Abstract

A novel polarimetric Fabry-Perot sensor concept, based on the phase detection of the transmitted light, is presented in detail. This concept has been successfully applied to measure static force by stress induced birefringence in an optical fiber with high sensitivity. The detection scheme consists of locking the optical frequency of a laser diode to a resonance peak, where the sensitivity is highest, and using heterodyne detection to measure the phase difference between the eigenpolarizations.

© 1989 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. A. Bertholds, R. Dändliker, “High-Resolution Photoelastic Pressure Sensor Using Low-Birefringence Fiber,” Appl. Opt. 25, 340–343 (1986).
    [CrossRef] [PubMed]
  2. D. A. Jackson, “Monomode Optical Fiber Interferometers for Precision Measurement,” J. Phys. E 18, 981 (1985).
    [CrossRef]
  3. Y. Namihira, M. Kudo, Y. Mushiaka, “Effect of Mechanical Stress on the Transmission Characteristics of Optical Fibers,” Trans. IECE Jpn. 60-C, 107 (1977).
  4. A. M. Smith, “Polarization and Magnetooptic Properties of Single-Mode Optical Fiber,” Appl. Opt. 17, 52–56 (1978).
    [CrossRef] [PubMed]
  5. E. I. Gordon, J. D. Ridgen, “The Fabry-Perot Electrooptic Modulator,” Bell Sys. Tech. J. 42, 155 (1963).
  6. J. T. Ruscio, “A Coherent Light Modulator,” IEEE J. Quantum Electron. QE-1, 182 (1965).
    [CrossRef]
  7. F. Maystre, P. Gannage, R. Dandliker, “High Sensitivity Fabry-Perot Optical Fiber Sensor for the Measurement of Mechanical Force,” in Technical Digest of Conference on Optical Fiber Sensors (Optical Society of America, Washington, DC, 1988), pp. 424–432.
  8. M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1980), pp. 323–331.
  9. T. W. Hansch, B. Couillaud, “Laser Frequency Stabilization by Polarization Spectroscopy of a Reflecting Reference Cavity,” Opt. Commun. 35, 441 (1980).
    [CrossRef]
  10. R. Ulrich, A. Simon, “Polarization Optics of Twisted Single-Mode Fibers,” Appl. Opt. 18, 2241–2251 (1979).
    [CrossRef] [PubMed]
  11. R. C. Jones, “A New Calculus for the Treatment of Optical Systems,” J. Opt. Soc. Am. 31, 488 (1941).
    [CrossRef]
  12. H. Hurwiz, R. C. Jones, “A New Calculus for the Treatment of Optical Systems,” J. Opt. Soc. Am. 31, 493 (1941).
    [CrossRef]
  13. J.-L. Picqué, S. Roizen, “Frequency-Controlled CW Tunable GaAs Laser,” Appl. Phys. Lett. 27, 340–342 (1975).
    [CrossRef]
  14. J. Stone, “Optical-Fibre Fabry-Perot Interferometer with Finesse 300,” Electron. Lett. 21, 504 (1985).

1986 (1)

1985 (2)

D. A. Jackson, “Monomode Optical Fiber Interferometers for Precision Measurement,” J. Phys. E 18, 981 (1985).
[CrossRef]

J. Stone, “Optical-Fibre Fabry-Perot Interferometer with Finesse 300,” Electron. Lett. 21, 504 (1985).

1980 (1)

T. W. Hansch, B. Couillaud, “Laser Frequency Stabilization by Polarization Spectroscopy of a Reflecting Reference Cavity,” Opt. Commun. 35, 441 (1980).
[CrossRef]

1979 (1)

1978 (1)

1977 (1)

Y. Namihira, M. Kudo, Y. Mushiaka, “Effect of Mechanical Stress on the Transmission Characteristics of Optical Fibers,” Trans. IECE Jpn. 60-C, 107 (1977).

