Abstract

Time domain techniques are used to analyze the response of a Fabry-Perot interferometer to an optically swept carrier. A technique which increases the sensitivity or dynamic range of a fiber-optic sensor Fabry-Perot interferometer is analyzed. At slow optical sweep rates, classical Fabry-Perot fringes are produced when a linearly swept optical carrier interrogates a Fabry-Perot sensor interferometer. As the optical sweep rate is increased, the finesse of the Fabry-Perot fringes begins to decrease. Fringe finesse continues to deteriorate with increasing sweep rates until the fringes are destroyed, unless certain discrete sweep rates are selected. The analysis shows how the discrete sweep rates are selected. The sensitivity or dynamic range of a Fabry-Perot sensor system is increased by placing a second Fabry-Perot of appropriate length in series with the sensor Fabry-Perot. The phase information of the sensor interferometer is preserved in time domain multiplication in a manner that is analogous to the radio frequency processing of phase information.

© 1986 Optical Society of America

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References

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  1. T. G. Giallorenzi, J. A. Bucaro, A. Dandridge, G. H. Sigel, J. H. Cole, S. C. Rashleigh, R. G. Priest, “Optical Fiber Sensor Technology,” IEEE J. Quantum Electron. QE-18, 626 (1982).
    [Crossref]
  2. S. J. Petuchowski, T. G. Giallorenzi, S. K. Sheem, “A Sensitive Fiber-Optic Fabry-Perot Interferometer,” IEEE J. Quantum Electron. QE-17, 2168 (1981).
    [Crossref]
  3. K. L. Belsley, J. B. Carroll, L. A. Hess, D. R. Huber, “Optically Multiplexed Interferometric Fiber Optic Sensor System,” Presented at SPIE 1985 Conference on Fiber Optics Technology (1985).
  4. A. Kastler, “Transmission d’une impulsion lumineuse au interferometre Fabry-Perot,” Nouv. Rev. Opt. 5, 3, 133 (1974).
    [Crossref]
  5. C. Roychoudhuri, “Response of Fabry-Perot Interferometers to Light Pulses of Very Short Duration,” J. Opt. Soc. Am. 65, 1418 (1975).
    [Crossref]
  6. J. O. Stoner, “PEPSIOS Purely Interferometric, High Resolution Scanning Spectrometer. III: Calculation of Interferometer Characteristics by a Method of Optical Transmission,” J. Opt. Soc. Am. 56, 370 (1966).
    [Crossref]
  7. G. Cisimi, G. Guattari, G. Lucarini, C. Palma, “Response of Fabry-Perot Interferometer to Amplitude Modulated Light Beams,” Opt. Acta 24, 1217 (1977).
    [Crossref]
  8. J. Strong, Concepts of Classical Optics (Freeman, San Francisco, 1958).
  9. A. E. Dangor, S. J. Fielding, “The Response of a Fabry-Perot Interferometer to Rapid changes in Optical Length,” J. Phys. D 3, 419 (1970).
    [Crossref]
  10. W. V. Huston, “A Compound Interferometer for Fine Structure Work,” Phys. Rev. 29, 478 (1927).
    [Crossref]
  11. M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1964).
  12. P. G. Cielo, “Fiber Optic Hydrophone: Improved Strain Configuration and Environmental Noise Protection,” Appl. Opt. 18, 2933 (1979).
    [Crossref] [PubMed]

1982 (1)

T. G. Giallorenzi, J. A. Bucaro, A. Dandridge, G. H. Sigel, J. H. Cole, S. C. Rashleigh, R. G. Priest, “Optical Fiber Sensor Technology,” IEEE J. Quantum Electron. QE-18, 626 (1982).
[Crossref]

1981 (1)

S. J. Petuchowski, T. G. Giallorenzi, S. K. Sheem, “A Sensitive Fiber-Optic Fabry-Perot Interferometer,” IEEE J. Quantum Electron. QE-17, 2168 (1981).
[Crossref]

1979 (1)

1977 (1)

G. Cisimi, G. Guattari, G. Lucarini, C. Palma, “Response of Fabry-Perot Interferometer to Amplitude Modulated Light Beams,” Opt. Acta 24, 1217 (1977).
[Crossref]

