending loss in carbon-coated optical fibers,” J. Appl. Phys. 88, 6987–6992 (2000).
    [CrossRef]
  9. G. B. Hocker, “Fiber-optic sensing of pressure and temperature,” Appl. Opt. 18, 1445–1448 (1979).
    [CrossRef] [PubMed]
  10. R. Hughes, J. Jarzynski, “Static pressure sensitivity amplification in interferometric fiber-optic hydrophones,” Appl. Opt. 19, 98–107 (1980).
    [CrossRef] [PubMed]
  11. V. S. Sudarshanam, K. Srinivasan, “Static phase change in a fiber optic coil hydrophone,” Appl. Opt. 29, 855–863 (1990).
    [CrossRef] [PubMed]
  12. K. S. Chiang, D. Wang, “Design of highly birefringent fibers to optimize or minimize pressure-induced birefringence,” IEEE Photon. Technol. Lett. 3, 654–656 (1991).
    [CrossRef]
  13. W. J. Chang, H. L. Lee, Y. C. Yang, “Hydrostatic pressure and thermal loading induced optical effects in double-coated optical fibers,” J. Appl. Phys. 88, 616–620 (2000).
    [CrossRef]
  14. S. P. Timoshenko, J. N. Goodier, Theory of Elasticity, 3rd ed. (McGraw-Hill, New York, 1970).
  15. E. Suhir, “Mechanical approach to the evaluation of the low temperature threshold of added transmission losses in single-coated optical fibers,” J. Lightwave Technol. 8, 863–868 (1990).
    [CrossRef]
  16. G. W. Scherer, “Stress-induced index profile distortion in optical waveguides,” Appl. Opt. 19, 2000–2006 (1980).
    [CrossRef] [PubMed]
  17. W. Primak, D. Post, “Photoelastic constants of vitreous silica and its elastic coefficient of refractive index,” J. Appl. Phys. 30, 779–788 (1959).
    [CrossRef]
  18. K. S. Chiang, “Pressure-induced birefringence in a coated highly birefringent optical fiber,” J. Lightwave Technol. 8, 1850–1855 (1990).
    [CrossRef]

2000

Y. C. Yang, W. J. Chang, H. L. Lee, “Transient thermal loading induced microbending loss in carbon-coated optical fibers,” J. Appl. Phys. 88, 6987–6992 (2000).
[CrossRef]

W. J. Chang, H. L. Lee, Y. C. Yang, “Hydrostatic pressure and thermal loading induced optical effects in double-coated optical fibers,” J. Appl. Phys. 88, 616–620 (2000).
[CrossRef]

1997

S. T. Shiue, “The spring constant in the buckling of tightly jacketed double-coated optical fibers,” J. Appl. Phys. 81, 3363–3368 (1997).
[CrossRef]

W. W. King, C. J. Aloisio, “Thermomechanical mechanism for delamination of polymer coatings from optical fibers,” J. Electron. Packaging 119, 133–137 (1997).
[CrossRef]

1991

K. S. Chiang, D. Wang, “Design of highly birefringent fibers to optimize or minimize pressure-induced birefringence,” IEEE Photon. Technol. Lett. 3, 654–656 (1991).
[CrossRef]

1990

E. Suhir, “Mechanical approach to the evaluation of the low temperature threshold of added transmission losses in single-coated optical fibers,” J. Lightwave Technol. 8, 863–868 (1990).
[CrossRef]

V. S. Sudarshanam, K. Srinivasan, “Static phase change in a fiber optic coil hydrophone,” Appl. Opt. 29, 855–863 (1990).
[CrossRef] [PubMed]

K. S. Chiang, “Pressure-induced birefringence in a coated highly birefringent optical fiber,” J. Lightwave Technol. 8, 1850–1855 (1990).
[CrossRef]

1989

C. R. Kurkjian, J. T. Krause, M. J. Matthewson, “Strength and fatigue of silica optical fibers,” J. Lightwave Technol. 12, 1360–1370 (1989).
[CrossRef]

1988

E. Suhir, “Effect of initial curvature on low temperature microbending in optical fibers,” J. Lightwave Technol. 6, 1321–1327 (1988).
[CrossRef]

