Abstract

Frequency-derived distributed optical-fiber sensing is a method for remote measurement of the spatial distribution of linear birefringence in an optical fiber, allowing a corresponding measurement of those external measurands that influence this birefringence. The method employs a pump–probe scheme, which, by use of the optical Kerr effect, generates an optical modulation of the probe beam, with a modulation frequency whose temporal variation maps the spatial distribution of birefringence. We provide a complete theoretical analysis of this method by using Jones calculus and graphic representation on the Poincaré sphere. The relevant characterization of the technique and some experimental results are also presented; these show good agreement with the theory.

© 2000 Optical Society of America

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Corrections

Farhad Parvaneh, Vincent A. Handerek, and Alan J. Rogers, "Frequency-derived distributed optical-fiber sensing technique: theory and characterization—errata," Appl. Opt. 39, 6150-6150 (2000)
https://www.osapublishing.org/ao/abstract.cfm?uri=ao-39-33-6150

References

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  1. A. J. Rogers, Essentials of Optoelectronics (Chapman & Hall, London, 1997), Chap. 9, p. 314.
  2. A. J. Rogers, V. A. Handerek, “Novel methods for distributed optical fiber sensing,” in Distributed and Multiplexed Fiber Optic Sensors, A. D. Kersey, J. P. Dakin, eds., Proc. SPIE1586, 2–12 (1991).
    [CrossRef]
  3. F. Parvaneh, L. C. G. Valente, V. A. Handerek, A. J. Rogers, “Forward-scatter frequency-derived distributed optical fibre sensing using the optical Kerr-effect,” Electron. Lett. 28, 1080–1082 (1992).
    [CrossRef]
  4. F. Parvaneh, V. A. Handerek, A. J. Rogers, “Frequency-derived remote measurement of birefringence in polarization-maintaining fiber by using the optical Kerr effect,” Opt. Lett. 17, 1346–1348 (1992).
    [CrossRef] [PubMed]
  5. W. Zhao, E. Bourkoff, “Nonlinear polarization coupling and its application to high resolution distributed fibre sensing,” IEEE J. Quantum Electron. 29, 2198–2210 (1993).
    [CrossRef]
  6. R. Feced, S. E. K. Kanellopoulos, M. Farhadiroushan, V. A. Handerek, A. J. Rogers, “Analysis of optical Kerr induced coupling among polarization modes in high-birefringence optical fibres,” Opt. Commun. 143, 268–278 (1997).
    [CrossRef]
  7. F. Parvaneh, M. Farhadiroushan, V. A. Handerek, A. J. Rogers, “Single-shot distributed optical-fiber temperature sensing by the frequency-derived technique,” Opt. Lett. 22, 343–345 (1997).
    [CrossRef] [PubMed]
  8. F. Parvaneh, M. Farhadiroushan, V. H. Handerek, A. J. Rogers, “High-resolution optical-fibre distributed temperature sensor based on the frequency-derived technique,” Electron. Lett. 32, 2263–2264 (1996).
    [CrossRef]
  9. S. U. Ahmed, V. A. Handerek, A. J. Rogers, “Characteristics and applications of birefringent-fiber Kerr couplers,” Appl. Opt. 33, 397–406 (1994).
    [CrossRef] [PubMed]
  10. D. S. Kliger, J. W. Lewis, C. E. Randall, Polarized Light in Optics and Spectroscopy (Academic, London, 1990), Chap. 4, p. 72.
  11. G. P. Agrawal, Nonlinear Fibre Optics, 2nd ed. (Academic, London, 1995), Chap. 7, p. 248.
  12. Ref. 10, Chap. 5, p. 114.
  13. I. P. Kaminow, “Polarization in optical fibres,” IEEE J. Quantum Electron. QE-17, 15–22 (1981).
    [CrossRef]
  14. R. Ulrich, S. C. Rashleigh, W. Eickhoff, “Bending induced birefringence in single-mode fiber,” Opt. Lett. 15, 273–275 (1980).
    [CrossRef]
  15. Ref. 11, Chap. 10, p. 412.
  16. W. A. Shurcliff, Polarized Light, Production and Use (Harvard U. Press, Cambridge, Mass., 1962), Chap. 2, p. 16.