1975 (1)

1974 (1)

A. Kastler, “Transmission d’une impulsion lumineuse au interferometre Fabry-Perot,” Nouv. Rev. Opt. 5, 3, 133 (1974).
[Crossref]

1970 (1)

A. E. Dangor, S. J. Fielding, “The Response of a Fabry-Perot Interferometer to Rapid changes in Optical Length,” J. Phys. D 3, 419 (1970).
[Crossref]

1966 (1)

1927 (1)

W. V. Huston, “A Compound Interferometer for Fine Structure Work,” Phys. Rev. 29, 478 (1927).
[Crossref]

Belsley, K. L.

K. L. Belsley, J. B. Carroll, L. A. Hess, D. R. Huber, “Optically Multiplexed Interferometric Fiber Optic Sensor System,” Presented at SPIE 1985 Conference on Fiber Optics Technology (1985).

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1964).

Bucaro, J. A.

T. G. Giallorenzi, J. A. Bucaro, A. Dandridge, G. H. Sigel, J. H. Cole, S. C. Rashleigh, R. G. Priest, “Optical Fiber Sensor Technology,” IEEE J. Quantum Electron. QE-18, 626 (1982).
[Crossref]

Carroll, J. B.

K. L. Belsley, J. B. Carroll, L. A. Hess, D. R. Huber, “Optically Multiplexed Interferometric Fiber Optic Sensor System,” Presented at SPIE 1985 Conference on Fiber Optics Technology (1985).

Cielo, P. G.

Cisimi, G.

G. Cisimi, G. Guattari, G. Lucarini, C. Palma, “Response of Fabry-Perot Interferometer to Amplitude Modulated Light Beams,” Opt. Acta 24, 1217 (1977).
[Crossref]

Cole, J. H.

T. G. Giallorenzi, J. A. Bucaro, A. Dandridge, G. H. Sigel, J. H. Cole, S. C. Rashleigh, R. G. Priest, “Optical Fiber Sensor Technology,” IEEE J. Quantum Electron. QE-18, 626 (1982).
[Crossref]

Dandridge, A.

T. G. Giallorenzi, J. A. Bucaro, A. Dandridge, G. H. Sigel, J. H. Cole, S. C. Rashleigh, R. G. Priest, “Optical Fiber Sensor Technology,” IEEE J. Quantum Electron. QE-18, 626 (1982).
[Crossref]

Dangor, A. E.

A. E. Dangor, S. J. Fielding, “The Response of a Fabry-Perot Interferometer to Rapid changes in Optical Length,” J. Phys. D 3, 419 (1970).
[Crossref]

Fielding, S. J.

A. E. Dangor, S. J. Fielding, “The Response of a Fabry-Perot Interferometer to Rapid changes in Optical Length,” J. Phys. D 3, 419 (1970).
[Crossref]

Giallorenzi, T. G.

T. G. Giallorenzi, J. A. Bucaro, A. Dandridge, G. H. Sigel, J. H. Cole, S. C. Rashleigh, R. G. Priest, “Optical Fiber Sensor Technology,” IEEE J. Quantum Electron. QE-18, 626 (1982).
[Crossref]

S. J. Petuchowski, T. G. Giallorenzi, S. K. Sheem, “A Sensitive Fiber-Optic Fabry-Perot Interferometer,” IEEE J. Quantum Electron. QE-17, 2168 (1981).
[Crossref]

Guattari, G.

G. Cisimi, G. Guattari, G. Lucarini, C. Palma, “Response of Fabry-Perot Interferometer to Amplitude Modulated Light Beams,” Opt. Acta 24, 1217 (1977).
[Crossref]

Hess, L. A.

K. L. Belsley, J. B. Carroll, L. A. Hess, D. R. Huber, “Optically Multiplexed Interferometric Fiber Optic Sensor System,” Presented at SPIE 1985 Conference on Fiber Optics Technology (1985).

Huber, D. R.

K. L. Belsley, J. B. Carroll, L. A. Hess, D. R. Huber, “Optically Multiplexed Interferometric Fiber Optic Sensor System,” Presented at SPIE 1985 Conference on Fiber Optics Technology (1985).

