Abstract

Thermal characteristics of optical pulse transit time delay and fiber strain in a single-mode optical fiber cable are investigated theoretically and experimentally. Measurements of the transit time delay shift are made by a spatial interference technique using a 1.5-m long fiber, six-fiber unit, and cable. Experimental results for a jacketed fiber whose fiber axis is well centered in nylon coating are in good agreement with those predicted from the theory. A jacketed fiber whose fiber axis is positioned eccentrically from the jacket center exhibits a small change in fiber strain at low temperature due to fiber buckling compared with that for the well-centered jacketed fiber. The loss increase for the off-centered jacketed fiber is explained by the buckling model. Furthermore, thermal characteristics of the unit-type cable examined here are found to coincide with those for the constituent six-fiber unit.

© 1983 Optical Society of America

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References

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  1. L. G. Cohen, J. W. Fleming, Bell Syst. Tech. J. 58, 945 (1979).
  2. A. H. Hartog, A. J. Conduit, D. N. Payne, Opt. Quantum Electron. 11, 265 (1979).
    [CrossRef]
  3. M. Tateda, S. Tanaka, Y. Sugawara, Appl. Opt. 19, 770 (1980).
    [CrossRef] [PubMed]
  4. N. Shibata, M. Tateda, S. Seikai, N. Uchida, Appl. Opt. 19, 1489 (1980).
    [CrossRef] [PubMed]
  5. N. Shibata, Y. Katsuyama, M. Tateda, S. Seikai, Electron. Lett. 17, 345 (1981).
    [CrossRef]
  6. S. E. Miller, A. G. Chynoweth, Optical Fiber Telecommunications (Academic, New York, 1979).
  7. N. Uchida, Y. Ishida, K. Ishihara, “Single-Mode and Graded-Index Mutimode Optical Cables for Use in Long Wavelength Transmission Systems,” at International Conference on Communications, Seattle, June 1981, p. 27-5.
  8. S. P. Timoshenko, J. N. Goodier, Theory of Elasticity (McGraw-Hill, New York, 1970).
  9. Y. Katsuyama, Y. Mitsunaga, Y. Ishida, K. Ishihara, Appl. Opt. 19, 4200 (1980).
    [CrossRef] [PubMed]
  10. D. Marcuse, J. Opt. Soc. Am. 66, 216 (1976).
    [CrossRef]

1981 (1)

N. Shibata, Y. Katsuyama, M. Tateda, S. Seikai, Electron. Lett. 17, 345 (1981).
[CrossRef]

1980 (3)

1979 (2)

L. G. Cohen, J. W. Fleming, Bell Syst. Tech. J. 58, 945 (1979).

A. H. Hartog, A. J. Conduit, D. N. Payne, Opt. Quantum Electron. 11, 265 (1979).
[CrossRef]

1976 (1)

Chynoweth, A. G.

S. E. Miller, A. G. Chynoweth, Optical Fiber Telecommunications (Academic, New York, 1979).

Cohen, L. G.

L. G. Cohen, J. W. Fleming, Bell Syst. Tech. J. 58, 945 (1979).

Conduit, A. J.

A. H. Hartog, A. J. Conduit, D. N. Payne, Opt. Quantum Electron. 11, 265 (1979).
[CrossRef]

Fleming, J. W.

L. G. Cohen, J. W. Fleming, Bell Syst. Tech. J. 58, 945 (1979).

Goodier, J. N.

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

Hartog, A. H.

A. H. Hartog, A. J. Conduit, D. N. Payne, Opt. Quantum Electron. 11, 265 (1979).
[CrossRef]

Ishida, Y.

Y. Katsuyama, Y. Mitsunaga, Y. Ishida, K. Ishihara, Appl. Opt. 19, 4200 (1980).
[CrossRef] [PubMed]

N. Uchida, Y. Ishida, K. Ishihara, “Single-Mode and Graded-Index Mutimode Optical Cables for Use in Long Wavelength Transmission Systems,” at International Conference on Communications, Seattle, June 1981, p. 27-5.

Ishihara, K.

Y. Katsuyama, Y. Mitsunaga, Y. Ishida, K. Ishihara, Appl. Opt. 19, 4200 (1980).
[CrossRef] [PubMed]

N. Uchida, Y. Ishida, K. Ishihara, “Single-Mode and Graded-Index Mutimode Optical Cables for Use in Long Wavelength Transmission Systems,” at International Conference on Communications, Seattle, June 1981, p. 27-5.

Katsuyama, Y.

N. Shibata, Y. Katsuyama, M. Tateda, S. Seikai, Electron. Lett. 17, 345 (1981).
[CrossRef]

Y. Katsuyama, Y. Mitsunaga, Y. Ishida, K. Ishihara, Appl. Opt. 19, 4200 (1980).
[CrossRef] [PubMed]

Marcuse, D.

Miller, S. E.

S. E. Miller, A. G. Chynoweth, Optical Fiber Telecommunications (Academic, New York, 1979).

Mitsunaga, Y.

Payne, D. N.

A. H. Hartog, A. J. Conduit, D. N. Payne, Opt. Quantum Electron. 11, 265 (1979).
[CrossRef]

Seikai, S.

N. Shibata, Y. Katsuyama, M. Tateda, S. Seikai, Electron. Lett. 17, 345 (1981).
[CrossRef]

N. Shibata, M. Tateda, S. Seikai, N. Uchida, Appl. Opt. 19, 1489 (1980).
[CrossRef] [PubMed]

Shibata, N.

