Abstract

Attenuation in multimode step-index fibers caused by diffusing species is modeled. Data for losses in As2S3 fiber at 6.3 μm that are due to water υapor are analyzed.

© 1992 Optical Society of America

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References

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  1. A. Iino, M. Kuwabara, K. Kohura, “Mechanisms of hydrogen-induced losses in silica-based optical fibers,” IEEE J. Lightwave Technol. 8, 1675–1679 (1990).
    [CrossRef]
  2. B. J. Ainslie, P. W. France, G. R. Newns, “Water impurity in low loss silica fibers,” Mater. Res. Bull. 12, 481–487 (1977).
    [CrossRef]
  3. M. Saito, M. Takizawa. “Teflon-clad As–S glass infrared fiber with low absorption loss,” J. Appl. Phys. 59, 1450–1452 (1986).
    [CrossRef]
  4. Q. Zhou, D. Kritz, L. Bonnell, G. H. Sigel, “Porous plastic optical fiber sensor for ammonia measurement,” Appl. Opt. 28, 2022–2025 (1989).
    [CrossRef] [PubMed]
  5. V. Ruddy, S. McCabe, B. D. MacCraith, “Detection of propane by IR-ATR in a teflon clad fluoride glass optical fiber,” Appl. Spectrosc. 44, 1461–1463 (1990).
    [CrossRef]
  6. M. Saito, “Optical loss increase in an As–S glass infrared fiber due to water diffusion,” Appl. Opt. 26, 202–203 (1987).
    [CrossRef] [PubMed]
  7. M. Saito, M. Takizawa, M. Miyagi, “Optical and mechanical properties of infrared fibers,” IEEE J. Lightwave Technol. 6, 233–239 (1988).
    [CrossRef]
  8. J. Crank, The Mathematics of Diffusion (Clarendon Press, Oxford, 1975), Eq. (5.22).
  9. A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983), Eq. (6-8).
  10. J. S. Gradshteyn, J. M. Ryzhik. Tables of Integrals, Series, and Products (Academic, New York, 1965), Section 6.511, No. 6.
  11. M. Abramowitz, I. A. Stegun, eds., Handbook of Mathematical Functions (U.S. Government Printing Office, Washington, D.C., 1968), Eq. (12.1.4).
  12. H. S. Carslaw, J. C. Jaeger, Conduction of Heat in Solids (Clarendon Press, Oxford, 1959), Appendix IV, Table III.
  13. E. Sacher, J. R. Susko, “Water permeation in Teflon FEP,” J. Appl. Polym. Sci. 24, 1997–2003 (1979).
    [CrossRef]
  14. K. Nassau, “The diffusion of water in optical fibers,” Mater. Res. Bull. 13, 67–76 (1978).
    [CrossRef]
  15. J. D. Rush, K. J. Beales, D. M. Cooper, W. J. Duncan, N. H. Rabone, “Hydrogen related degradation in optical fibers: system implications and practical solution,” Br. Telecom. Technol. J. 2, 84–93 (1984).
  16. V. Ruddy, “An effective attenuation coefficient for evanescent wave spectroscopy using multimode fiber,” Fiber Integr. Opt. 9, 142–151 (1990), Eq. (9).
  17. G. M. Hale, M. R. Querry, “Optical constants of water in the 200-nm to 200-μm wavelength region,” Appl. Opt. 12, 555–563 (1973).
    [CrossRef] [PubMed]

1990 (3)

A. Iino, M. Kuwabara, K. Kohura, “Mechanisms of hydrogen-induced losses in silica-based optical fibers,” IEEE J. Lightwave Technol. 8, 1675–1679 (1990).
[CrossRef]

V. Ruddy, S. McCabe, B. D. MacCraith, “Detection of propane by IR-ATR in a teflon clad fluoride glass optical fiber,” Appl. Spectrosc. 44, 1461–1463 (1990).
[CrossRef]

V. Ruddy, “An effective attenuation coefficient for evanescent wave spectroscopy using multimode fiber,” Fiber Integr. Opt. 9, 142–151 (1990), Eq. (9).

1989 (1)

1988 (1)

M. Saito, M. Takizawa, M. Miyagi, “Optical and mechanical properties of infrared fibers,” IEEE J. Lightwave Technol. 6, 233–239 (1988).
[CrossRef]

1987 (1)

1986 (1)

M. Saito, M. Takizawa. “Teflon-clad As–S glass infrared fiber with low absorption loss,” J. Appl. Phys. 59, 1450–1452 (1986).
[CrossRef]

1984 (1)

J. D. Rush, K. J. Beales, D. M. Cooper, W. J. Duncan, N. H. Rabone, “Hydrogen related degradation in optical fibers: system implications and practical solution,” Br. Telecom. Technol. J. 2, 84–93 (1984).

1979 (1)

E. Sacher, J. R. Susko, “Water permeation in Teflon FEP,” J. Appl. Polym. Sci. 24, 1997–2003 (1979).
[CrossRef]

1978 (1)

K. Nassau, “The diffusion of water in optical fibers,” Mater. Res. Bull. 13, 67–76 (1978).
[CrossRef]

1977 (1)

B. J. Ainslie, P. W. France, G. R. Newns, “Water impurity in low loss silica fibers,” Mater. Res. Bull. 12, 481–487 (1977).
[CrossRef]

1973 (1)

Ainslie, B. J.

