Abstract

The performance of birefringent fiber-optic sensors is examined theoretically, based on the extinction properties and leakage of the linear polarizers and the initial light beam's polarization state. Results indicate that polarizers with leakage factors as large as 0.01 can still be part of high-quality sensing systems. It is also shown that in certain input-beam polarization conditions, the presence of a leaky polarizer in the sensing system acts similarly to a perturbation point on the fiber, causing polarization mixing and signal degradation.

© 1996 Optical Society of America

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References

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  1. F. Ansari, J. Wang, “Rate sensitivity of high birefringent fiber optic sensors under large dynamic loads,” J. Lightwave Technol. 13, 1992–1997 (1995).
    [CrossRef]
  2. A. J. Rogers, “Distributed optical-fiber sensors for the measurement of pressure, strain, and temperature,” Phys. Rep. 169, 99–143 (1988).
    [CrossRef]
  3. R. C. Gauthier, “External birefringent fiber-optic heart rate monitor,” Opt. Laser Technol. 25, 9–15 (1993).
    [CrossRef]
  4. G. Cancellieri, Single-Mode Optical Fiber Measurement: Characterization and Sensing (Artech, Boston, 1993), Chap. 5.
  5. R. C. Gauthier, J. Dhliwayo, “Birefringent fibre-optic pressure sensor,” Opt. Laser Technol. 24, 139–143 (1992).
    [CrossRef]
  6. J. Calero, S. P. Wu, C. Pope, S. L. Chuang, J. P. Murtha, “Theory and experiments on birefringent optical fibers embedded in concrete structures,” J. Lightwave Technol. 9, 1081–1091 (1994).
    [CrossRef]
  7. A. Khomenko, M. Shlyagin, S. Miridonov, D. Tentori, “Wavelength-scanning technique for distributed fiber-optic sensors,” Opt. Lett. 18, 2065–2067 (1993).
    [CrossRef] [PubMed]
  8. M. Tsubokawa, T. Higashi, Y. Negishi, “Mode couplings due to external forces distributed along a polarization maintaining fiber: an evaluation,” Appl. Opt. 27, 166–173 (1988).
    [CrossRef] [PubMed]
  9. B. E. A. Saleh, M. C. Teich, Fundamentals of Photonics (Wiley, New York, 1991), Chap. 6.
    [CrossRef]
  10. R. C. Gauthier, “Polarization-maintaining distributed fiber-optic sensor: software elimination of second-order (ghost) coupling points,” Appl. Opt. 34, 1744–1748 (1995).
    [CrossRef] [PubMed]

1995

F. Ansari, J. Wang, “Rate sensitivity of high birefringent fiber optic sensors under large dynamic loads,” J. Lightwave Technol. 13, 1992–1997 (1995).
[CrossRef]

R. C. Gauthier, “Polarization-maintaining distributed fiber-optic sensor: software elimination of second-order (ghost) coupling points,” Appl. Opt. 34, 1744–1748 (1995).
[CrossRef] [PubMed]

1994

J. Calero, S. P. Wu, C. Pope, S. L. Chuang, J. P. Murtha, “Theory and experiments on birefringent optical fibers embedded in concrete structures,” J. Lightwave Technol. 9, 1081–1091 (1994).
[CrossRef]

1993

1992

R. C. Gauthier, J. Dhliwayo, “Birefringent fibre-optic pressure sensor,” Opt. Laser Technol. 24, 139–143 (1992).
[CrossRef]

1988

A. J. Rogers, “Distributed optical-fiber sensors for the measurement of pressure, strain, and temperature,” Phys. Rep. 169, 99–143 (1988).
[CrossRef]

M. Tsubokawa, T. Higashi, Y. Negishi, “Mode couplings due to external forces distributed along a polarization maintaining fiber: an evaluation,” Appl. Opt. 27, 166–173 (1988).
[CrossRef] [PubMed]

Ansari, F.

F. Ansari, J. Wang, “Rate sensitivity of high birefringent fiber optic sensors under large dynamic loads,” J. Lightwave Technol. 13, 1992–1997 (1995).
[CrossRef]

Calero, J.

J. Calero, S. P. Wu, C. Pope, S. L. Chuang, J. P. Murtha, “Theory and experiments on birefringent optical fibers embedded in concrete structures,” J. Lightwave Technol. 9, 1081–1091 (1994).
[CrossRef]

Cancellieri, G.

G. Cancellieri, Single-Mode Optical Fiber Measurement: Characterization and Sensing (Artech, Boston, 1993), Chap. 5.

Chuang, S. L.

J. Calero, S. P. Wu, C. Pope, S. L. Chuang, J. P. Murtha, “Theory and experiments on birefringent optical fibers embedded in concrete structures,” J. Lightwave Technol. 9, 1081–1091 (1994).
[CrossRef]

Dhliwayo, J.

