Abstract

Consideration is given to a new optical fiber technique for the measurement of the spatial distribution of physical fields (e.g., magnetic field, electric field, temperature, mechanical stress): polarization—optical time domain reflectometry (POTDR). The technique relies upon the time resolution of light backscattered from a pulse propagating in a monomode optical fiber to measure the spatial distribution of the fiber’s polarization properties. These properties are modified by the field under investigation. The technique appears feasible and could form the basis for a new measurement technology.

© 1981 Optical Society of America

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  1. M. K. Barnoski, S. M. Jensen, Appl. Opt. 15, 2112 (1976).
    [CrossRef] [PubMed]
  2. M. K. Barnoski, M. D. Rourke, S. M. Jensen, R. T. Melville, Appl. Opt. 16, 2375 (1977).
    [CrossRef] [PubMed]
  3. S. D. Personick, Bell Syst. Tech. J. 56, 355 (1977).
  4. E.-G. Neumann, Appl. Opt. 17, 1675 (1978).
    [CrossRef] [PubMed]
  5. D. Marcuse, Light Transmission Optics (Van Nostrand-Reinhold, New York, 1972).
  6. A. J. Rogers, IEE Electr. Power Appl. 2, 120 (1979).
    [CrossRef]
  7. A. M. Smith, Opt. Laser Technol. 1225 (1980).
    [CrossRef]
  8. A. J. Rogers, Proc. Inst. Electr. Eng. 123, 957 (1976).
    [CrossRef]
  9. J. F. Nye, Physical Properties of Crystals (Oxford U.P., London, 1957), Appendix H and Chap. 14.
  10. M. K. Barnoski, R. J. Morrison, Appl. Opt. 15, 253 (1976).
    [CrossRef] [PubMed]
  11. A. M. Frank, Appl. Opt. 18, 3111 (1979).
    [CrossRef] [PubMed]
  12. R. G. Smith, Appl. Opt. 11, 2489 (1972).
    [CrossRef] [PubMed]
  13. E. P. Ippen, R. H. Stolen, Appl. Phys. Lett. 21, 539 (1972).
    [CrossRef]
  14. J. D. Crow, Appl. Opt. 13, 467 (1974).
    [CrossRef] [PubMed]
  15. A. Simon, R. Ulrich, Appl. Phys. Lett. 31, 517 (1977).
    [CrossRef]
  16. J. Stone, Appl. Phys. Lett. 20, 239 (1972).
    [CrossRef]
  17. D. N. Payne, W. A. Gambling, Electron. Lett. 8, 374 (1972).
    [CrossRef]
  18. A. M. Smith, Appl. Opt. 19, 2606 (1980).
    [CrossRef] [PubMed]
  19. D. N. Payne, S. R. Norman, M. J. Adams, A. M. Smith, “Analysis, Fabrication and Properties of a Fibre Exhibiting Extremely Low Polarization Birefringence,” in Proceedings, Fifth European Conference on Optical Communications, Amsterdam (1979), paper 10.1.
  20. A. J. Rogers, “Electrogyration Effect in Crystalline Quartz and Its Use in High Voltage Measurements,” in Proceedings, Electro-Optics/Laser International, Brighton (1976), pp. 136–141.
  21. M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1959), p. 559.
  22. H. Poincaré, Theorie Mathématique de la Lumière (Gauthiers-Villars, Paris, 1892), Vol. 2, Chap. 12.
  23. H. G. Jerrard, J. Opt. Soc. Am. 44, 634 (1954).
    [CrossRef]
  24. R. C. Jones, J. Opt. Soc. Am. 31, 481 (1941); J. Opt. Soc. Am. 32, 486 (1942); J. Opt. Soc. Am. 37, 107 (1947); J. Opt. Soc. Am. 38, 671 (1948).
  25. R. H. Stolen, E. P. Ippen, A. R. Tynes, Appl. Phys. Lett. 20, 62 (1972).
    [CrossRef]

