Abstract

The spatially and temporally resolved birefringence of a single-mode optical fiber can be ascertained using backward stimulated Raman scattering. The magnitude of the birefringence is determined from the optical power exchanged between two counterpropagating light pulses. The degree to which a signal pulse is amplified by a pump pulse is governed by their relative states of polarization when they overlap. A novel normalization procedure is proposed that eliminates many of the unknowns. An example of how this technique could be used to evaluate a distributed strain field is provided.

© 1989 Optical Society of America

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References

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  1. A. J. Rogers, “Distributed Optical-Fibre Sensors,” J. Phys. D 19, 2237 (1986).
    [CrossRef]
  2. A. J. Rogers, “Polarization-Optical Time Domain Reflectometry: a Technique for the Measurement of Field Distributions,” Appl. Opt. 20, 1060–1074 (1981).
    [CrossRef] [PubMed]
  3. R. M. Measures, “PROBE: a New Technique for Measuring the Density Profile of a Specific Constituent Using Counterpropagating Laser Pulses,” Appl. Opt. 16, 3016–3026 (1977).
    [CrossRef] [PubMed]
  4. R. M. Measures, “PROBE—Profile Resolution Obtained By Excitation,” Appl. Spectrosc. 32, 381 (1978).
    [CrossRef]
  5. M. C. Farries, A. J. Rogers, “Distributed Sensing Using Stimulated Raman Interaction in a Monomode Optical Fibre,” Proc. Soc. Photo-Opt. Instrum. Eng. 514, 121 (1984).
  6. F. A. Hopf, G. I. Stegeman, Applied Classical Electrodynamics Volume II: Nonlinear Optics (Wiley, New York, 1986), p. 141.
  7. K. Mochizuki, “Optical Fiber Transmission Systems Using Stimulated Raman Scattering: Theory,” IEEE/OSA J. Lightwave Technol. LT-3, 688–694 (1985).
    [CrossRef]
  8. S. Chi, M.-S. Kao, “Bidirectional Optical Fiber Transmission Systems Using Raman Amplification,” IEEE/OSA J. Lightwave Technol. LT-6, 312–317 (1988).
    [CrossRef]
  9. For a purely classical description see R. H. Stolen, “Polarization Effects in Fiber Raman and Brillouin Lasers,” IEEE J. Quantum Electron. QE-15, 1157 (1979).
    [CrossRef]
  10. S. C. Rashleigh, “Origins and Control of Polarization Effects in Single-Mode Fibers,” IEEE/OSA J. Lightwave Technol. LT-1, 312–331 (1983).
    [CrossRef]
  11. W. A. Gambling, “Novel Optical Fibres for Sensing Applications,” J. Phys. E 20, 1091 (1987).
    [CrossRef]
  12. R. G. Smith, “Optical Power Handling Capacity of Low Loss Optical Fibers as Determined by Stimulated Raman and Brillouin Scattering,” Appl. Opt. 11, 2489–2494 (1972).
    [CrossRef] [PubMed]
  13. M. V. Tratnik, J. E. Sipe, “Nonlinear Polarization Dynamics,” Phys. Rev. A 35, 2965 (1987).
    [CrossRef] [PubMed]
  14. M. E. Lines, “Raman-Gain Estimates for High-Gain Optical Fibers,” J. Appl. Phys. 62, 4363 (1987).
    [CrossRef]

1988 (1)

S. Chi, M.-S. Kao, “Bidirectional Optical Fiber Transmission Systems Using Raman Amplification,” IEEE/OSA J. Lightwave Technol. LT-6, 312–317 (1988).
[CrossRef]

1987 (3)

W. A. Gambling, “Novel Optical Fibres for Sensing Applications,” J. Phys. E 20, 1091 (1987).
[CrossRef]

M. V. Tratnik, J. E. Sipe, “Nonlinear Polarization Dynamics,” Phys. Rev. A 35, 2965 (1987).
[CrossRef] [PubMed]

M. E. Lines, “Raman-Gain Estimates for High-Gain Optical Fibers,” J. Appl. Phys. 62, 4363 (1987).
[CrossRef]

1986 (1)

A. J. Rogers, “Distributed Optical-Fibre Sensors,” J. Phys. D 19, 2237 (1986).
[CrossRef]

1985 (1)

K. Mochizuki, “Optical Fiber Transmission Systems Using Stimulated Raman Scattering: Theory,” IEEE/OSA J. Lightwave Technol. LT-3, 688–694 (1985).
[CrossRef]

1984 (1)

M. C. Farries, A. J. Rogers, “Distributed Sensing Using Stimulated Raman Interaction in a Monomode Optical Fibre,” Proc. Soc. Photo-Opt. Instrum. Eng. 514, 121 (1984).

