Abstract

The dynamic temperature phase sensitivity of a three-layer optical fiber is calculated for unjacketed as well as Al- and Hytrel-coated fibers. The calculations include both the variation of the refractive index with temperature and the thermally induced axial and radial strains. The calculated phase sensitivity indicates that it is currently possible to measure a 1-μ°C temperature change at frequencies exceeding 50 kHz with 1 cm of a metal coated optical fiber.

© 1983 Optical Society of America

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References

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  1. G. B. Hocker, Appl. Opt. 18, 1445 (1979).
    [CrossRef] [PubMed]
  2. M. Tateda, S. Tanaka, Y. Sugawara, Appl. Opt. 19, 770 (1980).
    [CrossRef] [PubMed]
  3. W. Eickhoff, Opt. Lett. 6, 204 (1981).
    [CrossRef] [PubMed]
  4. T. Musha, J. Kamimura, M. Nakazawa, Appl. Opt. 21, 694 (1982).
    [CrossRef] [PubMed]
  5. N. Lagakos, J. A. Bucaro, J. Jarzynski, Appl. Opt. 20, 2305 (1981).
    [CrossRef] [PubMed]
  6. N. Lagakos, J. A. Bucaro, Appl. Opt. 20, 3276 (1981).
    [CrossRef] [PubMed]
  7. R. Hughes, R. Priest, Appl. Opt. 19, 1477 (1980).
    [CrossRef] [PubMed]
  8. W. Nowacki, I. N. Sneddon, Thermomechanics in Solids (Springer, New York, 1974), p. 8.
  9. N. M. Ozisik, Basic Heat Transfer (McGraw-Hill, New York, 1976), Chap. 8.
  10. J. F. Nye, Physical Properties of Crystals (Clarendon, Oxford, 1957), p. 176.
  11. B. Budiansky, D. C. Drucker, G. S. Kino, J. R. Rice, Appl. Opt. 18, 4085 (1979).
    [CrossRef] [PubMed]
  12. J. A. Bucaro, J. H. Cole, J. Jarzynski, W. K. Burns, T. G. Giallorenzi, “Optical Fiber Sensor Development,” in Physics of Fibers, Vol. 2, B. Bendow, S. S. Mitra, Eds. (American Ceramic Society, Columbus, Ohio, 1981.
  13. J. H. Cole, T. G. Giallorenzi, J. A. Bucaro, in Proceedings, Fiber Optics and Communication. (Information Gatekeepers, Inc., Brookline, Mass, March1981).

1982 (1)

1981 (3)

1980 (2)

1979 (2)

Bucaro, J. A.

N. Lagakos, J. A. Bucaro, J. Jarzynski, Appl. Opt. 20, 2305 (1981).
[CrossRef] [PubMed]

N. Lagakos, J. A. Bucaro, Appl. Opt. 20, 3276 (1981).
[CrossRef] [PubMed]

J. H. Cole, T. G. Giallorenzi, J. A. Bucaro, in Proceedings, Fiber Optics and Communication. (Information Gatekeepers, Inc., Brookline, Mass, March1981).

J. A. Bucaro, J. H. Cole, J. Jarzynski, W. K. Burns, T. G. Giallorenzi, “Optical Fiber Sensor Development,” in Physics of Fibers, Vol. 2, B. Bendow, S. S. Mitra, Eds. (American Ceramic Society, Columbus, Ohio, 1981.

Budiansky, B.

Burns, W. K.

J. A. Bucaro, J. H. Cole, J. Jarzynski, W. K. Burns, T. G. Giallorenzi, “Optical Fiber Sensor Development,” in Physics of Fibers, Vol. 2, B. Bendow, S. S. Mitra, Eds. (American Ceramic Society, Columbus, Ohio, 1981.

Cole, J. H.

J. H. Cole, T. G. Giallorenzi, J. A. Bucaro, in Proceedings, Fiber Optics and Communication. (Information Gatekeepers, Inc., Brookline, Mass, March1981).

J. A. Bucaro, J. H. Cole, J. Jarzynski, W. K. Burns, T. G. Giallorenzi, “Optical Fiber Sensor Development,” in Physics of Fibers, Vol. 2, B. Bendow, S. S. Mitra, Eds. (American Ceramic Society, Columbus, Ohio, 1981.

Drucker, D. C.

Eickhoff, W.

Giallorenzi, T. G.

J. H. Cole, T. G. Giallorenzi, J. A. Bucaro, in Proceedings, Fiber Optics and Communication. (Information Gatekeepers, Inc., Brookline, Mass, March1981).

J. A. Bucaro, J. H. Cole, J. Jarzynski, W. K. Burns, T. G. Giallorenzi, “Optical Fiber Sensor Development,” in Physics of Fibers, Vol. 2, B. Bendow, S. S. Mitra, Eds. (American Ceramic Society, Columbus, Ohio, 1981.