1980

A. M. Smith, Opt. Laser Technol. 1225 (1980).
[CrossRef]

A. M. Smith, Appl. Opt. 19, 2606 (1980).
[CrossRef] [PubMed]

1979

A. M. Frank, Appl. Opt. 18, 3111 (1979).
[CrossRef] [PubMed]

A. J. Rogers, IEE Electr. Power Appl. 2, 120 (1979).
[CrossRef]

1978

1977

S. D. Personick, Bell Syst. Tech. J. 56, 355 (1977).

A. Simon, R. Ulrich, Appl. Phys. Lett. 31, 517 (1977).
[CrossRef]

M. K. Barnoski, M. D. Rourke, S. M. Jensen, R. T. Melville, Appl. Opt. 16, 2375 (1977).
[CrossRef] [PubMed]

1976

1974

1972

J. Stone, Appl. Phys. Lett. 20, 239 (1972).
[CrossRef]

D. N. Payne, W. A. Gambling, Electron. Lett. 8, 374 (1972).
[CrossRef]

E. P. Ippen, R. H. Stolen, Appl. Phys. Lett. 21, 539 (1972).
[CrossRef]

R. H. Stolen, E. P. Ippen, A. R. Tynes, Appl. Phys. Lett. 20, 62 (1972).
[CrossRef]

R. G. Smith, Appl. Opt. 11, 2489 (1972).
[CrossRef] [PubMed]

1954

1941

R. C. Jones, J. Opt. Soc. Am. 31, 481 (1941); J. Opt. Soc. Am. 32, 486 (1942); J. Opt. Soc. Am. 37, 107 (1947); J. Opt. Soc. Am. 38, 671 (1948).

Adams, M. J.

D. N. Payne, S. R. Norman, M. J. Adams, A. M. Smith, “Analysis, Fabrication and Properties of a Fibre Exhibiting Extremely Low Polarization Birefringence,” in Proceedings, Fifth European Conference on Optical Communications, Amsterdam (1979), paper 10.1.

Barnoski, M. K.

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1959), p. 559.

Crow, J. D.

Frank, A. M.

Gambling, W. A.

D. N. Payne, W. A. Gambling, Electron. Lett. 8, 374 (1972).
[CrossRef]

Ippen, E. P.

E. P. Ippen, R. H. Stolen, Appl. Phys. Lett. 21, 539 (1972).
[CrossRef]

R. H. Stolen, E. P. Ippen, A. R. Tynes, Appl. Phys. Lett. 20, 62 (1972).
[CrossRef]

Jensen, S. M.

Jerrard, H. G.

Jones, R. C.

R. C. Jones, J. Opt. Soc. Am. 31, 481 (1941); J. Opt. Soc. Am. 32, 486 (1942); J. Opt. Soc. Am. 37, 107 (1947); J. Opt. Soc. Am. 38, 671 (1948).

Marcuse, D.

D. Marcuse, Light Transmission Optics (Van Nostrand-Reinhold, New York, 1972).

Melville, R. T.

Morrison, R. J.

Neumann, E.-G.

Norman, S. R.

D. N. Payne, S. R. Norman, M. J. Adams, A. M. Smith, “Analysis, Fabrication and Properties of a Fibre Exhibiting Extremely Low Polarization Birefringence,” in Proceedings, Fifth European Conference on Optical Communications, Amsterdam (1979), paper 10.1.

Nye, J. F.

J. F. Nye, Physical Properties of Crystals (Oxford U.P., London, 1957), Appendix H and Chap. 14.

Payne, D. N.

D. N. Payne, W. A. Gambling, Electron. Lett. 8, 374 (1972).
[CrossRef]

D. N. Payne, S. R. Norman, M. J. Adams, A. M. Smith, “Analysis, Fabrication and Properties of a Fibre Exhibiting Extremely Low Polarization Birefringence,” in Proceedings, Fifth European Conference on Optical Communications, Amsterdam (1979), paper 10.1.

Personick, S. D.

S. D. Personick, Bell Syst. Tech. J. 56, 355 (1977).

Poincaré, H.

H. Poincaré, Theorie Mathématique de la Lumière (Gauthiers-Villars, Paris, 1892), Vol. 2, Chap. 12.

Rogers, A. J.

A. J. Rogers, IEE Electr. Power Appl. 2, 120 (1979).
[CrossRef]

A. J. Rogers, Proc. Inst. Electr. Eng. 123, 957 (1976).
[CrossRef]

A. J. Rogers, “Electrogyration Effect in Crystalline Quartz and Its Use in High Voltage Measurements,” in Proceedings, Electro-Optics/Laser International, Brighton (1976), pp. 136–141.