1997 (2)

R. Feced, S. E. K. Kanellopoulos, M. Farhadiroushan, V. A. Handerek, A. J. Rogers, “Analysis of optical Kerr induced coupling among polarization modes in high-birefringence optical fibres,” Opt. Commun. 143, 268–278 (1997).
[CrossRef]

F. Parvaneh, M. Farhadiroushan, V. A. Handerek, A. J. Rogers, “Single-shot distributed optical-fiber temperature sensing by the frequency-derived technique,” Opt. Lett. 22, 343–345 (1997).
[CrossRef] [PubMed]

1996 (1)

F. Parvaneh, M. Farhadiroushan, V. H. Handerek, A. J. Rogers, “High-resolution optical-fibre distributed temperature sensor based on the frequency-derived technique,” Electron. Lett. 32, 2263–2264 (1996).
[CrossRef]

1994 (1)

1993 (1)

W. Zhao, E. Bourkoff, “Nonlinear polarization coupling and its application to high resolution distributed fibre sensing,” IEEE J. Quantum Electron. 29, 2198–2210 (1993).
[CrossRef]

1992 (2)

F. Parvaneh, L. C. G. Valente, V. A. Handerek, A. J. Rogers, “Forward-scatter frequency-derived distributed optical fibre sensing using the optical Kerr-effect,” Electron. Lett. 28, 1080–1082 (1992).
[CrossRef]

F. Parvaneh, V. A. Handerek, A. J. Rogers, “Frequency-derived remote measurement of birefringence in polarization-maintaining fiber by using the optical Kerr effect,” Opt. Lett. 17, 1346–1348 (1992).
[CrossRef] [PubMed]

1981 (1)

I. P. Kaminow, “Polarization in optical fibres,” IEEE J. Quantum Electron. QE-17, 15–22 (1981).
[CrossRef]

1980 (1)

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fibre Optics, 2nd ed. (Academic, London, 1995), Chap. 7, p. 248.

Ahmed, S. U.

Bourkoff, E.

W. Zhao, E. Bourkoff, “Nonlinear polarization coupling and its application to high resolution distributed fibre sensing,” IEEE J. Quantum Electron. 29, 2198–2210 (1993).
[CrossRef]

Eickhoff, W.

Farhadiroushan, M.

R. Feced, S. E. K. Kanellopoulos, M. Farhadiroushan, V. A. Handerek, A. J. Rogers, “Analysis of optical Kerr induced coupling among polarization modes in high-birefringence optical fibres,” Opt. Commun. 143, 268–278 (1997).
[CrossRef]

F. Parvaneh, M. Farhadiroushan, V. A. Handerek, A. J. Rogers, “Single-shot distributed optical-fiber temperature sensing by the frequency-derived technique,” Opt. Lett. 22, 343–345 (1997).
[CrossRef] [PubMed]

F. Parvaneh, M. Farhadiroushan, V. H. Handerek, A. J. Rogers, “High-resolution optical-fibre distributed temperature sensor based on the frequency-derived technique,” Electron. Lett. 32, 2263–2264 (1996).
[CrossRef]

Feced, R.

R. Feced, S. E. K. Kanellopoulos, M. Farhadiroushan, V. A. Handerek, A. J. Rogers, “Analysis of optical Kerr induced coupling among polarization modes in high-birefringence optical fibres,” Opt. Commun. 143, 268–278 (1997).
[CrossRef]

Handerek, V. A.

R. Feced, S. E. K. Kanellopoulos, M. Farhadiroushan, V. A. Handerek, A. J. Rogers, “Analysis of optical Kerr induced coupling among polarization modes in high-birefringence optical fibres,” Opt. Commun. 143, 268–278 (1997).
[CrossRef]

F. Parvaneh, M. Farhadiroushan, V. A. Handerek, A. J. Rogers, “Single-shot distributed optical-fiber temperature sensing by the frequency-derived technique,” Opt. Lett. 22, 343–345 (1997).
[CrossRef] [PubMed]

S. U. Ahmed, V. A. Handerek, A. J. Rogers, “Characteristics and applications of birefringent-fiber Kerr couplers,” Appl. Opt. 33, 397–406 (1994).
[CrossRef] [PubMed]

F. Parvaneh, L. C. G. Valente, V. A. Handerek, A. J. Rogers, “Forward-scatter frequency-derived distributed optical fibre sensing using the optical Kerr-effect,” Electron. Lett. 28, 1080–1082 (1992).
[CrossRef]

F. Parvaneh, V. A. Handerek, A. J. Rogers, “Frequency-derived remote measurement of birefringence in polarization-maintaining fiber by using the optical Kerr effect,” Opt. Lett. 17, 1346–1348 (1992).
[CrossRef] [PubMed]

A. J. Rogers, V. A. Handerek, “Novel methods for distributed optical fiber sensing,” in Distributed and Multiplexed Fiber Optic Sensors, A. D. Kersey, J. P. Dakin, eds., Proc. SPIE1586, 2–12 (1991).
[CrossRef]

Handerek, V. H.