B. J. Ainslie, P. W. France, G. R. Newns, “Water impurity in low loss silica fibers,” Mater. Res. Bull. 12, 481–487 (1977).
[CrossRef]

Beales, K. J.

J. D. Rush, K. J. Beales, D. M. Cooper, W. J. Duncan, N. H. Rabone, “Hydrogen related degradation in optical fibers: system implications and practical solution,” Br. Telecom. Technol. J. 2, 84–93 (1984).

Bonnell, L.

Carslaw, H. S.

H. S. Carslaw, J. C. Jaeger, Conduction of Heat in Solids (Clarendon Press, Oxford, 1959), Appendix IV, Table III.

Cooper, D. M.

J. D. Rush, K. J. Beales, D. M. Cooper, W. J. Duncan, N. H. Rabone, “Hydrogen related degradation in optical fibers: system implications and practical solution,” Br. Telecom. Technol. J. 2, 84–93 (1984).

Crank, J.

J. Crank, The Mathematics of Diffusion (Clarendon Press, Oxford, 1975), Eq. (5.22).

Duncan, W. J.

J. D. Rush, K. J. Beales, D. M. Cooper, W. J. Duncan, N. H. Rabone, “Hydrogen related degradation in optical fibers: system implications and practical solution,” Br. Telecom. Technol. J. 2, 84–93 (1984).

France, P. W.

B. J. Ainslie, P. W. France, G. R. Newns, “Water impurity in low loss silica fibers,” Mater. Res. Bull. 12, 481–487 (1977).
[CrossRef]

Gradshteyn, J. S.

J. S. Gradshteyn, J. M. Ryzhik. Tables of Integrals, Series, and Products (Academic, New York, 1965), Section 6.511, No. 6.

Hale, G. M.

Iino, A.

A. Iino, M. Kuwabara, K. Kohura, “Mechanisms of hydrogen-induced losses in silica-based optical fibers,” IEEE J. Lightwave Technol. 8, 1675–1679 (1990).
[CrossRef]

Jaeger, J. C.

H. S. Carslaw, J. C. Jaeger, Conduction of Heat in Solids (Clarendon Press, Oxford, 1959), Appendix IV, Table III.

Kohura, K.

A. Iino, M. Kuwabara, K. Kohura, “Mechanisms of hydrogen-induced losses in silica-based optical fibers,” IEEE J. Lightwave Technol. 8, 1675–1679 (1990).
[CrossRef]

Kritz, D.

Kuwabara, M.

A. Iino, M. Kuwabara, K. Kohura, “Mechanisms of hydrogen-induced losses in silica-based optical fibers,” IEEE J. Lightwave Technol. 8, 1675–1679 (1990).
[CrossRef]

Love, J. D.

A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983), Eq. (6-8).

MacCraith, B. D.

McCabe, S.

Miyagi, M.

M. Saito, M. Takizawa, M. Miyagi, “Optical and mechanical properties of infrared fibers,” IEEE J. Lightwave Technol. 6, 233–239 (1988).
[CrossRef]

Nassau, K.

K. Nassau, “The diffusion of water in optical fibers,” Mater. Res. Bull. 13, 67–76 (1978).
[CrossRef]

Newns, G. R.

B. J. Ainslie, P. W. France, G. R. Newns, “Water impurity in low loss silica fibers,” Mater. Res. Bull. 12, 481–487 (1977).
[CrossRef]

Querry, M. R.

Rabone, N. H.

J. D. Rush, K. J. Beales, D. M. Cooper, W. J. Duncan, N. H. Rabone, “Hydrogen related degradation in optical fibers: system implications and practical solution,” Br. Telecom. Technol. J. 2, 84–93 (1984).

Ruddy, V.

V. Ruddy, “An effective attenuation coefficient for evanescent wave spectroscopy using multimode fiber,” Fiber Integr. Opt. 9, 142–151 (1990), Eq. (9).

V. Ruddy, S. McCabe, B. D. MacCraith, “Detection of propane by IR-ATR in a teflon clad fluoride glass optical fiber,” Appl. Spectrosc. 44, 1461–1463 (1990).
[CrossRef]

Rush, J. D.

J. D. Rush, K. J. Beales, D. M. Cooper, W. J. Duncan, N. H. Rabone, “Hydrogen related degradation in optical fibers: system implications and practical solution,” Br. Telecom. Technol. J. 2, 84–93 (1984).

Ryzhik, J. M.

J. S. Gradshteyn, J. M. Ryzhik. Tables of Integrals, Series, and Products (Academic, New York, 1965), Section 6.511, No. 6.

Sacher, E.

E. Sacher, J. R. Susko, “Water permeation in Teflon FEP,” J. Appl. Polym. Sci. 24, 1997–2003 (1979).
[CrossRef]

Saito, M.