R. C. Gauthier, J. Dhliwayo, “Birefringent fibre-optic pressure sensor,” Opt. Laser Technol. 24, 139–143 (1992).
[CrossRef]

Gauthier, R. C.

R. C. Gauthier, “Polarization-maintaining distributed fiber-optic sensor: software elimination of second-order (ghost) coupling points,” Appl. Opt. 34, 1744–1748 (1995).
[CrossRef] [PubMed]

R. C. Gauthier, “External birefringent fiber-optic heart rate monitor,” Opt. Laser Technol. 25, 9–15 (1993).
[CrossRef]

R. C. Gauthier, J. Dhliwayo, “Birefringent fibre-optic pressure sensor,” Opt. Laser Technol. 24, 139–143 (1992).
[CrossRef]

Higashi, T.

Khomenko, A.

Miridonov, S.

Murtha, J. P.

J. Calero, S. P. Wu, C. Pope, S. L. Chuang, J. P. Murtha, “Theory and experiments on birefringent optical fibers embedded in concrete structures,” J. Lightwave Technol. 9, 1081–1091 (1994).
[CrossRef]

Negishi, Y.

Pope, C.

J. Calero, S. P. Wu, C. Pope, S. L. Chuang, J. P. Murtha, “Theory and experiments on birefringent optical fibers embedded in concrete structures,” J. Lightwave Technol. 9, 1081–1091 (1994).
[CrossRef]

Rogers, A. J.

A. J. Rogers, “Distributed optical-fiber sensors for the measurement of pressure, strain, and temperature,” Phys. Rep. 169, 99–143 (1988).
[CrossRef]

Saleh, B. E. A.

B. E. A. Saleh, M. C. Teich, Fundamentals of Photonics (Wiley, New York, 1991), Chap. 6.
[CrossRef]

Shlyagin, M.

Teich, M. C.

B. E. A. Saleh, M. C. Teich, Fundamentals of Photonics (Wiley, New York, 1991), Chap. 6.
[CrossRef]

Tentori, D.

Tsubokawa, M.

Wang, J.

F. Ansari, J. Wang, “Rate sensitivity of high birefringent fiber optic sensors under large dynamic loads,” J. Lightwave Technol. 13, 1992–1997 (1995).
[CrossRef]

Wu, S. P.

J. Calero, S. P. Wu, C. Pope, S. L. Chuang, J. P. Murtha, “Theory and experiments on birefringent optical fibers embedded in concrete structures,” J. Lightwave Technol. 9, 1081–1091 (1994).
[CrossRef]

Appl. Opt.

J. Lightwave Technol.

J. Calero, S. P. Wu, C. Pope, S. L. Chuang, J. P. Murtha, “Theory and experiments on birefringent optical fibers embedded in concrete structures,” J. Lightwave Technol. 9, 1081–1091 (1994).
[CrossRef]

F. Ansari, J. Wang, “Rate sensitivity of high birefringent fiber optic sensors under large dynamic loads,” J. Lightwave Technol. 13, 1992–1997 (1995).
[CrossRef]

Opt. Laser Technol.

R. C. Gauthier, “External birefringent fiber-optic heart rate monitor,” Opt. Laser Technol. 25, 9–15 (1993).
[CrossRef]

R. C. Gauthier, J. Dhliwayo, “Birefringent fibre-optic pressure sensor,” Opt. Laser Technol. 24, 139–143 (1992).
[CrossRef]

Opt. Lett.

Phys. Rep.

A. J. Rogers, “Distributed optical-fiber sensors for the measurement of pressure, strain, and temperature,” Phys. Rep. 169, 99–143 (1988).
[CrossRef]

Other

G. Cancellieri, Single-Mode Optical Fiber Measurement: Characterization and Sensing (Artech, Boston, 1993), Chap. 5.

B. E. A. Saleh, M. C. Teich, Fundamentals of Photonics (Wiley, New York, 1991), Chap. 6.
[CrossRef]

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Figures (7)

Fig. 1
Fig. 1

Typical optical system configuration. The input and output polarizers are oriented at angles ϕ and θ to the fast axis, respectively.

Fig. 2
Fig. 2

System parameters x in = 1, y in = 0, ϕ = 0, and θ = 0. Detected power is given by Eq. (13), with a maximum power of one.

Fig. 3
Fig. 3

System parameters x in = 1, y in = 0, ϕ = 0, and θ = 45; F in, F out, and z are variable. The amplitude of the oscillatory contribution to the output power given by Eq. (14) is plotted. Total available power is one, with a maximum of 0.5 showing a sinusoidal dependence on perturbation point location on the fiber.

Fig. 4
Fig. 4

System parameters x in = 1, y in = 0, ϕ = 0, and θ = 45; F in, F out, and z are variable. The amplitude of the oscillatory term in output power expression (15) is plotted. Total available power in the input beam is 2. A maximum of 1/4 of all power incident can show a z, coupling point location dependence.