F. Parvaneh, M. Farhadiroushan, V. H. Handerek, A. J. Rogers, “High-resolution optical-fibre distributed temperature sensor based on the frequency-derived technique,” Electron. Lett. 32, 2263–2264 (1996).
[CrossRef]

Kaminow, I. P.

I. P. Kaminow, “Polarization in optical fibres,” IEEE J. Quantum Electron. QE-17, 15–22 (1981).
[CrossRef]

Kanellopoulos, S. E. K.

R. Feced, S. E. K. Kanellopoulos, M. Farhadiroushan, V. A. Handerek, A. J. Rogers, “Analysis of optical Kerr induced coupling among polarization modes in high-birefringence optical fibres,” Opt. Commun. 143, 268–278 (1997).
[CrossRef]

Kliger, D. S.

D. S. Kliger, J. W. Lewis, C. E. Randall, Polarized Light in Optics and Spectroscopy (Academic, London, 1990), Chap. 4, p. 72.

Lewis, J. W.

D. S. Kliger, J. W. Lewis, C. E. Randall, Polarized Light in Optics and Spectroscopy (Academic, London, 1990), Chap. 4, p. 72.

Parvaneh, F.

F. Parvaneh, M. Farhadiroushan, V. A. Handerek, A. J. Rogers, “Single-shot distributed optical-fiber temperature sensing by the frequency-derived technique,” Opt. Lett. 22, 343–345 (1997).
[CrossRef] [PubMed]

F. Parvaneh, M. Farhadiroushan, V. H. Handerek, A. J. Rogers, “High-resolution optical-fibre distributed temperature sensor based on the frequency-derived technique,” Electron. Lett. 32, 2263–2264 (1996).
[CrossRef]

F. Parvaneh, V. A. Handerek, A. J. Rogers, “Frequency-derived remote measurement of birefringence in polarization-maintaining fiber by using the optical Kerr effect,” Opt. Lett. 17, 1346–1348 (1992).
[CrossRef] [PubMed]

F. Parvaneh, L. C. G. Valente, V. A. Handerek, A. J. Rogers, “Forward-scatter frequency-derived distributed optical fibre sensing using the optical Kerr-effect,” Electron. Lett. 28, 1080–1082 (1992).
[CrossRef]

Randall, C. E.

D. S. Kliger, J. W. Lewis, C. E. Randall, Polarized Light in Optics and Spectroscopy (Academic, London, 1990), Chap. 4, p. 72.

Rashleigh, S. C.

Rogers, A. J.

R. Feced, S. E. K. Kanellopoulos, M. Farhadiroushan, V. A. Handerek, A. J. Rogers, “Analysis of optical Kerr induced coupling among polarization modes in high-birefringence optical fibres,” Opt. Commun. 143, 268–278 (1997).
[CrossRef]

F. Parvaneh, M. Farhadiroushan, V. A. Handerek, A. J. Rogers, “Single-shot distributed optical-fiber temperature sensing by the frequency-derived technique,” Opt. Lett. 22, 343–345 (1997).
[CrossRef] [PubMed]

F. Parvaneh, M. Farhadiroushan, V. H. Handerek, A. J. Rogers, “High-resolution optical-fibre distributed temperature sensor based on the frequency-derived technique,” Electron. Lett. 32, 2263–2264 (1996).
[CrossRef]

S. U. Ahmed, V. A. Handerek, A. J. Rogers, “Characteristics and applications of birefringent-fiber Kerr couplers,” Appl. Opt. 33, 397–406 (1994).
[CrossRef] [PubMed]

F. Parvaneh, L. C. G. Valente, V. A. Handerek, A. J. Rogers, “Forward-scatter frequency-derived distributed optical fibre sensing using the optical Kerr-effect,” Electron. Lett. 28, 1080–1082 (1992).
[CrossRef]

F. Parvaneh, V. A. Handerek, A. J. Rogers, “Frequency-derived remote measurement of birefringence in polarization-maintaining fiber by using the optical Kerr effect,” Opt. Lett. 17, 1346–1348 (1992).
[CrossRef] [PubMed]

A. J. Rogers, Essentials of Optoelectronics (Chapman & Hall, London, 1997), Chap. 9, p. 314.

A. J. Rogers, V. A. Handerek, “Novel methods for distributed optical fiber sensing,” in Distributed and Multiplexed Fiber Optic Sensors, A. D. Kersey, J. P. Dakin, eds., Proc. SPIE1586, 2–12 (1991).
[CrossRef]

Shurcliff, W. A.