Huston, W. V.

W. V. Huston, “A Compound Interferometer for Fine Structure Work,” Phys. Rev. 29, 478 (1927).
[Crossref]

Kastler, A.

A. Kastler, “Transmission d’une impulsion lumineuse au interferometre Fabry-Perot,” Nouv. Rev. Opt. 5, 3, 133 (1974).
[Crossref]

Lucarini, G.

G. Cisimi, G. Guattari, G. Lucarini, C. Palma, “Response of Fabry-Perot Interferometer to Amplitude Modulated Light Beams,” Opt. Acta 24, 1217 (1977).
[Crossref]

Palma, C.

G. Cisimi, G. Guattari, G. Lucarini, C. Palma, “Response of Fabry-Perot Interferometer to Amplitude Modulated Light Beams,” Opt. Acta 24, 1217 (1977).
[Crossref]

Petuchowski, S. J.

S. J. Petuchowski, T. G. Giallorenzi, S. K. Sheem, “A Sensitive Fiber-Optic Fabry-Perot Interferometer,” IEEE J. Quantum Electron. QE-17, 2168 (1981).
[Crossref]

Priest, R. G.

T. G. Giallorenzi, J. A. Bucaro, A. Dandridge, G. H. Sigel, J. H. Cole, S. C. Rashleigh, R. G. Priest, “Optical Fiber Sensor Technology,” IEEE J. Quantum Electron. QE-18, 626 (1982).
[Crossref]

Rashleigh, S. C.

T. G. Giallorenzi, J. A. Bucaro, A. Dandridge, G. H. Sigel, J. H. Cole, S. C. Rashleigh, R. G. Priest, “Optical Fiber Sensor Technology,” IEEE J. Quantum Electron. QE-18, 626 (1982).
[Crossref]

Roychoudhuri, C.

Sheem, S. K.

S. J. Petuchowski, T. G. Giallorenzi, S. K. Sheem, “A Sensitive Fiber-Optic Fabry-Perot Interferometer,” IEEE J. Quantum Electron. QE-17, 2168 (1981).
[Crossref]

Sigel, G. H.

T. G. Giallorenzi, J. A. Bucaro, A. Dandridge, G. H. Sigel, J. H. Cole, S. C. Rashleigh, R. G. Priest, “Optical Fiber Sensor Technology,” IEEE J. Quantum Electron. QE-18, 626 (1982).
[Crossref]

Stoner, J. O.

Strong, J.

J. Strong, Concepts of Classical Optics (Freeman, San Francisco, 1958).

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1964).

Appl. Opt. (1)

IEEE J. Quantum Electron. (2)

T. G. Giallorenzi, J. A. Bucaro, A. Dandridge, G. H. Sigel, J. H. Cole, S. C. Rashleigh, R. G. Priest, “Optical Fiber Sensor Technology,” IEEE J. Quantum Electron. QE-18, 626 (1982).
[Crossref]

S. J. Petuchowski, T. G. Giallorenzi, S. K. Sheem, “A Sensitive Fiber-Optic Fabry-Perot Interferometer,” IEEE J. Quantum Electron. QE-17, 2168 (1981).
[Crossref]

J. Opt. Soc. Am. (2)

J. Phys. D (1)

A. E. Dangor, S. J. Fielding, “The Response of a Fabry-Perot Interferometer to Rapid changes in Optical Length,” J. Phys. D 3, 419 (1970).
[Crossref]

Nouv. Rev. Opt. (1)

A. Kastler, “Transmission d’une impulsion lumineuse au interferometre Fabry-Perot,” Nouv. Rev. Opt. 5, 3, 133 (1974).
[Crossref]

Opt. Acta (1)

G. Cisimi, G. Guattari, G. Lucarini, C. Palma, “Response of Fabry-Perot Interferometer to Amplitude Modulated Light Beams,” Opt. Acta 24, 1217 (1977).
[Crossref]

Phys. Rev. (1)

W. V. Huston, “A Compound Interferometer for Fine Structure Work,” Phys. Rev. 29, 478 (1927).
[Crossref]

Other (3)

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1964).