1983 (1)

S. C. Rashleigh, “Origins and Control of Polarization Effects in Single-Mode Fibers,” IEEE/OSA J. Lightwave Technol. LT-1, 312–331 (1983).
[CrossRef]

1981 (1)

1979 (1)

For a purely classical description see R. H. Stolen, “Polarization Effects in Fiber Raman and Brillouin Lasers,” IEEE J. Quantum Electron. QE-15, 1157 (1979).
[CrossRef]

1978 (1)

1977 (1)

1972 (1)

Chi, S.

S. Chi, M.-S. Kao, “Bidirectional Optical Fiber Transmission Systems Using Raman Amplification,” IEEE/OSA J. Lightwave Technol. LT-6, 312–317 (1988).
[CrossRef]

Farries, M. C.

M. C. Farries, A. J. Rogers, “Distributed Sensing Using Stimulated Raman Interaction in a Monomode Optical Fibre,” Proc. Soc. Photo-Opt. Instrum. Eng. 514, 121 (1984).

Gambling, W. A.

W. A. Gambling, “Novel Optical Fibres for Sensing Applications,” J. Phys. E 20, 1091 (1987).
[CrossRef]

Hopf, F. A.

F. A. Hopf, G. I. Stegeman, Applied Classical Electrodynamics Volume II: Nonlinear Optics (Wiley, New York, 1986), p. 141.

Kao, M.-S.

S. Chi, M.-S. Kao, “Bidirectional Optical Fiber Transmission Systems Using Raman Amplification,” IEEE/OSA J. Lightwave Technol. LT-6, 312–317 (1988).
[CrossRef]

Lines, M. E.

M. E. Lines, “Raman-Gain Estimates for High-Gain Optical Fibers,” J. Appl. Phys. 62, 4363 (1987).
[CrossRef]

Measures, R. M.

Mochizuki, K.

K. Mochizuki, “Optical Fiber Transmission Systems Using Stimulated Raman Scattering: Theory,” IEEE/OSA J. Lightwave Technol. LT-3, 688–694 (1985).
[CrossRef]

Rashleigh, S. C.

S. C. Rashleigh, “Origins and Control of Polarization Effects in Single-Mode Fibers,” IEEE/OSA J. Lightwave Technol. LT-1, 312–331 (1983).
[CrossRef]

Rogers, A. J.

A. J. Rogers, “Distributed Optical-Fibre Sensors,” J. Phys. D 19, 2237 (1986).
[CrossRef]

M. C. Farries, A. J. Rogers, “Distributed Sensing Using Stimulated Raman Interaction in a Monomode Optical Fibre,” Proc. Soc. Photo-Opt. Instrum. Eng. 514, 121 (1984).

A. J. Rogers, “Polarization-Optical Time Domain Reflectometry: a Technique for the Measurement of Field Distributions,” Appl. Opt. 20, 1060–1074 (1981).
[CrossRef] [PubMed]

Sipe, J. E.

M. V. Tratnik, J. E. Sipe, “Nonlinear Polarization Dynamics,” Phys. Rev. A 35, 2965 (1987).
[CrossRef] [PubMed]

Smith, R. G.

Stegeman, G. I.

F. A. Hopf, G. I. Stegeman, Applied Classical Electrodynamics Volume II: Nonlinear Optics (Wiley, New York, 1986), p. 141.

Stolen, R. H.

For a purely classical description see R. H. Stolen, “Polarization Effects in Fiber Raman and Brillouin Lasers,” IEEE J. Quantum Electron. QE-15, 1157 (1979).
[CrossRef]

Tratnik, M. V.

M. V. Tratnik, J. E. Sipe, “Nonlinear Polarization Dynamics,” Phys. Rev. A 35, 2965 (1987).
[CrossRef] [PubMed]

Appl. Opt. (3)

Appl. Spectrosc. (1)

IEEE J. Quantum Electron. (1)

For a purely classical description see R. H. Stolen, “Polarization Effects in Fiber Raman and Brillouin Lasers,” IEEE J. Quantum Electron. QE-15, 1157 (1979).
[CrossRef]

IEEE/OSA J. Lightwave Technol. (3)

S. C. Rashleigh, “Origins and Control of Polarization Effects in Single-Mode Fibers,” IEEE/OSA J. Lightwave Technol. LT-1, 312–331 (1983).
[CrossRef]

K. Mochizuki, “Optical Fiber Transmission Systems Using Stimulated Raman Scattering: Theory,” IEEE/OSA J. Lightwave Technol. LT-3, 688–694 (1985).
[CrossRef]

S. Chi, M.-S. Kao, “Bidirectional Optical Fiber Transmission Systems Using Raman Amplification,” IEEE/OSA J. Lightwave Technol. LT-6, 312–317 (1988).
[CrossRef]

J. Appl. Phys. (1)

M. E. Lines, “Raman-Gain Estimates for High-Gain Optical Fibers,” J. Appl. Phys. 62, 4363 (1987).
[CrossRef]

J. Phys. D (1)

A. J. Rogers, “Distributed Optical-Fibre Sensors,” J. Phys. D 19, 2237 (1986).
[CrossRef]

J. Phys. E (1)

W. A. Gambling, “Novel Optical Fibres for Sensing Applications,” J. Phys. E 20, 1091 (1987).
[CrossRef]

Phys. Rev. A (1)

M. V. Tratnik, J. E. Sipe, “Nonlinear Polarization Dynamics,” Phys. Rev. A 35, 2965 (1987).
[CrossRef] [PubMed]

Proc. Soc. Photo-Opt. Instrum. Eng. (1)

M. C. Farries, A. J. Rogers, “Distributed Sensing Using Stimulated Raman Interaction in a Monomode Optical Fibre,” Proc. Soc. Photo-Opt. Instrum. Eng. 514, 121 (1984).