1983

1980

1979

1975

D. Gloge, “Optical-fiber packaging and its influence on fiber straightness and loss,” Bell Syst. Tech. J. 54, 245–262 (1975).
[CrossRef]

W. B. Gardner, “Microbending loss in optical fibers,” Bell Syst. Tech. J. 54, 457–465 (1975).
[CrossRef]

1959

W. Primak, D. Post, “Photoelastic constants of vitreous silica and its elastic coefficient of refractive index,” J. Appl. Phys. 30, 779–788 (1959).
[CrossRef]

Aloisio, C. J.

W. W. King, C. J. Aloisio, “Thermomechanical mechanism for delamination of polymer coatings from optical fibers,” J. Electron. Packaging 119, 133–137 (1997).
[CrossRef]

Chang, W. J.

W. J. Chang, H. L. Lee, Y. C. Yang, “Hydrostatic pressure and thermal loading induced optical effects in double-coated optical fibers,” J. Appl. Phys. 88, 616–620 (2000).
[CrossRef]

Y. C. Yang, W. J. Chang, H. L. Lee, “Transient thermal loading induced microbending loss in carbon-coated optical fibers,” J. Appl. Phys. 88, 6987–6992 (2000).
[CrossRef]

Chiang, K. S.

K. S. Chiang, D. Wang, “Design of highly birefringent fibers to optimize or minimize pressure-induced birefringence,” IEEE Photon. Technol. Lett. 3, 654–656 (1991).
[CrossRef]

K. S. Chiang, “Pressure-induced birefringence in a coated highly birefringent optical fiber,” J. Lightwave Technol. 8, 1850–1855 (1990).
[CrossRef]

Gardner, W. B.

W. B. Gardner, “Microbending loss in optical fibers,” Bell Syst. Tech. J. 54, 457–465 (1975).
[CrossRef]

Gloge, D.

D. Gloge, “Optical-fiber packaging and its influence on fiber straightness and loss,” Bell Syst. Tech. J. 54, 245–262 (1975).
[CrossRef]

Goodier, J. N.

S. P. Timoshenko, J. N. Goodier, Theory of Elasticity, 3rd ed. (McGraw-Hill, New York, 1970).

Hocker, G. B.

Hughes, R.

Ishihara, K.

Jarzynski, J.

King, W. W.

W. W. King, C. J. Aloisio, “Thermomechanical mechanism for delamination of polymer coatings from optical fibers,” J. Electron. Packaging 119, 133–137 (1997).
[CrossRef]

Krause, J. T.

C. R. Kurkjian, J. T. Krause, M. J. Matthewson, “Strength and fatigue of silica optical fibers,” J. Lightwave Technol. 12, 1360–1370 (1989).
[CrossRef]

Kurkjian, C. R.

C. R. Kurkjian, J. T. Krause, M. J. Matthewson, “Strength and fatigue of silica optical fibers,” J. Lightwave Technol. 12, 1360–1370 (1989).
[CrossRef]

Lee, H. L.

Y. C. Yang, W. J. Chang, H. L. Lee, “Transient thermal loading induced microbending loss in carbon-coated optical fibers,” J. Appl. Phys. 88, 6987–6992 (2000).
[CrossRef]

W. J. Chang, H. L. Lee, Y. C. Yang, “Hydrostatic pressure and thermal loading induced optical effects in double-coated optical fibers,” J. Appl. Phys. 88, 616–620 (2000).
[CrossRef]

Matthewson, M. J.

C. R. Kurkjian, J. T. Krause, M. J. Matthewson, “Strength and fatigue of silica optical fibers,” J. Lightwave Technol. 12, 1360–1370 (1989).
[CrossRef]

Post, D.

W. Primak, D. Post, “Photoelastic constants of vitreous silica and its elastic coefficient of refractive index,” J. Appl. Phys. 30, 779–788 (1959).
[CrossRef]

Primak, W.

W. Primak, D. Post, “Photoelastic constants of vitreous silica and its elastic coefficient of refractive index,” J. Appl. Phys. 30, 779–788 (1959).
[CrossRef]

Scherer, G. W.