W. A. Shurcliff, Polarized Light, Production and Use (Harvard U. Press, Cambridge, Mass., 1962), Chap. 2, p. 16.

Ulrich, R.

Valente, L. C. G.

F. Parvaneh, L. C. G. Valente, V. A. Handerek, A. J. Rogers, “Forward-scatter frequency-derived distributed optical fibre sensing using the optical Kerr-effect,” Electron. Lett. 28, 1080–1082 (1992).
[CrossRef]

Zhao, W.

W. Zhao, E. Bourkoff, “Nonlinear polarization coupling and its application to high resolution distributed fibre sensing,” IEEE J. Quantum Electron. 29, 2198–2210 (1993).
[CrossRef]

Appl. Opt. (1)

Electron. Lett. (2)

F. Parvaneh, L. C. G. Valente, V. A. Handerek, A. J. Rogers, “Forward-scatter frequency-derived distributed optical fibre sensing using the optical Kerr-effect,” Electron. Lett. 28, 1080–1082 (1992).
[CrossRef]

F. Parvaneh, M. Farhadiroushan, V. H. Handerek, A. J. Rogers, “High-resolution optical-fibre distributed temperature sensor based on the frequency-derived technique,” Electron. Lett. 32, 2263–2264 (1996).
[CrossRef]

IEEE J. Quantum Electron. (2)

W. Zhao, E. Bourkoff, “Nonlinear polarization coupling and its application to high resolution distributed fibre sensing,” IEEE J. Quantum Electron. 29, 2198–2210 (1993).
[CrossRef]

I. P. Kaminow, “Polarization in optical fibres,” IEEE J. Quantum Electron. QE-17, 15–22 (1981).
[CrossRef]

Opt. Commun. (1)

R. Feced, S. E. K. Kanellopoulos, M. Farhadiroushan, V. A. Handerek, A. J. Rogers, “Analysis of optical Kerr induced coupling among polarization modes in high-birefringence optical fibres,” Opt. Commun. 143, 268–278 (1997).
[CrossRef]

Opt. Lett. (3)

Other (7)

A. J. Rogers, Essentials of Optoelectronics (Chapman & Hall, London, 1997), Chap. 9, p. 314.

A. J. Rogers, V. A. Handerek, “Novel methods for distributed optical fiber sensing,” in Distributed and Multiplexed Fiber Optic Sensors, A. D. Kersey, J. P. Dakin, eds., Proc. SPIE1586, 2–12 (1991).
[CrossRef]

D. S. Kliger, J. W. Lewis, C. E. Randall, Polarized Light in Optics and Spectroscopy (Academic, London, 1990), Chap. 4, p. 72.

G. P. Agrawal, Nonlinear Fibre Optics, 2nd ed. (Academic, London, 1995), Chap. 7, p. 248.

Ref. 10, Chap. 5, p. 114.

Ref. 11, Chap. 10, p. 412.

W. A. Shurcliff, Polarized Light, Production and Use (Harvard U. Press, Cambridge, Mass., 1962), Chap. 2, p. 16.

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Figures (15)

Fig. 1
Fig. 1

Schematic representation of evolution of state of polarization along a beat length in a high-birefringent optical fiber.

Fig. 2
Fig. 2

Schematic representation of the pump and probe architecture.

Fig. 3
Fig. 3

Representation of the frequency-derived signal in the low-birefringence case: (a) experimentally measured signal and (b) theoretically generated signal.

Fig. 4
Fig. 4

Schematic representation of the polarization beat pattern of the pump and probe with small and large wavelength offsets showing spatial beat length.

Fig. 5
Fig. 5

Diagrammatical representation of the coupling action in the high-birefringence case.