Other (1)

F. A. Hopf, G. I. Stegeman, Applied Classical Electrodynamics Volume II: Nonlinear Optics (Wiley, New York, 1986), p. 141.

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Figures (11)

Fig. 1
Fig. 1

Range and time diagram of two counterpropagating pulses.

Fig. 2
Fig. 2

Spatial localization in a measurand field.

Fig. 3
Fig. 3

Backward stimulated Raman scattering in an optical fiber.

Fig. 4
Fig. 4

Energy level diagram for the stimulated Raman transition.

Fig. 5
Fig. 5

Launch conditions of input polarizations.

Fig. 6
Fig. 6

Sample signal gain functions for obtaining the normalized polarization dependent gain.

Fig. 7
Fig. 7

Phase evolution of two counterpropagating waves.

Fig. 8
Fig. 8

Spatial evolution of the states of polarization in a linearly birefringent fiber.

Fig. 9
Fig. 9

Phasor form of the polarization evolution for two counterpropagating waves.

Fig. 10
Fig. 10

Block diagram of the proposed system configuration.

Fig. 11
Fig. 11

Poincare sphere trajectories for normalization and measurement.

Equations (41)

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t = 1 2 τ p ( location z + l )
l = 1 2 c n τ p .
d S ( z ) d z = g ( z ) P ( z ) S ( z ) A ( z ) α ( z ) S ( z ) ,
S p ( z ) = S p ( 0 ) exp ( α z ) ,
S p ( z + l ) = S p ( z ) exp [ g ( z ) P ( z ) l A α l ] ,
S p ( L ) = S p ( z + l ) exp [ α ( L z l ) ] ,
S a ( L ) = S a ( 0 ) exp ( α L ) .
G 10 log S p ( L ) S a ( L ) .
G ( z ) = 4 . 43 g ( z ) P ( z ) l A ,
S signal + S pump = 2 S signal ,
γ = | ϕ p | ϕ s | 2 .
| ϕ p = i = 1 2 | i i | ϕ p ,
| ϕ s = j = 1 2 | j j | ϕ s .
γ = | J p * · J s | 2 .
g = γ g .
g = γ ( g g ) + g .
G ( z ) = [ γ ( z ) ( g g ) + g ] 4 . 43 P ( z ) l A .
G ( z ) = 4 . 43 g P ( z ) l A ,
G ( z ) = 4 . 43 g P ( z ) l A .
γ ( z ) = G ( z ) G ( z ) G ( z ) G ( z ) ,
G ( t ) G ( t ) G ( t ) G ( t )
J p = [ A x A y ] , J s = [ B x B y ] .
J p ( z = L ) = [ A 0 x A 0 y ] , J s ( z = 0 ) = [ B 0 x B 0 y ] .
J s ( z ) = [ 1 0 0 exp ( i β z ) ] J s ( z = 0 ) ,
J p ( z ) = [ 1 0 0 exp ( i β z ) ] J p ( z = 0 ) ,
z = L z .
J p ( z ) = [ 1 0 0 exp [ i β ( L z ) ] ] J p ( L ) .
J p ( 0 ) = [ 1 0 0 exp [ i β ( L ) ] ] J p ( L ) .
T ( ± ) = [ 1 0 0 exp ( ± i β z ) ] .
J s ( z ) = T ( + ) J s ( 0 ) ,
J p ( z ) = T ( ) J p ( 0 )
| J p * ( z ) · J s ( z ) | 2 = | A 0 x | 2 | B 0 x | 2 + | A 0 y | 2 | B 0 y | 2 + 2 R ( A 0 x A 0 y B 0 x B 0 y ) cos ( 2 β z ) ,
| A 0 x | 2 = | A 0 y | 2 = | B 0 x | 2 = | B 0 y | 2 = 1 2 .
γ ( z ) = G ( z ) G ( z ) G ( z ) G ( z ) = cos 2 [ 0 z β ( z ) d z + δ ] ,
β ( z ) = d d z [ cos 1 γ ( z ) ] .
β ( z ) = c 1 V m ( z ) ,
l b = 2 π c 1 V max .
P ( 0 ) c 1 V max A 2 π g G
G G G G
l = 1 2 c n τ p .
G G = 4 . 43 [ ( g g ) P ( 0 ) c τ p 2 n A ] ,

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