K. L. Belsley, J. B. Carroll, L. A. Hess, D. R. Huber, “Optically Multiplexed Interferometric Fiber Optic Sensor System,” Presented at SPIE 1985 Conference on Fiber Optics Technology (1985).

J. Strong, Concepts of Classical Optics (Freeman, San Francisco, 1958).

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Figures (8)

Fig. 1
Fig. 1

Block diagram of a fiber Fabry-Perot sensor system. Analyzer Fabry-Perots are connected in series with the sensor Fabry-Perot to increase system sensitivity and dynamic range.

Fig. 2
Fig. 2

Time domain output of a frequency swept Fabry-Perot. The solid line shows deterioration in finesse as the optical sweep rate is increased. The dotted line is the classical Fabry-Perot fringe pattern. Plot parameters: Wavelength of the initial optical frequency, λ0 = 1.3 μm; sensor length, D1 = 1 m; sweep rate, ζ = 1.0 × 1014 Hz/s; time from t = 0 to t = 1 in the figure, 1.07 μs; sensor reflectivity, R1 = 0.6; sensor phase, Φ2 = 0 rad.

Fig. 3
Fig. 3

Time domain output of a frequency swept Fabry-Perot. The optical sweep rate is so high that the fringe waveform has greatly degenerated. Plot parameters: wavelength of the initial optical frequency, λ0 = 1.3 μm; sensor length, D1 = 1 m; sweep rate, ζ = 1.0 × 1016 Hz/s; time from t = 0 to t = 1 in the figure, 10.7 ns; sensor reflectivity, R1 = 0.6; sensor phase, Φ2 = 0 rad.

Fig. 4
Fig. 4

Finesse is high even though the optical sweep rate is higher than in Fig. 3. The sweep rate is set to the first phase resonance. Plot parameters: wavelength of the initial optical frequency, λ0 = 1.3 μm; sensor length, D1 = 1 m; sweep rate, ζ1 = 5.7 × 1015 Hz/s; time from t = 0 to t = 1 in the figure, 18.7 ns; sensor reflectivity, R1 = 0.6; sensor phase, Φ2 = 0 rad.

Fig. 5
Fig. 5

Time domain output of two optically swept Fabry-Perot interferometers connected in series. The analyzer interferometer is fixed in length and phase. The phase information from the sensor interferometer may be recovered from the time domain output. Plot parameters: wavelength of the initial optical frequency, λ0 = 1.3 μm; sensor length, D1 = 1 m; sweep rate, ζ1 = 5.7 × 1015 Hz/s; time from t = 0 to t = 1 in the figure, 18.7 ns; sensor reflectivity, R1 = 0.6; sensor phase, Φ2 = 0 rad; analyzer length, D2 = 5 m; analyzer reflectivity, R2 = 0.6.

Fig. 6
Fig. 6

Plot is the same as in Fig. 5 except that the phase of the sensor interferometer is set to π/4 rad rather than 0 rad. Plot parameters: wavelength of the initial optical frequency, λ0 = 1.3 μm; sensor length, D1 = 1 m; sweep rate, ζ1 = 5.7 × 1015 Hz/s; time from t = 0 to t = 1 in the figure, 18.7 ns; sensor reflectivity, R1 = 0.6; sensor phase, Φ2 = π/4 rad; analyzer length, D2 = 5 m; analyzer reflectivity, R2 = 0.6.

Fig. 7
Fig. 7

Solid line is the time domain output of two Fabry-Perot interferometers which are connected in series. The difference in length between sensor and analyzer interferometers is a fraction of the sensor length. The dotted line corresponds to a single Fabry-Perot whose length is the difference between the length of the sensor and analyzer Fabry-Perots. The phase of the single Fabry-Perot is the same as the sensor Fabry-Perot. Plot parameters: wavelength of the initial optical frequency, λ0 = 1.3 μm; sensor length, D1 = 1 m; sweep rate, ζ1 = 5.7 × 109 Hz/s; time from t = 0 to t = 1 in the figure, 149 ns; sensor reflectivity, R1 = 0.6; sensor phase, Φ2 = 0 rad; analyzer length, D2 = 1.1 m; analyzer reflectivity, R2 = 0.6.