1975 (1)

J.-L. Picqué, S. Roizen, “Frequency-Controlled CW Tunable GaAs Laser,” Appl. Phys. Lett. 27, 340–342 (1975).
[CrossRef]

1965 (1)

J. T. Ruscio, “A Coherent Light Modulator,” IEEE J. Quantum Electron. QE-1, 182 (1965).
[CrossRef]

1963 (1)

E. I. Gordon, J. D. Ridgen, “The Fabry-Perot Electrooptic Modulator,” Bell Sys. Tech. J. 42, 155 (1963).

1941 (2)

Bertholds, A.

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1980), pp. 323–331.

Couillaud, B.

T. W. Hansch, B. Couillaud, “Laser Frequency Stabilization by Polarization Spectroscopy of a Reflecting Reference Cavity,” Opt. Commun. 35, 441 (1980).
[CrossRef]

Dandliker, R.

F. Maystre, P. Gannage, R. Dandliker, “High Sensitivity Fabry-Perot Optical Fiber Sensor for the Measurement of Mechanical Force,” in Technical Digest of Conference on Optical Fiber Sensors (Optical Society of America, Washington, DC, 1988), pp. 424–432.

Dändliker, R.

Gannage, P.

F. Maystre, P. Gannage, R. Dandliker, “High Sensitivity Fabry-Perot Optical Fiber Sensor for the Measurement of Mechanical Force,” in Technical Digest of Conference on Optical Fiber Sensors (Optical Society of America, Washington, DC, 1988), pp. 424–432.

Gordon, E. I.

E. I. Gordon, J. D. Ridgen, “The Fabry-Perot Electrooptic Modulator,” Bell Sys. Tech. J. 42, 155 (1963).

Hansch, T. W.

T. W. Hansch, B. Couillaud, “Laser Frequency Stabilization by Polarization Spectroscopy of a Reflecting Reference Cavity,” Opt. Commun. 35, 441 (1980).
[CrossRef]

Hurwiz, H.

Jackson, D. A.

D. A. Jackson, “Monomode Optical Fiber Interferometers for Precision Measurement,” J. Phys. E 18, 981 (1985).
[CrossRef]

Jones, R. C.

Kudo, M.

Y. Namihira, M. Kudo, Y. Mushiaka, “Effect of Mechanical Stress on the Transmission Characteristics of Optical Fibers,” Trans. IECE Jpn. 60-C, 107 (1977).

Maystre, F.

F. Maystre, P. Gannage, R. Dandliker, “High Sensitivity Fabry-Perot Optical Fiber Sensor for the Measurement of Mechanical Force,” in Technical Digest of Conference on Optical Fiber Sensors (Optical Society of America, Washington, DC, 1988), pp. 424–432.

Mushiaka, Y.

Y. Namihira, M. Kudo, Y. Mushiaka, “Effect of Mechanical Stress on the Transmission Characteristics of Optical Fibers,” Trans. IECE Jpn. 60-C, 107 (1977).

Namihira, Y.

Y. Namihira, M. Kudo, Y. Mushiaka, “Effect of Mechanical Stress on the Transmission Characteristics of Optical Fibers,” Trans. IECE Jpn. 60-C, 107 (1977).

Picqué, J.-L.

J.-L. Picqué, S. Roizen, “Frequency-Controlled CW Tunable GaAs Laser,” Appl. Phys. Lett. 27, 340–342 (1975).
[CrossRef]

Ridgen, J. D.

E. I. Gordon, J. D. Ridgen, “The Fabry-Perot Electrooptic Modulator,” Bell Sys. Tech. J. 42, 155 (1963).

Roizen, S.

J.-L. Picqué, S. Roizen, “Frequency-Controlled CW Tunable GaAs Laser,” Appl. Phys. Lett. 27, 340–342 (1975).
[CrossRef]

Ruscio, J. T.

J. T. Ruscio, “A Coherent Light Modulator,” IEEE J. Quantum Electron. QE-1, 182 (1965).
[CrossRef]

Simon, A.

Smith, A. M.

Stone, J.

J. Stone, “Optical-Fibre Fabry-Perot Interferometer with Finesse 300,” Electron. Lett. 21, 504 (1985).

Ulrich, R.

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1980), pp. 323–331.