Hocker, G. B.

Hughes, R.

Jarzynski, J.

N. Lagakos, J. A. Bucaro, J. Jarzynski, Appl. Opt. 20, 2305 (1981).
[CrossRef] [PubMed]

J. A. Bucaro, J. H. Cole, J. Jarzynski, W. K. Burns, T. G. Giallorenzi, “Optical Fiber Sensor Development,” in Physics of Fibers, Vol. 2, B. Bendow, S. S. Mitra, Eds. (American Ceramic Society, Columbus, Ohio, 1981.

Kamimura, J.

Kino, G. S.

Lagakos, N.

Musha, T.

Nakazawa, M.

Nowacki, W.

W. Nowacki, I. N. Sneddon, Thermomechanics in Solids (Springer, New York, 1974), p. 8.

Nye, J. F.

J. F. Nye, Physical Properties of Crystals (Clarendon, Oxford, 1957), p. 176.

Ozisik, N. M.

N. M. Ozisik, Basic Heat Transfer (McGraw-Hill, New York, 1976), Chap. 8.

Priest, R.

Rice, J. R.

Sneddon, I. N.

W. Nowacki, I. N. Sneddon, Thermomechanics in Solids (Springer, New York, 1974), p. 8.

Sugawara, Y.

Tanaka, S.

Tateda, M.

Appl. Opt. (7)

Opt. Lett. (1)

Other (5)

W. Nowacki, I. N. Sneddon, Thermomechanics in Solids (Springer, New York, 1974), p. 8.

N. M. Ozisik, Basic Heat Transfer (McGraw-Hill, New York, 1976), Chap. 8.

J. F. Nye, Physical Properties of Crystals (Clarendon, Oxford, 1957), p. 176.

J. A. Bucaro, J. H. Cole, J. Jarzynski, W. K. Burns, T. G. Giallorenzi, “Optical Fiber Sensor Development,” in Physics of Fibers, Vol. 2, B. Bendow, S. S. Mitra, Eds. (American Ceramic Society, Columbus, Ohio, 1981.

J. H. Cole, T. G. Giallorenzi, J. A. Bucaro, in Proceedings, Fiber Optics and Communication. (Information Gatekeepers, Inc., Brookline, Mass, March1981).

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Figures (4)

Fig. 1
Fig. 1

Normalized fiber phase response for three fiber types as a function of frequency. The horizontal line represents the limit for the aluminum jacket where the aluminum is at the fiber surface temperature and the silica is at ambient, T(o).

Fig. 2
Fig. 2

Magnitude of the contributing components to the normalized phase response for the unjacketed fiber as a function of frequency.

Fig. 3
Fig. 3

Magnitude of the contributing components to the normalized phase response for the metal coated fiber as a function of frequency

Fig. 4
Fig. 4

Magnitude of the contributing components to the normalized phase response for the Hytrel coated fiber as a function of frequency. Note that the frequency is plotted on a semilog axis to better illustrate the rapid decrease in response at low frequencies.

Tables (1)

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Table I Fiber Parameters

Equations (35)

