Abstract

The use of a fiber-optic Mach-Zehnder interferometer to measure differences in temperature or pressure between two single-mode fiber arms is described. Temperature or pressure changes are observed as a motion of an optical interference fringe pattern. Values are calculated for the pressure and temperature dependence of the fringe motion. Pressure and temperature measurements are made with the interferometer, and the experimental values for sensitivity are in good agreement with those calculated.

© 1979 Optical Society of America

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References

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  1. C. D. Butter, G. B. Hocker, Appl. Opt. 17, 2867 (1978).
    [CrossRef] [PubMed]
  2. C. D. Butter, G. B. Hocker, “Fiber Optic Strain Gauge,” presented at Electro Optics/Laser 78, 19–21 September 1978, Boston, Mass.
  3. J. A. Bucaro et al., Appl. Opt. 16, 1761 (1977).
    [CrossRef] [PubMed]
  4. D. A. Pinnow, “Elastooptical Materials,” in Handbook of Lasers, R. J. Pressley, Ed. (CRC, Cleveland, Ohio, 1971).
  5. G. B. Hocker, W. K. Burns, IEEE J. Quantum Electron. QE-11, 270 (1975); D. B. Keck, in Fundamentals of Optical Fiber Communications, M. K. Barnoski, Ed. (Academic, New York, 1976), Chap. 1.
    [CrossRef]
  6. “Optical Fused Quartz and Fused Silica,” Amersil Inc. publication EM-9227 (1975).
  7. D. E. Gray, Ed., AIP Handbook (McGraw-Hill, New York, 1972), p. 6–29.
  8. G. B. Morey, “Properties of Glass,” in International Critical Tables, Vol. 2 (McGraw-Hill, New York, 1933).
  9. M. Hudson, Valtec Corporation; private communication.

1978

1977

1975

G. B. Hocker, W. K. Burns, IEEE J. Quantum Electron. QE-11, 270 (1975); D. B. Keck, in Fundamentals of Optical Fiber Communications, M. K. Barnoski, Ed. (Academic, New York, 1976), Chap. 1.
[CrossRef]

“Optical Fused Quartz and Fused Silica,” Amersil Inc. publication EM-9227 (1975).

Bucaro, J. A.

Burns, W. K.

G. B. Hocker, W. K. Burns, IEEE J. Quantum Electron. QE-11, 270 (1975); D. B. Keck, in Fundamentals of Optical Fiber Communications, M. K. Barnoski, Ed. (Academic, New York, 1976), Chap. 1.
[CrossRef]

Butter, C. D.

C. D. Butter, G. B. Hocker, Appl. Opt. 17, 2867 (1978).
[CrossRef] [PubMed]

C. D. Butter, G. B. Hocker, “Fiber Optic Strain Gauge,” presented at Electro Optics/Laser 78, 19–21 September 1978, Boston, Mass.

Hocker, G. B.

C. D. Butter, G. B. Hocker, Appl. Opt. 17, 2867 (1978).
[CrossRef] [PubMed]

G. B. Hocker, W. K. Burns, IEEE J. Quantum Electron. QE-11, 270 (1975); D. B. Keck, in Fundamentals of Optical Fiber Communications, M. K. Barnoski, Ed. (Academic, New York, 1976), Chap. 1.
[CrossRef]

C. D. Butter, G. B. Hocker, “Fiber Optic Strain Gauge,” presented at Electro Optics/Laser 78, 19–21 September 1978, Boston, Mass.

Hudson, M.

M. Hudson, Valtec Corporation; private communication.

Morey, G. B.

G. B. Morey, “Properties of Glass,” in International Critical Tables, Vol. 2 (McGraw-Hill, New York, 1933).

Pinnow, D. A.

D. A. Pinnow, “Elastooptical Materials,” in Handbook of Lasers, R. J. Pressley, Ed. (CRC, Cleveland, Ohio, 1971).

Amersil Inc. publication EM-9227

“Optical Fused Quartz and Fused Silica,” Amersil Inc. publication EM-9227 (1975).

Appl. Opt.

IEEE J. Quantum Electron.

