Abstract

Sagnac fiber interferometer with the dynamic population grating formed in the rare-earth doped fiber is proposed for homodyne adaptive detection of optical phase modulation. The configuration is shown to be a simple all-optical fiber sensor suitable for linear high sensitivity detection of mechanical vibrations, acoustic signals, thermo-optic effect etc. Theoretical consideration shows that the quadratic response of this interferometric configuration associated with the amplitude dynamic grating is observed in the reflected wave mainly, while the recorded phase grating results in the linear energy exchange between the transmitted and reflected from the Sagnac loop light waves. Experiments with the erbium- and ytterbium-doped fiber based adaptive Sagnac configurations (with the operation wavelengths 1485 and 1064nm respectively) of the fiber accelerometers confirmed these general conclusions and demonstrated sensitivity of the fiber based interferometric configurations (~3*10−5 rad/Hz1/2) governed basically by the noise of the utilized lasers.

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References

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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  13. S. Stepanov, E. Hernández, and M. Plata, “Two-wave mixing by means of dynamic Bragg gratings recorded by saturation of absorption in erbium-doped fibers,” Opt. Lett.29(12), 1327–1329 (2004).
    [CrossRef] [PubMed]
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    [CrossRef]
  15. S. Stepanov and C. Nuñez Santiago, “Intensity dependence of the transient two-wave mixing by population grating in Er-doped fiber,” Opt. Commun.264(1), 105–115 (2006).
    [CrossRef]
  16. A. V. Tveten, A. Dandridge, C. M. Davis, and T. G. Giallorenzi, “Fibre optic accelerometer,” Electron. Lett.16(22), 854–856 (1980).
    [CrossRef]
  17. P. C. Becker, N. A. Olsson, and J. R. Simpson, Erbium-Doped Fiber Amplifiers: Fundamentals and Technology (Academic, 1999).
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    [CrossRef] [PubMed]

2009

S. Stepanov, F. P. Cota, A. N. Quintero, and P. R. Montero, “Population gratings in rare-earth doped fibers for adaptive detection of laser induced ultra-sound,” J. of Holography and Speckle5(3), 303–309 (2009).
[CrossRef]

A. A. Kamshilin, V. R. Romashko, and N. Y. Kulchin, “Adaptive interferometry with photorefractive crystals,” J. Appl. Phys.105(3), 031101 (2009).
[CrossRef]

2008

S. Stepanov, “Dynamic population gratings in rare-earth doped optical fibers,”J. of Phys. D: Appl. Phys. 41, 224002/1–23, (2008).

2007

S. Stepanov and E. H. Hernández, “Phase contribution to dynamic gratings recorded in Er-doped fiber with saturable absorption,” Opt. Commun.271(1), 91–95 (2007).
[CrossRef]

S. Stepanov, A. Fotiadi, and P. Mégret, “Effective recording of dynamic phase gratings in Yb-doped fibers with saturable absorption at 1064nm,” Opt. Express15(14), 8832–8837 (2007).
[CrossRef] [PubMed]

2006

S. Stepanov and C. Nuñez Santiago, “Intensity dependence of the transient two-wave mixing by population grating in Er-doped fiber,” Opt. Commun.264(1), 105–115 (2006).
[CrossRef]

2005

H.-C. Chien, C.-H. Yeh, C.-C. Lee, and S. Chi, “A tunable and single-frequency S-band erbium fiber laser with saturable absorber-based autotracking filter,” Opt. Commun.250(1-3), 163–167 (2005).
[CrossRef]

2004

1999

1998

M. D. Feuer, “Length and power dependence of self-adjusting optical fiber filters,” IEEE Photon. Technol. Lett.10(11), 1587–1589 (1998).
[CrossRef]

1995

1994

1992

1988

D. B. Mortimore, “Fiber loop reflectors,” J. Lightwave Technol.6(7), 1217–1224 (1988).
[CrossRef]

1987

J. W. Wagner and J. B. Spicer, “Theoretical noise-limited sensitivity of classical interferometry,” JOSA B4(8), 1316–1326 (1987).
[CrossRef]

1980

A. V. Tveten, A. Dandridge, C. M. Davis, and T. G. Giallorenzi, “Fibre optic accelerometer,” Electron. Lett.16(22), 854–856 (1980).
[CrossRef]

Cheng, Y.