Fig. 5
Fig. 5

System parameters as for Fig. 4. The sum of the power terms that are independent of coupling point location z are plotted. The maximum power available is 2 and is observed when both polarizers pass all incident light. The minimum in this curve is 0.5, which corresponds to the maximum in Fig. 4.

Fig. 6
Fig. 6

Input polarizer acts as though it was a coupling point located at distance L, input position, with the nondiagonal elements (−B 1, B 1) given by Eq. (19). The relationship between (F in, ϕ) and B 1 is plotted.

Fig. 7
Fig. 7

Output power expression (16) is plotted for various combinations of F in and F out over one cycle of the sinusoidal variations. For leakage factors smaller than 0.01, no significant deviation is observed to the curve obtained when the leakage factors are zero. When one or both leakage factors are large, the maximums and minimums of the curves are displaced from their ideal positions and start to show structure caused by the cross-coupling cosine term L − 2z dependence as its argument.

Equations (19)

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V in = [ x in y in ] ,
P in = [ cos ( ϕ ) sin ( ϕ ) sin ( ϕ ) cos ( ϕ ) ] [ 1 0 0 F in ] × [ cos ( ϕ ) sin ( ϕ ) sin ( ϕ ) cos ( ϕ ) ] = [ A in B in C in D in ] ,
A in = cos 2 ( ϕ ) + F in sin 2 ( ϕ ) , B in = ( 1 F in ) * sin ( ϕ ) cos ( ϕ ) , C in = B in , D in = sin 2 ( ϕ ) + F in cos 2 ( ϕ ) .
L in = [ exp [ i 2 π λ N f ( L z ) ] 0 0 exp [ i 2 π λ N s ( L z ) ] ] .
C = [ A B B A ] ,
L out = [ exp ( i 2 π λ N f z ) 0 0 exp ( i 2 π λ N s z ) ] .
P out = [ cos ( θ ) sin ( θ ) sin ( θ ) cos ( θ ) ] [ 1 0 0 F out ] × [ cos ( θ ) sin ( θ ) sin ( θ ) cos ( θ ) ] = [ A out B out C out D out ] ,
system = P out L out C L in P in V in = [ V x out V y out ] .
V x out = ( x in A in + y in B in ) ( A out A + B out T 2 B ) + T 1 ( x in B in + y in D in ) ( B out T 2 A A out B ) , V y out = ( x in A in + y in B in ) ( B out A + D out T 2 B ) + T 1 ( x in B in + y in D in ) ( D out T 2 A B out B ) ,
T 1 = exp [ i Γ ( λ ) ( L z ) ] , T 2 = exp [ i Γ ( λ ) z ] , Γ ( λ ) = 2 π λ ( N f N s ) .
P out = | V x out | 2 + | V y out | 2 .
P out = 1 2 { 1 + 2 AB cos [ Γ ( λ ) z ] } .
P out = A 2 + F out 2 B 2
P out = 1 2 [ ( 1 + F out 2 ) + 2 AB cos [ Γ ( λ ) z ] [ ( 1 F out 2 ) ] .
P out = A 2 ( 1 + F in 2 F out 2 ) + B 2 ( F in 2 + F out 2 ) + 2 AB cos [ Γ ( λ ) ( L z ) ] F in ( 1 F out 2 ) .
P out = 1 2 ( 1 + F in 2 + F out 2 + F in 2 F out 2 ) + F in ( F out 2 1 ) B 2 cos [ Γ ( λ ) ( L 2 z ) ] + F in ( 1 F out 2 ) A 2 cos [ Γ ( λ ) L ] + AB ( 1 F in 2 F out 2 + F in 2 F out 2 ) cos [ Γ ( λ ) z ] .
P out = 1 2 ( 1 + F in 2 ) F in B 2 cos [ Γ ( λ ) ( L 2 z ) ] + F in A 2 cos [ Γ ( λ ) L ] + AB ( 1 F in 2 ) cos [ Γ ( λ ) z ] .
P out = P in × ( 1 2 + A 1 2 A 2 2 { B 1 A 1 cos [ Γ ( λ ) z 1 ] + B 2 A 2 cos [ Γ ( λ ) z 2 ] } A 1 A 2 B 1 B 2 { B 2 A 2 cos [ Γ ( λ ) ( z 1 2 z 2 ) ] + B 1 A 1 cos [ Γ ( λ ) ] z 2 } ) .
B 1 = ( { 1 + ( F in 1 ) [ cos 2 ( ϕ ) cos ( ϕ ) sin ( ϕ ) ] } { 1 + ( F in 1 ) [ sin 2 ( ϕ ) cos ( ϕ ) sin ( ϕ ) ] } ) .

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