Fig. 6
Fig. 6

Representation of the frequency-derived signal in the high-birefringence case: (a) experimentally measured signal at 540 MHz and (b) comparison of the experimentally measured and theoretically generated signals at 540 MHz.

Fig. 7
Fig. 7

Experimental setup for measurement of the frequency-derived signal for the low-birefringence case.

Fig. 8
Fig. 8

Experimental setup for measurement of the frequency-derived signal for the high-birefringence case: C 1, charged cable; C 2, C 3: delay lines; C 4, attenuating cable; PM1–PM4, prisms; M1, M2, mirrors; P1–P4, polarizers; PC1, PC2, Pockels cells; BSC, Babinet–Soleil compensator; R p , limiting resistor; HT, high tension.

Fig. 9
Fig. 9

Experimental result for the spectral characteristic curve for the polarization coupler.

Fig. 10
Fig. 10

Spectral characteristic curve for the pump pulse. Inset shows the pulse.

Fig. 11
Fig. 11

Variation of the derived frequency with wavelength shift.

Fig. 12
Fig. 12

Dependence on the signal amplitude with variation of (a) pump and (b) probe polarization.

Fig. 13
Fig. 13

Pump power limitations. Frequency-derived signals at pump powers of (a) 2.5 W, (b) 1.6 W, (c) 0.5 W, (d) 0.2 W. (e)–(h) Corresponding four-wave mixing and Raman spectra. The four-wave mixing lines are closely spaced on either side of the pump; the Raman Stokes line is broad and situated away from the pump.

Fig. 14
Fig. 14

Evolution of the probe state of polarization on the Poincaré sphere for the low-birefringence case.

Fig. 15
Fig. 15

Evolution of the probe state of polarization on the Poincaré sphere for the high-birefringence case. The dashed curves represent the plane that divides the vertically and horizontally biased hemispheres.

Equations (32)

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linear retardercosδZ2+j cos 2θ sinδZ2j sin 2θ sinδZ2j sin 2θ sinδZ2cosδZ2-j cos 2θ sinδZ2,
RZ=expjδZ200exp-jδZ2.
Δβpr=bprkpr=2πbprλpr.
PprL=1211.
PprZ=RL-ZPprL.
PprZ=12expjΔβprL-Z2exp-jΔβprL-Z2.
PpuZ=12expjΔβpuZ2exp-jΔβpuZ2,
b/a=tan(1/2 sin-1sin2αsinδZ),
a2-b2a2+b2=cos δZ.
ΔpZ=Δpˆ cosΔβpuZ,
JZ=cosΔpZ2j sinΔpZ2j sinΔpZ2cosΔpZ2.
AxAy=JZPprZ.
AxAx*=cos2ΔpZ2-ΔβprL-Z2+sin2ΔpZ2+ΔβprL-Z2.
AxAx*=1+sin ΔpZsin ΔβprL-Z.
AxAx*1+Δpˆ cosΔβpuZsinΔβprL-Z.
AxAx*1-Δpˆ2sinΔβpuZ+ΔβprL-Z-sinΔβpuZ-ΔβprL-Z.
Δβpu-ΔβprZ=2πbpuλpu-bprλprctobs2=2πf1tobs.
f1=c2bpuλpu-bprλpr,
f2=c2bpuλpu+bprλpr.
Ra=expjΔβprfZ200exp-jΔβprfZ2.
JiZ1001+ΔpZ20jj0.
1001=I,
JiZ=I+pcΔZ20jj0cos ΔβpuZ.
AxAy=RaJ1R1J2R2JnRb1212.
pcΔZ20jj0cos ΔβpuZ=δJ
RaJ1R1J2R2JnRb=RaI+δJ1R1I+δJ2R2I+δJnRb.
expjΔβprL200exp-jΔβprL2+i=1nexpjΔβprL-Zi200exp-jΔβprL-Zi2×0jj0pcΔZ2cos ΔβpuZi×expjΔβprZi200exp-jΔβprZi2.
Ax=12expjΔβprL2+12 j pcΔZ2i=1nexpjΔβprL-Zi2×cos ΔβpuZi exp-jΔβprZi2.
AxAx*121+pc2 sin2Δβpu-Δβprcτ2Δβpu-Δβpr2-2pc cosΔβpu-Δβprct2sinΔβpu-Δβprcτ4Δβpu-Δβpr.
2πft=Δβpu-Δβprct2.
f=c2bpuλpu-bprλpr.
pc=sin2πRQ4n020λ0Aeff,

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