Fig. 8
Fig. 8

Same as Fig. 7 except that the phase of the sensor interferometer has been increased by π/4 rad. The dotted line corresponds to a single Fabry-Perot, as in Fig. 7; however, the phase of the single Fabry-Perot is set to π/4 rad. Plot parameters: wavelength of the inital optical frequency, λ0 = 1.3 μm; sensor length, D1 = 1 m; sweep rate, ζ1 = 5.7 × 109 Hz/s; time from t = 0 to t = 1 in the figure, 149 ms; sensor reflectivity, R1 = 0.6; sensor phase, Φ2 = π/4 rad; analyzer length, D2 = 1.1 m; analyzer reflectivity, R2 = 0.6.

Equations (32)

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h 1 ( t ) = n = 1 a 1 n δ [ t - 2 ( n - 1 ) τ 1 ] ,
S i ( t ) = exp [ - i ( ω 0 t + α t 2 ) ]
S 1 ( t ) = S i ( t ) * h 1 ( t )
S 1 ( t ) = - exp [ - i ( ω 0 σ + σ 2 ) ] × n = 1 a 1 n δ [ t - σ - 2 ( n - 1 ) τ 1 ] d σ
= n = 1 a 1 n exp ( - i { ω 0 [ t - 2 ( n - 1 ) τ 1 ] + α [ t - 2 ( n - 1 ) τ 1 ] 2 } )
= S i ( t ) n - 1 g n ,
g n = a 1 n exp [ i ( n - 1 ) ϕ n ] ,
ϕ n = [ 2 ω 0 τ 1 - 4 α ( n - 1 ) τ 1 2 + 4 α τ 1 t ] .
I 1 ( t ) = S i ( t ) S i * ( t ) [ n = 1 g n ] [ l = 1 g l * ]
= [ Real n = 1 g n ] 2 + [ lm n = 1 g n ] 2 ,
M eff = 3 R / ( 1 - R ) .
ϕ n = [ 2 ω 0 τ 1 - 4 α ( n - 1 ) τ 1 2 + 4 α τ 1 t ] .
ϕ n = Φ 1 ( ω 0 , α , τ 1 ) + 4 α τ 1 t
m π = 4 α τ 1 2 ,
α m = m π c 2 4 ( D 1 N ) 2
τ 1 = D 1 N c
α m = m 3.6 × 10 16 rad / s 2
ζ m = α m / 2 π ,
ζ m = m 5.73 × 10 15 Hz / s .
h 3 ( t ) = h 1 ( t ) * h 2 ( t )
h 3 ( t ) = - n = 1 a 1 n δ [ σ - 2 ( n - 1 ) τ 1 ] × p = 1 a 2 p δ [ t - σ - 2 ( p - 1 ) τ 2 ] d σ
= n , p = 1 a 1 n a 2 p δ [ t - 2 ( n - 1 ) τ 1 - 2 ( p - 1 ) τ 2 ] .
S 3 ( t ) = S i ( t ) * h 3 ( t )
S 3 ( t ) = - exp [ - i ( ω 0 σ + α σ 2 ) ] × n , p = 1 a 1 n a 2 p δ [ t - 2 ( n - 1 ) τ 1 - 2 ( p - 1 ) τ 2 - σ ] d σ
= S i ( t ) n = 1 g n d n ,
g n = a 1 n exp [ i ( n - 1 ) ϕ n ( t ) ] ,
d n = p = 1 a 2 p exp [ i ( p - 1 ) ϕ p ] exp ( - i ϕ n , p )
ϕ n = [ 2 ω 0 τ 1 - 4 α ( n - 1 ) τ 1 2 + 4 α τ 1 t + ϕ 2 ( t ) ] ,
ϕ p = [ 2 ω 0 τ 2 - 4 α ( p - 1 ) τ 2 2 + 4 α τ 2 t ] ,
ϕ n , p = 8 ( n - 1 ) ( p - 1 ) τ 1 τ 2 ,
I 3 ( t ) = S i ( t ) * S i * ( t ) [ n = 1 g n d n ] [ l = 1 g l d l ] *
= [ Real n = 1 g n d n ] 2 + [ Im l = 1 g l d l ] 2 .

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