Appl. Opt. (3)

Appl. Phys. Lett. (1)

J.-L. Picqué, S. Roizen, “Frequency-Controlled CW Tunable GaAs Laser,” Appl. Phys. Lett. 27, 340–342 (1975).
[CrossRef]

Bell Sys. Tech. J. (1)

E. I. Gordon, J. D. Ridgen, “The Fabry-Perot Electrooptic Modulator,” Bell Sys. Tech. J. 42, 155 (1963).

Electron. Lett. (1)

J. Stone, “Optical-Fibre Fabry-Perot Interferometer with Finesse 300,” Electron. Lett. 21, 504 (1985).

IEEE J. Quantum Electron. (1)

J. T. Ruscio, “A Coherent Light Modulator,” IEEE J. Quantum Electron. QE-1, 182 (1965).
[CrossRef]

J. Opt. Soc. Am. (2)

J. Phys. E (1)

D. A. Jackson, “Monomode Optical Fiber Interferometers for Precision Measurement,” J. Phys. E 18, 981 (1985).
[CrossRef]

Opt. Commun. (1)

T. W. Hansch, B. Couillaud, “Laser Frequency Stabilization by Polarization Spectroscopy of a Reflecting Reference Cavity,” Opt. Commun. 35, 441 (1980).
[CrossRef]

Trans. IECE Jpn. (1)

Y. Namihira, M. Kudo, Y. Mushiaka, “Effect of Mechanical Stress on the Transmission Characteristics of Optical Fibers,” Trans. IECE Jpn. 60-C, 107 (1977).

Other (2)

F. Maystre, P. Gannage, R. Dandliker, “High Sensitivity Fabry-Perot Optical Fiber Sensor for the Measurement of Mechanical Force,” in Technical Digest of Conference on Optical Fiber Sensors (Optical Society of America, Washington, DC, 1988), pp. 424–432.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1980), pp. 323–331.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (6)

Fig. 1
Fig. 1

Intensity and phase of a monochromatic wave reflected by a Fabry-Perot resonator of finesse F = 10 as a function of the accumulated single-pass phase ϕ. The cases of an input mirror with higher reflectivity than the output mirror μ > 0 (e.g., R1 = 76%, R2 = 71%) and the opposite case μ < 0 (e.g., R1 = 71%, R2 = 76%) are shown. The dashed line represents the limiting case of a symmetrical resonator (μ = ∞).

Fig. 2
Fig. 2

Intensity and phase of the transmitted eigenpolarizations in a birefringent Fabry-Perot resonator of finesse F = 10 as a function of the mean accumulated single-pass phase.

Fig. 3
Fig. 3

Numerical calculation of the sensor response curve for a nonmonochromatic source. ΔνL is the laser linewidth and ΔνF.P. is the Fabry-Perot resonance width. The calculation is made for a resonator of finesse F = 20. The response for α = 0 is the same as for α = 0.1.

Fig. 4
Fig. 4

Experimental setup for the measurement of the accumulated birefringence in a Fabry-Perot resonator (FFP) using heterodyne polarimetry: LD, laser diode; L, lenses; OI, optical isolator; M, acoustooptic modulators; PBS, polarizing beam splitter; BS, beam splitter; P, polarizers; D, detectors.

Fig. 5
Fig. 5

Measured phase difference Δψ of the transmitted eigenmodes vs applied transverse load. Solid line: theoretical curves computed from Eq. (6) for a silica fiber of 125 μm outer diameter and resonators with finesses 17 and 8, respectively. Dashed line: single pass sensor for comparison. The circles are experimental data points.

Fig. 6
Fig. 6

Time response of the measurement system when a load of 10 g is applied and removed. The upper trace shows the noise of the heterodyne interferometer alone.

Equations (36)

Equations on this page are rendered with MathJax. Learn more.

