Abstract

The static thermal sensitivity of the optical phase in bare and jacketed fibers has been studied both analytically and experimentally. Taking into account the exact fiber composition and geometry, the strains have been determined from the thermally induced stresses using the appropriate boundary conditions, and the resulting phase shift has been calculated. The results of this analysis are found to be in agreement with experimental results obtained from measurements employing a Mach-Zehnder fiber interferometer.

© 1981 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]
  3. B. Budiansky, D. C. Drucker, G. S. Kino, J. R. Rice, Appl. Opt. 18, 4085 (1979).
    [CrossRef] [PubMed]
  4. J. F. Nye, Physical Properties of Crystals (Oxford U.P., New York, 1976).
  5. S. P. Timoshenko, J. N. Goudier, Theory of Elasticity (McGraw-Hill, New York, 1970), Chap. 4.
  6. N. Lagakos, J. A. Bucaro, R. Hughes, Appl. Opt. 19, 3668 (1980).
    [CrossRef] [PubMed]
  7. G. Weast, Ed., Handbook of Chemistry and Physics (CRC Press, Cleveland, 1975).
  8. T. Izawa, T. Miyashita, F. Hanawa, U.S. Patent4,062,655 (Dec.1977).
  9. R. Bruckner, J. Non-Cryst. Solids 5, 123 (1970).
    [CrossRef]
  10. R. Hughes, J. Jarzynski, Appl. Opt. 19, 98 (1980).
    [CrossRef] [PubMed]
  11. General Electric, Technical Data Book, S-35A.
  12. N. Lagakos, J. Jarzynski (unpublished results).
  13. Du Pont, HYT-501A data sheet.
  14. G. N. Ramachandran, Proc. Ind. Acad. Sci. 25, 498 (1947).

1980 (3)

1979 (2)

1970 (1)

R. Bruckner, J. Non-Cryst. Solids 5, 123 (1970).
[CrossRef]

1947 (1)

G. N. Ramachandran, Proc. Ind. Acad. Sci. 25, 498 (1947).

Bruckner, R.

R. Bruckner, J. Non-Cryst. Solids 5, 123 (1970).
[CrossRef]

Bucaro, J. A.

Budiansky, B.

Drucker, D. C.

Goudier, J. N.

S. P. Timoshenko, J. N. Goudier, Theory of Elasticity (McGraw-Hill, New York, 1970), Chap. 4.

Hanawa, F.

T. Izawa, T. Miyashita, F. Hanawa, U.S. Patent4,062,655 (Dec.1977).

Hocker, G. B.

Hughes, R.

Izawa, T.

T. Izawa, T. Miyashita, F. Hanawa, U.S. Patent4,062,655 (Dec.1977).

Jarzynski, J.

R. Hughes, J. Jarzynski, Appl. Opt. 19, 98 (1980).
[CrossRef] [PubMed]

N. Lagakos, J. Jarzynski (unpublished results).

Kino, G. S.

Lagakos, N.

Miyashita, T.

T. Izawa, T. Miyashita, F. Hanawa, U.S. Patent4,062,655 (Dec.1977).

Nye, J. F.

J. F. Nye, Physical Properties of Crystals (Oxford U.P., New York, 1976).

Ramachandran, G. N.

G. N. Ramachandran, Proc. Ind. Acad. Sci. 25, 498 (1947).

Rice, J. R.

Sugawara, Y.

Tanaka, S.

Tateda, M.

Timoshenko, S. P.

S. P. Timoshenko, J. N. Goudier, Theory of Elasticity (McGraw-Hill, New York, 1970), Chap. 4.

Appl. Opt. (5)

J. Non-Cryst. Solids (1)

R. Bruckner, J. Non-Cryst. Solids 5, 123 (1970).
[CrossRef]

Proc. Ind. Acad. Sci. (1)

G. N. Ramachandran, Proc. Ind. Acad. Sci. 25, 498 (1947).

Other (7)

G. Weast, Ed., Handbook of Chemistry and Physics (CRC Press, Cleveland, 1975).

T. Izawa, T. Miyashita, F. Hanawa, U.S. Patent4,062,655 (Dec.1977).

General Electric, Technical Data Book, S-35A.

N. Lagakos, J. Jarzynski (unpublished results).

Du Pont, HYT-501A data sheet.

J. F. Nye, Physical Properties of Crystals (Oxford U.P., New York, 1976).

S. P. Timoshenko, J. N. Goudier, Theory of Elasticity (McGraw-Hill, New York, 1970), Chap. 4.

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Figures (5)

Fig. 1
Fig. 1

Fiber geometry: core (A), clad (B), substrate (C), soft coating (D), hard coating (E).

Fig. 2
Fig. 2

Mach-Zehnder interferometer arrangement for measuring the temperature-induced phase shift in a single-mode fiber.

Fig. 3
Fig. 3

Calculated temperature sensitivity, Δϕ/ϕΔT, and its contributions to the jacketed-fiber vs Hytrel thickness. z l is the part due to the length change, and r p and z p are the refractive-index modulation terms.

Fig. 4
Fig. 4

Calculated temperature sensitivity, Δϕ/ϕΔT, and its contributions to the jacketed-fiber vs thermal expansion coefficient of the outer hard coating.

Fig. 5
Fig. 5

Calculated temperature sensitivity, Δϕ/ϕΔT, and its contributions to the jacketed-fiber vs Young's modulus of the outer hard coating.

Tables (1)

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Table I Temperature Sensitivity of Two Commercially Available (ITT) Fibers

Equations (16)

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ϕ = nkl ,
Δ ϕ ϕ = Δ l l + Δ n n = z + 1 n ( n T ) ρ Δ T + ( δ n n ) T ,
Δ ϕ ϕ Δ T = 1 n ( n T ) ρ + 1 Δ T { z n 2 2 [ ( P 11 + P 12 ) r + P 12 z ] } .
[ 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 θ i z i ] ,
λ i = ν i E i ( 1 + ν i ) ( 1 2 ν i ) , μ i = E i 2 ( 1 + ν i ) .
r i = U 0 i + U 1 i r 2 , θ i = U 0 i U 1 i r 2 , z i = W o i ,
i = α i Δ T ,
r i r i α i Δ T , θ i θ i α i Δ T , z i z i α i Δ T .
σ r i | r = r i = σ r i + 1 | , ( i = 0 , 1 , , m 1 ) ,
u r i | r = r i = u r i + 1 | r = r i , ( i = 0 , 1 , , m 1 ) ,
σ r m | r = r m = 0 ,
i = 0 m σ z i A i = 0 ,
z 0 = z 1 = = z m ,
Δ ϕ ϕ Δ T | bare , exp = 0.68 × 10 5 / ° C , Δ ϕ ϕ Δ T | jack . , exp = 1.80 × 10 5 / ° C .
Δ ϕ ϕ Δ T | bare , anal = 0.70 × 10 5 / ° C , Δ ϕ ϕ Δ T | jack . , anal = 1.64 × 10 5 / ° C .
Δ ϕ ϕ Δ T

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