Rourke, M. D.

Simon, A.

A. Simon, R. Ulrich, Appl. Phys. Lett. 31, 517 (1977).
[CrossRef]

Smith, A. M.

A. M. Smith, Appl. Opt. 19, 2606 (1980).
[CrossRef] [PubMed]

A. M. Smith, Opt. Laser Technol. 1225 (1980).
[CrossRef]

D. N. Payne, S. R. Norman, M. J. Adams, A. M. Smith, “Analysis, Fabrication and Properties of a Fibre Exhibiting Extremely Low Polarization Birefringence,” in Proceedings, Fifth European Conference on Optical Communications, Amsterdam (1979), paper 10.1.

Smith, R. G.

Stolen, R. H.

R. H. Stolen, E. P. Ippen, A. R. Tynes, Appl. Phys. Lett. 20, 62 (1972).
[CrossRef]

E. P. Ippen, R. H. Stolen, Appl. Phys. Lett. 21, 539 (1972).
[CrossRef]

Stone, J.

J. Stone, Appl. Phys. Lett. 20, 239 (1972).
[CrossRef]

Tynes, A. R.

R. H. Stolen, E. P. Ippen, A. R. Tynes, Appl. Phys. Lett. 20, 62 (1972).
[CrossRef]

Ulrich, R.

A. Simon, R. Ulrich, Appl. Phys. Lett. 31, 517 (1977).
[CrossRef]

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1959), p. 559.

Appl. Opt.

Appl. Phys. Lett.

R. H. Stolen, E. P. Ippen, A. R. Tynes, Appl. Phys. Lett. 20, 62 (1972).
[CrossRef]

E. P. Ippen, R. H. Stolen, Appl. Phys. Lett. 21, 539 (1972).
[CrossRef]

A. Simon, R. Ulrich, Appl. Phys. Lett. 31, 517 (1977).
[CrossRef]

J. Stone, Appl. Phys. Lett. 20, 239 (1972).
[CrossRef]

Bell Syst. Tech. J.

S. D. Personick, Bell Syst. Tech. J. 56, 355 (1977).

Electron. Lett.

D. N. Payne, W. A. Gambling, Electron. Lett. 8, 374 (1972).
[CrossRef]

IEE Electr. Power Appl.

A. J. Rogers, IEE Electr. Power Appl. 2, 120 (1979).
[CrossRef]

J. Opt. Soc. Am.

R. C. Jones, J. Opt. Soc. Am. 31, 481 (1941); J. Opt. Soc. Am. 32, 486 (1942); J. Opt. Soc. Am. 37, 107 (1947); J. Opt. Soc. Am. 38, 671 (1948).

H. G. Jerrard, J. Opt. Soc. Am. 44, 634 (1954).
[CrossRef]

Opt. Laser Technol.

A. M. Smith, Opt. Laser Technol. 1225 (1980).
[CrossRef]

Proc. Inst. Electr. Eng.

A. J. Rogers, Proc. Inst. Electr. Eng. 123, 957 (1976).
[CrossRef]

Other

J. F. Nye, Physical Properties of Crystals (Oxford U.P., London, 1957), Appendix H and Chap. 14.

D. N. Payne, S. R. Norman, M. J. Adams, A. M. Smith, “Analysis, Fabrication and Properties of a Fibre Exhibiting Extremely Low Polarization Birefringence,” in Proceedings, Fifth European Conference on Optical Communications, Amsterdam (1979), paper 10.1.

A. J. Rogers, “Electrogyration Effect in Crystalline Quartz and Its Use in High Voltage Measurements,” in Proceedings, Electro-Optics/Laser International, Brighton (1976), pp. 136–141.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1959), p. 559.

H. Poincaré, Theorie Mathématique de la Lumière (Gauthiers-Villars, Paris, 1892), Vol. 2, Chap. 12.

D. Marcuse, Light Transmission Optics (Van Nostrand-Reinhold, New York, 1972).

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Figures (6)

Fig. 1
Fig. 1

Basic arrangement for optical time domain reflectometry.

Fig. 2
Fig. 2

(a) Time dependence of backscattered signal from 400-m fiber showing localized features. (b) Backscattered signal from joined fibers with differing loss characteristics. Photos reproduced by permission of Orionics, Inc.