Chi, S.

H.-C. Chien, C.-H. Yeh, C.-C. Lee, and S. Chi, “A tunable and single-frequency S-band erbium fiber laser with saturable absorber-based autotracking filter,” Opt. Commun.250(1-3), 163–167 (2005).
[CrossRef]

Chien, H.-C.

H.-C. Chien, C.-H. Yeh, C.-C. Lee, and S. Chi, “A tunable and single-frequency S-band erbium fiber laser with saturable absorber-based autotracking filter,” Opt. Commun.250(1-3), 163–167 (2005).
[CrossRef]

Cota, F. P.

S. Stepanov, F. P. Cota, A. N. Quintero, and P. R. Montero, “Population gratings in rare-earth doped fibers for adaptive detection of laser induced ultra-sound,” J. of Holography and Speckle5(3), 303–309 (2009).
[CrossRef]

Daisy, R.

Dandridge, A.

A. V. Tveten, A. Dandridge, C. M. Davis, and T. G. Giallorenzi, “Fibre optic accelerometer,” Electron. Lett.16(22), 854–856 (1980).
[CrossRef]

Davis, C. M.

A. V. Tveten, A. Dandridge, C. M. Davis, and T. G. Giallorenzi, “Fibre optic accelerometer,” Electron. Lett.16(22), 854–856 (1980).
[CrossRef]

Feuer, M. D.

M. D. Feuer, “Length and power dependence of self-adjusting optical fiber filters,” IEEE Photon. Technol. Lett.10(11), 1587–1589 (1998).
[CrossRef]

Fischer, B.

Fotiadi, A.

Frisken, S. J.

Giallorenzi, T. G.

A. V. Tveten, A. Dandridge, C. M. Davis, and T. G. Giallorenzi, “Fibre optic accelerometer,” Electron. Lett.16(22), 854–856 (1980).
[CrossRef]

Havstad, S. A.

Hernández, E.

Hernández, E. H.

S. Stepanov and E. H. Hernández, “Phase contribution to dynamic gratings recorded in Er-doped fiber with saturable absorption,” Opt. Commun.271(1), 91–95 (2007).
[CrossRef]

Horowitz, M.

Kamshilin, A. A.

A. A. Kamshilin, V. R. Romashko, and N. Y. Kulchin, “Adaptive interferometry with photorefractive crystals,” J. Appl. Phys.105(3), 031101 (2009).
[CrossRef]

Kringlebotn, J. T.

Kulchin, N. Y.

A. A. Kamshilin, V. R. Romashko, and N. Y. Kulchin, “Adaptive interferometry with photorefractive crystals,” J. Appl. Phys.105(3), 031101 (2009).
[CrossRef]

Laming, R. I.

Lee, C.-C.

H.-C. Chien, C.-H. Yeh, C.-C. Lee, and S. Chi, “A tunable and single-frequency S-band erbium fiber laser with saturable absorber-based autotracking filter,” Opt. Commun.250(1-3), 163–167 (2005).
[CrossRef]

Loh, W. H.

Mégret, P.

Montero, P. R.

S. Stepanov, F. P. Cota, A. N. Quintero, and P. R. Montero, “Population gratings in rare-earth doped fibers for adaptive detection of laser induced ultra-sound,” J. of Holography and Speckle5(3), 303–309 (2009).
[CrossRef]

Mortimore, D. B.

D. B. Mortimore, “Fiber loop reflectors,” J. Lightwave Technol.6(7), 1217–1224 (1988).
[CrossRef]

Nuñez Santiago, C.

S. Stepanov and C. Nuñez Santiago, “Intensity dependence of the transient two-wave mixing by population grating in Er-doped fiber,” Opt. Commun.264(1), 105–115 (2006).
[CrossRef]

Payne, D. N.

Plata, M.

Quintero, A. N.

S. Stepanov, F. P. Cota, A. N. Quintero, and P. R. Montero, “Population gratings in rare-earth doped fibers for adaptive detection of laser induced ultra-sound,” J. of Holography and Speckle5(3), 303–309 (2009).
[CrossRef]

Romashko, V. R.

A. A. Kamshilin, V. R. Romashko, and N. Y. Kulchin, “Adaptive interferometry with photorefractive crystals,” J. Appl. Phys.105(3), 031101 (2009).
[CrossRef]

Spicer, J. B.