M. Saito, M. Takizawa, M. Miyagi, “Optical and mechanical properties of infrared fibers,” IEEE J. Lightwave Technol. 6, 233–239 (1988).
[CrossRef]

M. Saito, “Optical loss increase in an As–S glass infrared fiber due to water diffusion,” Appl. Opt. 26, 202–203 (1987).
[CrossRef] [PubMed]

M. Saito, M. Takizawa. “Teflon-clad As–S glass infrared fiber with low absorption loss,” J. Appl. Phys. 59, 1450–1452 (1986).
[CrossRef]

Sigel, G. H.

Snyder, A. W.

A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983), Eq. (6-8).

Susko, J. R.

E. Sacher, J. R. Susko, “Water permeation in Teflon FEP,” J. Appl. Polym. Sci. 24, 1997–2003 (1979).
[CrossRef]

Takizawa, M.

M. Saito, M. Takizawa, M. Miyagi, “Optical and mechanical properties of infrared fibers,” IEEE J. Lightwave Technol. 6, 233–239 (1988).
[CrossRef]

M. Saito, M. Takizawa. “Teflon-clad As–S glass infrared fiber with low absorption loss,” J. Appl. Phys. 59, 1450–1452 (1986).
[CrossRef]

Zhou, Q.

Appl. Opt. (3)

Appl. Spectrosc. (1)

Br. Telecom. Technol. J. (1)

J. D. Rush, K. J. Beales, D. M. Cooper, W. J. Duncan, N. H. Rabone, “Hydrogen related degradation in optical fibers: system implications and practical solution,” Br. Telecom. Technol. J. 2, 84–93 (1984).

Fiber Integr. Opt. (1)

V. Ruddy, “An effective attenuation coefficient for evanescent wave spectroscopy using multimode fiber,” Fiber Integr. Opt. 9, 142–151 (1990), Eq. (9).

IEEE J. Lightwave Technol. (2)

A. Iino, M. Kuwabara, K. Kohura, “Mechanisms of hydrogen-induced losses in silica-based optical fibers,” IEEE J. Lightwave Technol. 8, 1675–1679 (1990).
[CrossRef]

M. Saito, M. Takizawa, M. Miyagi, “Optical and mechanical properties of infrared fibers,” IEEE J. Lightwave Technol. 6, 233–239 (1988).
[CrossRef]

J. Appl. Phys. (1)

M. Saito, M. Takizawa. “Teflon-clad As–S glass infrared fiber with low absorption loss,” J. Appl. Phys. 59, 1450–1452 (1986).
[CrossRef]

J. Appl. Polym. Sci. (1)

E. Sacher, J. R. Susko, “Water permeation in Teflon FEP,” J. Appl. Polym. Sci. 24, 1997–2003 (1979).
[CrossRef]

Mater. Res. Bull. (2)

K. Nassau, “The diffusion of water in optical fibers,” Mater. Res. Bull. 13, 67–76 (1978).
[CrossRef]

B. J. Ainslie, P. W. France, G. R. Newns, “Water impurity in low loss silica fibers,” Mater. Res. Bull. 12, 481–487 (1977).
[CrossRef]

Other (5)

J. Crank, The Mathematics of Diffusion (Clarendon Press, Oxford, 1975), Eq. (5.22).

A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983), Eq. (6-8).

J. S. Gradshteyn, J. M. Ryzhik. Tables of Integrals, Series, and Products (Academic, New York, 1965), Section 6.511, No. 6.

M. Abramowitz, I. A. Stegun, eds., Handbook of Mathematical Functions (U.S. Government Printing Office, Washington, D.C., 1968), Eq. (12.1.4).

H. S. Carslaw, J. C. Jaeger, Conduction of Heat in Solids (Clarendon Press, Oxford, 1959), Appendix IV, Table III.

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Figures (2)

Fig. 1
Fig. 1

Fiber parameters.

Fig. 2
Fig. 2

Time-dependent attenuation of As2S3 fiber. The solid curve represents the best fit of Eq. (8) to the experimental data.

Tables (1)

Tables Icon

Table I Values of β n and C n in Eq. (8)

Equations (9)

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

c ( R , t ) c = 1 2 n exp ( B n 2 T ) J 0 ( B n R ) / B n J 1 ( B n ) ,
γ = ( a sin θ ) 1 0 a α ( r , t ) d r
P ( z ) = P ( o ) exp ( γ z ) .
γ ( θ , t ) = c sin θ [ 1 2 n exp ( B n 2 T ) B n J 1 ( B n ) 0 1 J 0 ( R B n ) d R ] ,
γ ( θ , t ) = c sin θ [ 1 π n exp ( B n 2 T ) B n H 0 ( B n ) ] ,
γ ( θ , t ) = c sin θ [ 1 n C n exp ( B n 2 T ) ] ,
γ ( t ) = C ln tan ( θ c / 2 ) ( π / 2 θ c ) [ 1 n C n exp ( B n 2 T ) ] ,
γ ( t ) = γ [ 1 n C n exp ( B n 2 T ) ] with n C n = 1 .
γ = 5 . 8 dB / m ; D / a 2 = 1 . 4625 × 10 3 days 1

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