G. B. Hocker, W. K. Burns, IEEE J. Quantum Electron. QE-11, 270 (1975); D. B. Keck, in Fundamentals of Optical Fiber Communications, M. K. Barnoski, Ed. (Academic, New York, 1976), Chap. 1.
[CrossRef]

Other

D. A. Pinnow, “Elastooptical Materials,” in Handbook of Lasers, R. J. Pressley, Ed. (CRC, Cleveland, Ohio, 1971).

C. D. Butter, G. B. Hocker, “Fiber Optic Strain Gauge,” presented at Electro Optics/Laser 78, 19–21 September 1978, Boston, Mass.

D. E. Gray, Ed., AIP Handbook (McGraw-Hill, New York, 1972), p. 6–29.

G. B. Morey, “Properties of Glass,” in International Critical Tables, Vol. 2 (McGraw-Hill, New York, 1933).

M. Hudson, Valtec Corporation; private communication.

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Figures (1)

Fig. 1
Fig. 1

Single-mode fiber-optic Mach-Zehnder interferometer used for temperature and pressure measurement.

Equations (24)

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σ = [ - P - P - P ] .
= [ x y z ] = [ - P ( 1 - 2 μ ) / E - P ( 1 - 2 μ ) / E - P ( 1 - 2 μ ) / E ] .
Δ ϕ = β Δ L + L Δ β .
β Δ L = β z L = - β ( 1 - 2 μ ) L P / E .
L Δ β = L d β d n Δ n + L d β d D Δ D .
( d β ) / ( d n ) = k 0 .
Δ ( 1 n 2 ) i = j = 1 6 p i j j
P i j = [ p 11 p 12 p 12 p 12 p 11 p 12 p 12 p 12 p 11 ] .
Δ ( 1 n 2 ) x , y , z = - p 11 P ( 1 - 2 μ ) / E - 2 p 12 P ( 1 - 2 μ ) / E = - ( P / E ) ( 1 - 2 μ ) ( p 11 + 2 p 12 ) .
Δ n = - 1 2 n 3 Δ ( 1 n 2 ) x , y = 1 2 n 3 ( P / E ) ( 1 - 2 μ ) ( 2 p 12 + p 11 ) .
Δ D = x D = - P D ( 1 - 2 μ ) / E .
b = β 2 / k 0 2 - n clad 2 n core 2 - n clad 2 V = k 0 D ( n core 2 - n clad 2 ) 1 / 2 } .
d β d D = d β d b d b d V d V d D ,
d V d D = k 0 ( n core 2 - n clad 2 ) 1 / 2 = V / D ,
d β d b = ( n core 2 - n clad 2 ) k 0 2 2 β = V 2 / 2 β D 2 ,
Δ ϕ = - β ( 1 - 2 μ ) L P / E + k 0 n 3 L ( P / E ) ( 1 - 2 μ ) ( 2 p 12 + p 11 ) / 2 - L P D ( 1 - 2 μ ) E ( V / D ) ( V 2 / 2 β D 2 ) d b d V ,
Δ ϕ P L = - β ( 1 - 2 μ ) E + β n 2 2 E ( 1 - 2 μ ) ( 2 p 12 + p 11 ) - V 3 ( 1 - 2 μ ) 2 β E D 2 d b d V .
n = 1.456 , λ = 0.633 × 10 - 6 m , β = 2 π n / λ = 1.446 × 10 7 m - 1 , μ = 0.17 , E = 7.0 × 10 10 N / m 2 , p 12 = + 0.270. p 11 = + 0.121 ,
Δ ϕ P L = - 13.63 × 10 - 5 + 9.55 × 10 - 5 - 9 × 10 - 8 = - 4.09 × 10 - 5 rad / Pa - m ,
Δ P L one fringe = 154 kPa - m = 22.3 psi - m .
Δ ϕ P L = - β ( 1 - 2 μ ) E + β n 2 2 E ( 1 - 2 μ ) ( 2 p 12 + p 11 ) .
Δ ϕ Δ T L = 2 π λ ( n L d L d T + d n d T ) ,
1 L d L d T = 5 × 10 - 7 / ° C ,             d n d T = 10 × 10 - 6 / ° C , n = 1.456 ,             λ = 0.6328 × 10 - 6 m ,
Δ ϕ Δ T L = 107 radians / ° C - m .

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