Fig. 3
Fig. 3

Basic POTDR arrangement.

Fig. 4
Fig. 4

POTDR measurement of high voltage.

Fig. 5
Fig. 5

(a) Normal modes on the Poincaré sphere. (b) Rotation of Poincaré sphere about the normal mode eigenvector.

Fig. 6
Fig. 6

Derivation of birefringence vector for resolution element of fiber.

Equations (73)

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d E ( l ) E ( l ) = [ α s ( l ) + α a ( l ) ] d l ,
E ( l ) = E 0 exp [ 0 l ( α s + α s ) d l ] ,
S = 3 ( n 1 2 n 2 2 ) / 8 n 1 2 ,
d E s ( l ) = S ( l ) E 0 exp { 0 l [ α s ( l ) + α a ( l ) ] d l } d l .
d E s , 0 ( l ) = d E s ( l ) exp { 0 l [ α s ( l ) + α a ( l ) ] d l } ,
α s α s , α a α a ,
d E s , 0 ( l ) = S ( l ) α s ( l ) E 0 exp [ 0 l ( α s + α s + α a + α a ) d l ] d l .
0 l ( α s + α s + α a + α a ) d l = 2 a ( l ) ,
d E s , 0 ( l ) = S ( l ) α s ( l ) E 0 exp [ 2 a ( l ) ] d l .
2 l = c g t ,
S ( l ) S ( t ) , α s ( l ) α s ( t ) , a ( l ) a ( t ) ,
p ( t ) = ( c g / 2 ) E 0 S ( t ) α s ( t ) exp [ 2 a ( t ) ] ,
τ Δ T ,
Δ l c g τ / 2 .
L max ( Δ T ) / ( 2 δ ) .
α s ( l ) = α s ( l ) = α , say , α a ( l ) = α a ( l ) = 0 , S ( l ) = S ,
p ( t ) = ( c g / 2 ) E 0 S α exp ( α c g t ) .
π d λ · ( n 1 2 n 2 2 ) 1 / 2 2.405 ,
d Φ ( l ) = 2 π λ Δ n ( l ) d l = k F ( l ) d l ,
Φ ( l ) = k 0 l F ( l ) d l .
2 Φ ( l ) Φ ( t ) ; t = ( 2 l ) / ( c g ) .
Π ( t ) = p ( t ) A { Φ ( t ) }
F ( l ) = F ( O ) + 1 c g k · d Φ ( t ) d t ·
Φ ( t ) = A 1 { Π ( t ) p ( t ) } ,
F ( l ) = F ( O ) + 1 c g k · d d t { A 1 [ Π ( t ) p ( t ) ] } .
d A = A d Π Π A d p p .
d A = A Π ( Δ Π q + Δ Π t + Δ Π d ) + A p ( Δ p q + Δ p t + Δ p d ) ,
Δ Π t Δ p t = Δ n t , say , Δ Π d Δ p d = Δ n d , say .
d A = A Π ( Δ Π q + Δ n ) + A p ( Δ p q + Δ n ) .
Δ Π q Π = ( r π τ ) 1 / 2 , Δ p q p = ( r p τ ) 1 / 2 ,
Δ p q p = ( h ν c g 2 p Δ l ) 1 / 2 , Δ Π q Π = ( h ν c g 2 Π Δ l ) 1 / 2 = A 1 / 2 Δ p q p ,
d A = ( h ν c g 2 p Δ l ) 1 / 2 ( A + A 1 / 2 ) + Δ n p ( A + 1 ) .
F ( l ) F ( O ) = [ Φ ( t + τ ) Φ ( t ) c g k τ ] ,
d F 2 = γ 2 [ d Φ 2 ( t + τ ) + d Φ 2 ( t ) ] ,
A c ( Φ ) = cos Φ A s ( Φ ) = sin Φ ,
d Φ = d A c , s ( 1 A c , s 2 ) 1 / 2 .
d Φ = [ u ( A c , s + A c , s 1 / 2 ) + υ ( A c , s + 1 ) ] ( 1 A c , s 2 ) 1 / 2 ,