Shiue, S. T.

S. T. Shiue, “The spring constant in the buckling of tightly jacketed double-coated optical fibers,” J. Appl. Phys. 81, 3363–3368 (1997).
[CrossRef]

Srinivasan, K.

Sudarshanam, V. S.

Suhir, E.

E. Suhir, “Mechanical approach to the evaluation of the low temperature threshold of added transmission losses in single-coated optical fibers,” J. Lightwave Technol. 8, 863–868 (1990).
[CrossRef]

E. Suhir, “Effect of initial curvature on low temperature microbending in optical fibers,” J. Lightwave Technol. 6, 1321–1327 (1988).
[CrossRef]

Timoshenko, S. P.

S. P. Timoshenko, J. N. Goodier, Theory of Elasticity, 3rd ed. (McGraw-Hill, New York, 1970).

Wang, D.

K. S. Chiang, D. Wang, “Design of highly birefringent fibers to optimize or minimize pressure-induced birefringence,” IEEE Photon. Technol. Lett. 3, 654–656 (1991).
[CrossRef]

Yabuta, T.

Yang, Y. C.

W. J. Chang, H. L. Lee, Y. C. Yang, “Hydrostatic pressure and thermal loading induced optical effects in double-coated optical fibers,” J. Appl. Phys. 88, 616–620 (2000).
[CrossRef]

Y. C. Yang, W. J. Chang, H. L. Lee, “Transient thermal loading induced microbending loss in carbon-coated optical fibers,” J. Appl. Phys. 88, 6987–6992 (2000).
[CrossRef]

Yoshizawa, N.

Appl. Opt.

Bell Syst. Tech. J.

D. Gloge, “Optical-fiber packaging and its influence on fiber straightness and loss,” Bell Syst. Tech. J. 54, 245–262 (1975).
[CrossRef]

W. B. Gardner, “Microbending loss in optical fibers,” Bell Syst. Tech. J. 54, 457–465 (1975).
[CrossRef]

IEEE Photon. Technol. Lett.

K. S. Chiang, D. Wang, “Design of highly birefringent fibers to optimize or minimize pressure-induced birefringence,” IEEE Photon. Technol. Lett. 3, 654–656 (1991).
[CrossRef]

J. Appl. Phys.

W. J. Chang, H. L. Lee, Y. C. Yang, “Hydrostatic pressure and thermal loading induced optical effects in double-coated optical fibers,” J. Appl. Phys. 88, 616–620 (2000).
[CrossRef]

S. T. Shiue, “The spring constant in the buckling of tightly jacketed double-coated optical fibers,” J. Appl. Phys. 81, 3363–3368 (1997).
[CrossRef]

Y. C. Yang, W. J. Chang, H. L. Lee, “Transient thermal loading induced microbending loss in carbon-coated optical fibers,” J. Appl. Phys. 88, 6987–6992 (2000).
[CrossRef]

W. Primak, D. Post, “Photoelastic constants of vitreous silica and its elastic coefficient of refractive index,” J. Appl. Phys. 30, 779–788 (1959).
[CrossRef]

J. Electron. Packaging

W. W. King, C. J. Aloisio, “Thermomechanical mechanism for delamination of polymer coatings from optical fibers,” J. Electron. Packaging 119, 133–137 (1997).
[CrossRef]

J. Lightwave Technol.

C. R. Kurkjian, J. T. Krause, M. J. Matthewson, “Strength and fatigue of silica optical fibers,” J. Lightwave Technol. 12, 1360–1370 (1989).
[CrossRef]

E. Suhir, “Effect of initial curvature on low temperature microbending in optical fibers,” J. Lightwave Technol. 6, 1321–1327 (1988).
[CrossRef]

K. S. Chiang, “Pressure-induced birefringence in a coated highly birefringent optical fiber,” J. Lightwave Technol. 8, 1850–1855 (1990).
[CrossRef]

E. Suhir, “Mechanical approach to the evaluation of the low temperature threshold of added transmission losses in single-coated optical fibers,” J. Lightwave Technol. 8, 863–868 (1990).
[CrossRef]

Other

S. P. Timoshenko, J. N. Goodier, Theory of Elasticity, 3rd ed. (McGraw-Hill, New York, 1970).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (9)

Fig. 1
Fig. 1

Stress distributions of σ r , σθ, and σ z in a double-coated optical fiber.