J. W. Wagner and J. B. Spicer, “Theoretical noise-limited sensitivity of classical interferometry,” JOSA B4(8), 1316–1326 (1987).
[CrossRef]

Stepanov, S.

S. Stepanov, F. P. Cota, A. N. Quintero, and P. R. Montero, “Population gratings in rare-earth doped fibers for adaptive detection of laser induced ultra-sound,” J. of Holography and Speckle5(3), 303–309 (2009).
[CrossRef]

S. Stepanov, “Dynamic population gratings in rare-earth doped optical fibers,”J. of Phys. D: Appl. Phys. 41, 224002/1–23, (2008).

S. Stepanov, A. Fotiadi, and P. Mégret, “Effective recording of dynamic phase gratings in Yb-doped fibers with saturable absorption at 1064nm,” Opt. Express15(14), 8832–8837 (2007).
[CrossRef] [PubMed]

S. Stepanov and E. H. Hernández, “Phase contribution to dynamic gratings recorded in Er-doped fiber with saturable absorption,” Opt. Commun.271(1), 91–95 (2007).
[CrossRef]

S. Stepanov and C. Nuñez Santiago, “Intensity dependence of the transient two-wave mixing by population grating in Er-doped fiber,” Opt. Commun.264(1), 105–115 (2006).
[CrossRef]

S. Stepanov, E. Hernández, and M. Plata, “Two-wave mixing by means of dynamic Bragg gratings recorded by saturation of absorption in erbium-doped fibers,” Opt. Lett.29(12), 1327–1329 (2004).
[CrossRef] [PubMed]

Tveten, A. V.

A. V. Tveten, A. Dandridge, C. M. Davis, and T. G. Giallorenzi, “Fibre optic accelerometer,” Electron. Lett.16(22), 854–856 (1980).
[CrossRef]

Wagner, J. W.

J. W. Wagner and J. B. Spicer, “Theoretical noise-limited sensitivity of classical interferometry,” JOSA B4(8), 1316–1326 (1987).
[CrossRef]

Wickham, M. G.

Willner, A. E.

Yeh, C.-H.

H.-C. Chien, C.-H. Yeh, C.-C. Lee, and S. Chi, “A tunable and single-frequency S-band erbium fiber laser with saturable absorber-based autotracking filter,” Opt. Commun.250(1-3), 163–167 (2005).
[CrossRef]

Zyskind, J. L.

Electron. Lett.

A. V. Tveten, A. Dandridge, C. M. Davis, and T. G. Giallorenzi, “Fibre optic accelerometer,” Electron. Lett.16(22), 854–856 (1980).
[CrossRef]

IEEE Photon. Technol. Lett.

M. D. Feuer, “Length and power dependence of self-adjusting optical fiber filters,” IEEE Photon. Technol. Lett.10(11), 1587–1589 (1998).
[CrossRef]

J. Appl. Phys.

A. A. Kamshilin, V. R. Romashko, and N. Y. Kulchin, “Adaptive interferometry with photorefractive crystals,” J. Appl. Phys.105(3), 031101 (2009).
[CrossRef]

J. Lightwave Technol.

D. B. Mortimore, “Fiber loop reflectors,” J. Lightwave Technol.6(7), 1217–1224 (1988).
[CrossRef]

J. of Holography and Speckle

S. Stepanov, F. P. Cota, A. N. Quintero, and P. R. Montero, “Population gratings in rare-earth doped fibers for adaptive detection of laser induced ultra-sound,” J. of Holography and Speckle5(3), 303–309 (2009).
[CrossRef]

J. of Phys. D: Appl. Phys

S. Stepanov, “Dynamic population gratings in rare-earth doped optical fibers,”J. of Phys. D: Appl. Phys. 41, 224002/1–23, (2008).

JOSA B

J. W. Wagner and J. B. Spicer, “Theoretical noise-limited sensitivity of classical interferometry,” JOSA B4(8), 1316–1326 (1987).
[CrossRef]

Opt. Commun.