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E = 1 2 ( u + u T ) ,
div S = ρ u ¨ ,
S = 2 μ E + { λ ( t r E ) + M T } 1 ,
div q + M T 0 t r E ˙ = ρ c T ˙ ,
q = k T .
α i 1 r r ( r T i r ) = T i t ,
k i T i r = k i + 1 T i + 1 r
T i ( r , t ) = f ( t ) + Γ i ( r , t ) , Γ i ( r , t ) = j = 1 m τ = 0 t d τ a j a j + i r G i j ( r , t | r , τ ) [ d f ( τ ) d τ ] d r ,
G i j ( r , t | r , τ ) = n = 1 exp [ β n 2 ( t τ ) ] 1 N n k j α j ψ i n ( r ) ψ i n ( r ) , N n = j = 1 k j α j a j 1 a j r ψ j n 2 ( r ) d r , ψ i n ( r ) = A 1 i n J 0 ( β n α i r ) + A 2 i n Y 0 ( β n α i r ) ,
f ( t ) = Re [ j W exp ( j ω 0 t ) ] ,
T i ( r , t ) = Re { j W exp ( j ω 0 t n = 1 ω 0 W β n 2 D n ψ i n ( r ) · ( j ω o + β 2 β n 4 + ω 0 2 ) [ exp ( j ω 0 t ) exp ( β n 2 t ) ] }
D n = 1 N n β n 2 h = 1 m k h α h a h 1 a h r ψ h n ( r ) d r .
[ σ r i σ θ i σ z i ] = [ λ i + 2 μ i λ i λ i λ i λ i + 2 μ i λ i λ i λ i λ i + 2 μ i ] [ r i γ i T θ i γ i T z i γ i T ] ,
σ r r + σ r σ θ r = 0 ,
r = u r d r , θ = u r r ,
d d r 1 r d ( r u r ) d r = L i d T d r ,
L i = γ i ( 3 λ i + 2 μ i ) λ i + 2 μ i ,
u r = L i r a i 1 r r T ( r ) d r + C i r + D i r , r = L i T ( r ) L i r 2 a i 1 r r T ( r ) d r + C i D i r 2 .
| Δ ϕ ϕ T a | = | 1 n ( n T ) T ( o , t ) T a + 1 T a [ z ( 0 , t ) ( 1 n 2 P 12 2 ) r ( 0 , t ) n 2 2 ( P 11 + P 12 ) ] | ,
T min = 1 k n l 2 h ν Δ f q W 0 ( Δ ϕ ϕ T a ) ,
u z = W 0 z ,
ρ u ¨ z = ρ ω 0 2 W 0 z .
| div S | z component = σ z z = ρ u ¨ z .
σ ˆ z = 0.5 ρ ω 2 W 0 z 2 .
z = 0.5 ρ ω 2 W 0 z 2 Y ˆ ,
0.5 ρ ω 2 W 0 z 2 Y ˆ W 0 ,
ω 1 z 2 Y ˆ ρ .
Y ˆ 70 × 10 10 dyn / cm 2 and ρ 2 gm / cm 2 respectively ; resulting in ω 1 z ( 8 × 10 5 ) cm / sec .
Y ˆ 3 × 10 10 dyn / cm 2 and ρ 1.3 gm / cm 3 , respectively ; yielding f 0 = ω 2 π 34 kHz for a 1 - cm length of fiber .
Q d d t ,
P r = 3 γ 2 ( 3 λ + 2 μ ) T 0 ρ c 1.
J 0 ( η 1 a 1 ) J 0 ( η 2 a 1 ) Y 0 ( η 2 a 1 ) 0 0 K 1 J 1 ( η 1 a 1 ) J 1 ( η 2 a 1 ) Y 1 ( η 2 a 1 ) 0 0 0 J 0 ( η 2 a 2 ) Y 0 ( η 2 a 2 ) J 0 ( η 3 a 3 ) Y 0 ( η 3 a 3 ) 0 K 2 J 1 ( η 2 a 2 ) K 2 Y 1 ( η 2 a 2 ) J 1 ( η 3 a 2 ) Y 1 ( η 3 a 2 ) 0 0 0 J 0 ( η 3 a 3 ) Y 0 ( η 3 a 3 ) ,
η i = β n / α i , K i = k i k i + 1 α i + 1 α i ,
[ J 0 ( η 2 a 1 ) Y 0 ( η 2 a 1 ) 0 0 J 1 ( η 2 a 1 ) Y 1 ( η 2 a 1 ) 0 0 J 0 ( η 2 a 2 ) Y 0 ( η 2 a 2 ) J 0 ( η 3 a 2 ) Y 0 ( η 3 a 2 ) K 2 J 1 ( η 2 a 2 ) K 2 Y 1 ( η 2 a 2 ) J 1 ( η 3 a 2 ) Y 1 ( η 3 a 2 ) ] [ A 12 n A 22 n A 13 n A 23 n = J 0 ( η 1 a 1 ) K 1 J 1 ( η 1 a 1 ) 0 0 ] .
[ ( λ 1 + μ 1 ) a 2 , ( λ 2 + μ 2 ) a 1 , μ 2 , 0 , 0 , 1 2 ( λ 1 + λ 2 ) a 1 2 μ a 1 2 , μ a 1 2 , μ 1 , 0 , 0 , 0 0 , ( λ 2 + μ 2 ) a 2 2 , μ 2 , ( λ 3 + μ 3 ) a 2 2 , μ 3 , 1 2 ( λ 2 λ 3 ) a 2 0 , μ 2 a 2 2 , + μ 2 , μ 2 a 2 2 , μ 2 , 0 0 , 0 , 0 , ( λ 3 + μ 3 ) a 3 2 , μ 3 , λ 3 a 3 2 λ 1 a 1 2 , λ 2 ( a 2 2 a 1 2 ) , 0 , λ 3 ( a 3 2 a 2 2 ) , 0 , 1 2 i = 1 3 ( λ i + 2 μ i ) ( a 2 a i 1 2 ) ] [ C 1 C 2 D C 3 D 3 W 0 ] = [ μ 1 L 1 a 0 a 1 r T ( r ) d r μ 1 L 1 a 0 a 1 r T ( r ) d r μ 2 L 2 a 1 a 2 r T ( r ) d r μ 2 L 2 a 1 a 2 r T ( r ) d r μ 3 L 3 a 2 a 3 r T ( r ) d r i = 1 3 2 μ i L i a i 1 a i r T ( r ) d r . ]

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