Fig. 2
Fig. 2

Effects of thickness of the primary and secondary coatings on the microbending loss Γ.

Fig. 3
Fig. 3

Effects of Young’s modulus of the primary and secondary coatings on the microbending loss Γ.

Fig. 4
Fig. 4

Effects of the Poisson’s ratio of the primary and secondary coatings on the microbending loss Γ.

Fig. 5
Fig. 5

Effects of thickness of the primary and secondary coatings on refractive-index changes Δn r , Δn θ, and Δn z .

Fig. 6
Fig. 6

Effects of Young’s modulus of the primary and secondary coatings on refractive-index changes Δn r , Δn θ, and Δn z .

Fig. 7
Fig. 7

Effects of the Poisson’s ratio of the primary and secondary coatings on refractive-index changes Δn r , Δn θ, and Δn z .

Fig. 8
Fig. 8

Effects of axial strain and hydrostatic pressure on microbending loss Γ.

Fig. 9
Fig. 9

Effects of axial strain and hydrostatic pressure on refractive-index changes Δn r , Δn θ, and Δn z .

Equations (32)

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

εr=1Eσr-vσθ+σz,
εθ=1Eσθ-vσr+σz,
εz=1Eσz-vσr+σθ,
u=rεθ=-vεzr+1-v2Eσθ-v1-v σrr.
σr=pia2-peb2b2-a2+a2b2pe-pib2-a2r2,
σθ=pia2-peb2b2-a2-a2b2pe-pib2-a2r2,
u=-vεzr+1+vE1-ξ21-2vpiξ2-pe×r-a2pe-pi/r,
u01=-v0εzr0-p1r0E01+v01-2v0,
u11=-v1εzr0+1+v1r0E11-ξ121-2v1p1ξ12-p2-p2-p1,
u12=-v1εzr1+1+v1r1E11-ξ121-2v1p1ξ12-p2-ξ12p2-p1,
u22=-v2εzr1+1+v2r1E21-ξ221-2v2ξ22+1p2-21-v2p,
p1=1Yφ1εz+φ2p,
p2=1Yϕ1εz+ϕ2p,
Y=1+v11-2v11+v2+E11-2v1ξ12+ξ121-2v2ξ22+ξ22E21-ξ121-ξ22,
φ1=E11+v1v1-v0E1E21-2v2ξ22+ξ221-ξ22-1+v11+v2+2v2-v01+v11+v21-v11-ξ12,
φ2=4E11-v11-v2E21-ξ121-ξ22,
ϕ1=E11+v2v2-v01-2v1ξ12+ξ121-ξ12-v1-v0,
ϕ2=2E11-v21-2v1ξ12+ξ12E21-ξ121-ξ22.
σr=σθ=-p1.
σr=p1r02-p2r12r12-r02+r02r12p2-p1r12-r02r2, r0rr1,
σθ=p1r02-p2r12r12-r02-r02r12p2-p1r12-r02r2, r0rr1.
σr=p2r12-pr22r22-r12+r12r22p-p2r22-r12r2, r1rr2,
σθ=p2r12-pr22r22-r12-r12r22p-p2r22-r12r2, r1rr2.
σz=Eεz+vσr+σθ.
σz=E0εz-2v0p1, rr0,
σz=E1εz+2v1p1r02-p2r12r12-r02, r0rr1,
σz=E2εz+2v2p2r12-pr22r22-r12, r1rr2,
Γ=kp1,
Δnr=nr-n=-B2σr-B1σθ+σz,
Δnθ=nθ-n=-B2σθ-B1σr+σz,
Δnz=nz-n=-B2σz-B1σr+σθ,
r0=62.5 μm, r1=100 μm, r2=125 μm, E0=72.5 GPa, E1=10 MPa, E2=1.3 GPa, v0=0.17, v1=0.495, v2=0.452.

Metrics