S. Stepanov and E. H. Hernández, “Phase contribution to dynamic gratings recorded in Er-doped fiber with saturable absorption,” Opt. Commun.271(1), 91–95 (2007).
[CrossRef]

S. Stepanov and C. Nuñez Santiago, “Intensity dependence of the transient two-wave mixing by population grating in Er-doped fiber,” Opt. Commun.264(1), 105–115 (2006).
[CrossRef]

H.-C. Chien, C.-H. Yeh, C.-C. Lee, and S. Chi, “A tunable and single-frequency S-band erbium fiber laser with saturable absorber-based autotracking filter,” Opt. Commun.250(1-3), 163–167 (2005).
[CrossRef]

Opt. Express

Opt. Lett.

Other

P. C. Becker, N. A. Olsson, and J. R. Simpson, Erbium-Doped Fiber Amplifiers: Fundamentals and Technology (Academic, 1999).

S. I. Stepanov, “Adaptive interferometry: A new area of applications of photorefractive crystals” in International trends in Optics, ed. by J.Goodman (Academic, Boston, 1991), 125–140.

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Figures (7)

Fig. 1
Fig. 1

Schematic of the adaptive fiber Sagnac configuration - a, and the reflection and transmission coefficients of the conventional configuration (i.e. without dynamic grating) as functions of the division ratio of the input coupler – b

Fig. 2
Fig. 2

The real set up utilized in the experiments – a (inset shows how the phase modulation is introduced via piezo-electric modulator PZ and the inertial mass m), and the experimentally measured average output (transmitted) light power as a function of the incident light power – b.

Fig. 3
Fig. 3

Typical shapes of the signals detected in the transmitted (a) and reflected (b) waves at a moderate sinusoidal modulation amplitude 3 Vp-p, (c) and (d) are the same signals but observed at relatively large modulation amplitude 10 Vp-p (modulation frequency – 700 Hz, input light power – 0.9 mW).

Fig. 4
Fig. 4

Experimental dependencies of the normalized amplitude of the fundamental (◼) and the second (⬤) harmonic component in the transmitted (a) and reflected (b) waves (modulation frequency – 700 Hz, input light power – 0.9 mW). Dashed lines correspond to the linear and quadratic dependences expected in low modulation approximation from these two dependences.

Fig. 5
Fig. 5

Frequency transfer function (i.e. dependence of the output signal amplitude on the modulation frequency) of the Sagnac adaptive configuration (input light power – 0.9 mW, low amplitude modulation, stretched fiber segment length – 2.5 cm, inertial mass – 50 g).

Fig. 6
Fig. 6

Input light power dependence of the normalized output signal amplitude at the fundamental harmonic of modulation (modulation frequency – 700 Hz, modulation voltage – 2.5 Vp-p).

Fig. 7
Fig. 7

Frequency spectra of the output signal detected in transmitted wave: a – with the laser turned-off, b – with the laser turned-on but without inertial mass, c – the same with inertial mass, and d – the same with applied modulation voltage 6 Vp-p of 700 Hz (incident light power – 0.9 mW).

Equations (9)

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T= | r r 1-r 1-r | 2 = (2r1) 2 .
R= | 1r r + r 1r | 2 =4r(1r)=1T.
T= T l | r ( r + η 1r ) 1r ( 1r + η r ) | 2 = T l ( 2r1 ) 2 .
R= T l | 1r ( r + η 1r )+ r ( 1r + η r ) | 2 T l [ 4r( 1r )+4 η r 1r ].
exp(iΔsinΩt),
T= T l | r [ r +exp(iΔsinΩt) η 1r ] 1r [ 1r +exp(iΔsinΩt) η r ] | 2 = T l | (2r1)2isin(ΔsinΩt) r η 1r | 2 T l (2r1) 2 ,
R= T l [ 1r ( r +exp( iΔsinΩt ) η 1r )+ r ( 1r +exp( iΔsinΩt ) η r ) ] 2 = T l [ 2 r 1r +i( 2r1 ) η sin( ΔsinΩt )+ η cos( ΔsinΩt ) ] 2 T l { 4r( 1r )+4 n r 1r [ 1+ ( ΔsinΩt ) 2 2 ] }.
T= T l | ( 2r1 )+2sin( ΔsinΩt ) r η 1r | 2 T l | ( 2r1 ) 2 +4 η ΔsinΩt( 2r1 ) r 1r |,
R= T l | 2 r 1r ( 2r1 ) η sin( ΔsinΩt )+i η cos( ΔsinΩt ) | 2 T l { [ 4r( 1r ) ]4 η ΔsinΩt( 2r1 ) r 1r }.

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