ψ R = tan 1 [ ρ tan ( ϕ i ) ] tan 1 [ μ tan ( ϕ i ) ] ,
ϕ i = ( 2 π / c ) ν n i d ,
ρ 2 = 1 + 4 F 2 / π 2 ,
μ = R 1 / ( 1 A 1 ) + R 2 R 1 / ( 1 A 1 ) R 2 ,
Δ ψ R = 2 tan 1 [ ρ tan ( Δ ϕ / 2 ) ] 2 tan 1 [ μ tan ( Δ ϕ / 2 ) ] ,
ψ T = tan 1 [ ρ tan ( ϕ i ) ] .
Δ ψ T = 2 tan 1 [ ρ tan ( Δ ϕ / 2 ) ] .
β = ( 8 C / λ r ) p ,
α = g τ ,
B = ( cos γ z i ( β / 2 γ ) sin γ z ( α / γ ) sin γ z ( α / γ ) sin γ z cos γ z + i ( β / 2 γ ) sin γ z )
λ 1 , 2 = exp ( ± i Δ ϕ ) .
λ 1 , 2 = exp ( ± i Δ ϕ ) = exp ( ± i 2 γ z ) ,
Δ ϕ = ( 8 C / λ r ) P .
M = A R B R 1 ,
A ( α ) = ( cos α sin α sin α cos α ) ,
R ( θ ) B ( δ ) R 1 ( θ ) = ( cos θ sin θ sin θ cos θ ) ( exp ( i δ ) 0 0 exp ( i δ ) ) × ( cos θ sin θ sin θ cos θ )
U = S R 1 B R A S A R B R 1 ,
S = ( 1 0 0 1 )
U = ( cos 2 θ e i 2 δ + sin 2 θ e i 2 δ sin θ cos θ ( e i 2 δ e i 2 δ ) sin θ cos θ ( e i 2 δ e i 2 δ ) cos 2 θ e i 2 δ + sin 2 θ e i 2 δ ) ,
U = ( cos θ sin θ sin θ cos θ ) ( exp ( i 2 δ ) 0 0 exp ( i 2 δ ) ) ( cos θ sin θ sin θ cos θ ) ,
V 1 ( z = 0 , t ) = d ν U 1 ( ν ) exp ( i 2 π ν t ) ,
V 2 ( z = 0 , t ) = d ν U 2 ( ν ) exp ( i 2 π ν t ) ,
U L ( ν ν 0 ) = u L ( ν ν 0 ) exp [ φ ( ν ν 0 ) ] ,
ν 0 n 0 d 2 π / c = ϕ 0 = m π ,
U 1 ( ν ) = u L ( ν ν 0 + δ ν / 2 ) exp [ i φ ( ν ν 0 + δ ν / 2 ) ] ,
U 2 ( ν ) = u L ( ν ν 0 δ ν / 2 ) exp [ i φ ( ν ν 0 δ ν / 2 ) ] ,
V i ( z = d , t ) = d ν H i ( ν ) U i ( ν ) exp ( i 2 π ν t ) , i = 1 , 2 .
H i ( ν ) = a i exp ( i ψ i ) ,
a i ( ν ) = T ( 1 R ) 2 + 4 R sin 2 ϕ i ( ν ) ,
ψ i ( ν ) = tan 1 [ ρ tan ϕ i ( ν ) ] ,
2 I ( t ) = | d ν H 1 U 1 exp ( i 2 π ν t ) + d ν H 2 U 2 exp ( i 2 π ν t ) | 2 .
i ( t ) = 1 / T T / 2 T / 2 d t I ( t ) = I ( t ) φ ,
i ( t ) d ν a 1 2 u L 2 + d ν a 2 2 u L 2 + exp ( i 2 π δ ν t ) d ν 2 a 1 a 2 u L 2 exp ( i Δ ψ ) + exp ( i 2 π δ ν t ) d ν 2 a 1 a 2 u L 2 exp ( i Δ ψ ) ,
i ( t ) = ( I 1 + I 2 ) / 2 + Re { I 0 exp ( i 2 π δ ν t + Ψ ) } ,
Ψ = arg { d ν a 1 a 2 u L 2 exp ( i Δ ψ ) } ,
tan Ψ = d ν a 1 a 2 u L 2 sin ( Δ ψ ) d ν a 1 a 2 u L 2 cos ( Δ ψ ) .

Metrics