u = ( h ν c g 2 p Δ l ) 1 / 2 , υ = ( Δ n ) / p .
d Φ 1.4 u + 1.75 υ .
d F ¯ = d F N 1 / 2 = γ ( 2 u + 2.5 υ ) N 1 / 2 .
S = 1 d F ¯ = N 1 / 2 γ ( 2 u + 2.5 υ ) .
Δ W = 1 T = c g / ( 2 N L max ) .
S × Δ W = c g N 1 / 2 L max q ( 4 u + 5 υ ) .
ν = 5 × 10 14 Hz ( λ = 600 nm ) , E 0 = 2 × 10 7 J ( 0.2 μ J ) , Δ T = 10 10 sec ( 100 psec ) .
α a = 0 ( Rayleigh scatter only ) , α s = 5 × 10 3 m 1 ( 20 dB km 1 ) , S = 5 × 10 3 ( Rayleigh scatter ) , c g = 2 × 10 8 m sec 1 , Δ l = 0.1 m ( τ 1 nsec ) , L max = 100 m .
Δ f 1 GHz ( τ 1 nsec ) , responsivity ( 600 nm ) 50 A W 1 , dark current 50 nA , load resistor 100 Ω , capacitance 2 pF , noise equivalent power 2 × 10 14 W Hz 1 / 2 .
p = c g 2 · E 0 α S exp ( 2 α L max ) ,
γ = 5 / k , u = 1.3 × 10 3 , υ 5 × 10 5 ,
d F ¯ = ( 1.3 × 10 2 ) k N 1 / 2 .
Φ ( t ) = 2 ρ ( t ) = 4 V 0 l H ( l ) · d l = 4 V 0 l H l ( l ) · d l ; l = ( c g t ) / 2 ,
H l ( l ) H l ( O ) = 1 2 V c g · d Φ ( t ) d t = 1 c g V · d ρ ( t ) d t ,
d H ¯ = ( 433 / N 1 / 2 ) A m 1 .
Φ ( t ) = 4 π B 0 l E T 2 ( l ) d l , l = ( c g t ) / 2
E T 2 ( l ) E T 2 ( O ) = 1 2 π B c g · d Φ ( t ) d t ,
d ( E T 2 ¯ ) = 2.32 × 10 13 / N 1 / 2 ,
| d E T ¯ | 5 × 10 6 / N 1 / 4 .
d ( E T 2 ) ( E T 2 ) = 2 d E T E T ,
Φ ( t ) = 2 π n 3 λ M ( 1 + σ ) ( p 12 p 11 ) 0 l T ( l ) d l , l = ( c g t ) / 2 ,
T ( l ) T ( O ) = λ M π n 3 ( 1 + σ ) ( p 12 p 11 ) c g · d Φ ( t ) d t ,
k T = π n 3 ( 1 + σ ) ( p 12 p 11 ) / λ M .
Φ ( t ) = 2 k T η T 0 l θ ( l ) d l , l = ( c g t ) / 2 ,
θ ( l ) θ ( O ) = 1 k T η T c g · d Φ ( t ) d t ,
S 0 = I ( 0 ° , 0 ) + I ( 90 ° , 0 ) , S 1 = I ( 0 ° , 0 ) I ( 90 ° , 0 ) , S 2 = I ( 45 ° , 0 ) I ( 135 ° , 0 ) , S 3 = I ( 45 ° , π / 2 ) I ( 135 ° , π / 2 ) .
e = minor axis major axis = tan η , say , sin 2 η = ( S 3 ) / ( S 0 ) , tan 2 ψ = ( S 2 ) / ( S 1 ) .
e = ± tan η , tan 2 η = 2 ρ / δ .
Δ 2 = ( 4 ρ 2 + δ 2 ) .
ρ = 0 , δ 0 ( 2 ρ ) / δ = 0 , ρ 0 , δ = 0 ( 2 ρ ) / δ .
p crit 20 ( A α ) / γ ,
p = ( 4 A ) / ( γ c g Δ T ) ,
E = ( 4 A ) / ( γ c g ) ,
F = Δ ν Brillouin , Raman Δ ν laser ; F 1.
A = 2 × 10 11 m 2 ( 5 μ m diam core ) , c g = 2 × 10 8 m sec 1 , Δ ν laser = 10 10 Hz .
E = ( 4 A ) / γ c g F ) ,

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