N. Shibata, Y. Katsuyama, M. Tateda, S. Seikai, Electron. Lett. 17, 345 (1981).
[CrossRef]

N. Shibata, M. Tateda, S. Seikai, N. Uchida, Appl. Opt. 19, 1489 (1980).
[CrossRef] [PubMed]

Sugawara, Y.

Tanaka, S.

Tateda, M.

Timoshenko, S. P.

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

Uchida, N.

N. Shibata, M. Tateda, S. Seikai, N. Uchida, Appl. Opt. 19, 1489 (1980).
[CrossRef] [PubMed]

N. Uchida, Y. Ishida, K. Ishihara, “Single-Mode and Graded-Index Mutimode Optical Cables for Use in Long Wavelength Transmission Systems,” at International Conference on Communications, Seattle, June 1981, p. 27-5.

Appl. Opt. (3)

Bell Syst. Tech. J. (1)

L. G. Cohen, J. W. Fleming, Bell Syst. Tech. J. 58, 945 (1979).

Electron. Lett. (1)

N. Shibata, Y. Katsuyama, M. Tateda, S. Seikai, Electron. Lett. 17, 345 (1981).
[CrossRef]

J. Opt. Soc. Am. (1)

Opt. Quantum Electron. (1)

A. H. Hartog, A. J. Conduit, D. N. Payne, Opt. Quantum Electron. 11, 265 (1979).
[CrossRef]

Other (3)

S. E. Miller, A. G. Chynoweth, Optical Fiber Telecommunications (Academic, New York, 1979).

N. Uchida, Y. Ishida, K. Ishihara, “Single-Mode and Graded-Index Mutimode Optical Cables for Use in Long Wavelength Transmission Systems,” at International Conference on Communications, Seattle, June 1981, p. 27-5.

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

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Figures (10)

Fig. 1
Fig. 1

Jacketed fiber, six-fiber unit, and cable structures used in the experiments.

Fig. 2
Fig. 2

Fiber cross-sectional areas for two jacketed fibers.

Fig. 3
Fig. 3

Two-beam interferometer for measuring the transit time delay shift due to temperature change: S, pulsed laser diode; F1, reference bare fiber; F2, test fiber; HM1 and HM2, half-mirrors; M1,M2,M3, mirrors; P, polarizer; D, Si-vidicon.

Fig. 4
Fig. 4

Relationship between the optical path difference and fringe visibility at various temperatures for fiber 1. The arrows above the horizontal axis indicate the maximum visibility positions at each temperature.

Fig. 5
Fig. 5

Temperature dependence of the transit time delay shift for fiber 1.

Fig. 6
Fig. 6

Tensile strength dependence of the transit time delay shift for fiber 1.

Fig. 7
Fig. 7

Young’s modulus of nylon as a function of temperature.

Fig. 8
Fig. 8

Calculated thermal coefficient of fiber stress for jacketed fiber and a six-fiber unit as a function of temperature.

Fig. 9
Fig. 9

Transit time delay shift as a function of temperature for (a) fiber 2 and (b) fiber 3 with the forms of a jacketed fiber, six-fiber unit, and cable.

Fig. 10
Fig. 10

Fiber strain as a function of temperature for (a) jacketed fiber structure and (b) six-fiber unit and cable structures.

Tables (3)

Tables Icon

Table I Structural Parameters of Test Fibers

Tables Icon

Table II Values of Young’s Modulus and Thermal Expansion Coefficient for Constituent Materials

Tables Icon

Table III Magnitudes of Fiber Strain for Fibers 2 and 3 with Jacketed Fiber, Six-Fiber Unit, and Cable

Equations (13)

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( d τ / d T ) e = ( τ / σ ) f ( d σ f / d T ) e + ( τ / T ) f ,
[ τ ( T ) ] e = [ τ ( T 0 ) ] e + ( τ / σ ) f T 0 T ( d σ f / d T ) e d T + ( τ / T ) f ( T T 0 ) ,
( d σ f / d T ) j = ( k s k f ) A s E s + ( k n k f ) A n E n ( T ) A f E f + A s E s + A n E n ( T ) E f ,
( d σ f / d T ) u = 6 [ ( k s k f ) A s E s + ( k n k f ) A n E n ( T ) ] + ( k m k f ) A m E m 6 [ A f E f + A s E s + A n E n ( T ) ] + A m E m E f ,
( d f / d T ) e = ( 1 / E f ) ( d σ f / d T ) e + k f .
[ f ( T ) ] e = [ f ( T 0 ) ] e + T 0 T [ k eff ] e d T .
[ k eff ] j = k f A f E f + k s A s E s + k n A n E n ( T ) A f E f + A s E s + A n E n ( T ) ,
[ k eff ] u = 6 [ k f A f E f + k s A s E s + k n A n E n ( T ) ] + k m A m E m 6 [ A f E f + A s E s + A n E n ( T ) ] + A m E m .
[ k eff ] e = k f + ( 1 / E f ) ( d τ / d T ) e ( τ / T ) f ( τ / σ ) F .
[ f ( T ) ] e = [ f ( T 0 ) ] e + [ k f ( 1 / E f ) ( τ / T ) f ( τ / σ ) f ] ( T T 0 ) + ( 1 / E f ) [ τ ( T ) ] e [ τ ( T 0 ) ] e ( τ / σ ) f .
[ k eff ] c = k i E i ( A i ) i = f , s , n , m , t , p E i ( A i ) i = f , s , n , m , t , p ,
ρ = b 2 * 4 π E f 4 E s ,
α = π κ 2 exp [ ( 2 / 3 ) ( γ 3 / β 2 ) ρ ] 2 γ 3 / 2 υ 2 ρ K 1 ( γ a ) K 1 ( γ a ) ,

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