Abstract

A fiber optic heterodyne detection processing system is devised to investigate the spectral property and the dynamic response of fluctuating optical waves propagating in an externally perturbed birefringent single-mode fiber. The correlation processing for the complex amplitudes of the excited and cross-coupled modes guided along the birefringent axes of the fiber is made by extracting the significant spectral components from a photocurrent spectrum. The spectral and dynamic characteristics for the guided modes are proved experimentally and theoretically for the axial and lateral vibrations of the fiber.

© 1990 Optical Society of America

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References

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  1. T. G. Giallorenzi et al., “Optical Fiber Sensor Technology,” IEEE J. Quantum Electron. QE-18, 626–665 (1982).
    [CrossRef]
  2. D. A. Jackson, J. D. C. Jones, “Fiber Optic Sensors,” Opt. Acta 33, 1469–1503 (1986).
    [CrossRef]
  3. W. Eickhoff, “Temperature Sensing by Mode–Mode Interference in Birefringent Optical Fibers,” Opt. Lett. 6, 204–206 (1981).
    [CrossRef] [PubMed]
  4. M. P. Varnham, A. J. Barlow, D. N. Payne, K. Okamoto, “Polarimetric Strain Gauge Using High Birefringence Fiber,” Electron. Lett. 19, 699–700 (1983).
    [CrossRef]
  5. Y. Imai, Y. Ohtsuka, “Retardation Characteristics of a Bent Birefringent Fiber and Its Application to Fiber-Optic Sensing Techniques Using Polarization Mode Interference,” IEEE/OSA J. Lightwave Technol. LT-5, 1008–1013 (1987).
    [CrossRef]
  6. M. Martinelli, “The Dynamic Behavior of a Single-Mode Optical Fiber Strain Gage,” IEEE J. Quantum Electron. 18, 666–670 (1982).
    [CrossRef]
  7. Y. Namihira, Y. Horiuchi, H. Wakabayashi, “Dynamic Polarisation Fluctuation Characteristics of Optical Fibre Submarine Cable Coupling under Periodic Variable Tension,” Electron. Lett. 23, 1201–1202 (1987).
    [CrossRef]
  8. Y. Ohtsuka, M. Tsukada, Y. Imai, “Correlation Processing of Fluctuating Optical Waves Guided in an Externally Perturbed Birefringent Single-Mode Fiber by Optical Heterodyne Interferometry,” IEEE/OSA J. Lightwave Technol. LT-6, 191–196 (1988).
    [CrossRef]
  9. H. Z. Cummins, H. L. Swinney, “Light Beating Spectroscopy,” Prog. Optics 8, 133–200 (1970).
    [CrossRef]
  10. H. E. Rowe, Signals and Noise in Communication Systems (D. Van Nostrand, Princeton, 1965), Chap. IV.

1988 (1)

Y. Ohtsuka, M. Tsukada, Y. Imai, “Correlation Processing of Fluctuating Optical Waves Guided in an Externally Perturbed Birefringent Single-Mode Fiber by Optical Heterodyne Interferometry,” IEEE/OSA J. Lightwave Technol. LT-6, 191–196 (1988).
[CrossRef]

1987 (2)

Y. Imai, Y. Ohtsuka, “Retardation Characteristics of a Bent Birefringent Fiber and Its Application to Fiber-Optic Sensing Techniques Using Polarization Mode Interference,” IEEE/OSA J. Lightwave Technol. LT-5, 1008–1013 (1987).
[CrossRef]

Y. Namihira, Y. Horiuchi, H. Wakabayashi, “Dynamic Polarisation Fluctuation Characteristics of Optical Fibre Submarine Cable Coupling under Periodic Variable Tension,” Electron. Lett. 23, 1201–1202 (1987).
[CrossRef]

1986 (1)

D. A. Jackson, J. D. C. Jones, “Fiber Optic Sensors,” Opt. Acta 33, 1469–1503 (1986).
[CrossRef]

1983 (1)

M. P. Varnham, A. J. Barlow, D. N. Payne, K. Okamoto, “Polarimetric Strain Gauge Using High Birefringence Fiber,” Electron. Lett. 19, 699–700 (1983).
[CrossRef]

1982 (2)

M. Martinelli, “The Dynamic Behavior of a Single-Mode Optical Fiber Strain Gage,” IEEE J. Quantum Electron. 18, 666–670 (1982).
[CrossRef]

T. G. Giallorenzi et al., “Optical Fiber Sensor Technology,” IEEE J. Quantum Electron. QE-18, 626–665 (1982).
[CrossRef]

1981 (1)

1970 (1)

H. Z. Cummins, H. L. Swinney, “Light Beating Spectroscopy,” Prog. Optics 8, 133–200 (1970).
[CrossRef]

Barlow, A. J.

M. P. Varnham, A. J. Barlow, D. N. Payne, K. Okamoto, “Polarimetric Strain Gauge Using High Birefringence Fiber,” Electron. Lett. 19, 699–700 (1983).
[CrossRef]

Cummins, H. Z.

H. Z. Cummins, H. L. Swinney, “Light Beating Spectroscopy,” Prog. Optics 8, 133–200 (1970).
[CrossRef]

Eickhoff, W.

Giallorenzi, T. G.

T. G. Giallorenzi et al., “Optical Fiber Sensor Technology,” IEEE J. Quantum Electron. QE-18, 626–665 (1982).
[CrossRef]

Horiuchi, Y.

Y. Namihira, Y. Horiuchi, H. Wakabayashi, “Dynamic Polarisation Fluctuation Characteristics of Optical Fibre Submarine Cable Coupling under Periodic Variable Tension,” Electron. Lett. 23, 1201–1202 (1987).
[CrossRef]

Imai, Y.

Y. Ohtsuka, M. Tsukada, Y. Imai, “Correlation Processing of Fluctuating Optical Waves Guided in an Externally Perturbed Birefringent Single-Mode Fiber by Optical Heterodyne Interferometry,” IEEE/OSA J. Lightwave Technol. LT-6, 191–196 (1988).
[CrossRef]

Y. Imai, Y. Ohtsuka, “Retardation Characteristics of a Bent Birefringent Fiber and Its Application to Fiber-Optic Sensing Techniques Using Polarization Mode Interference,” IEEE/OSA J. Lightwave Technol. LT-5, 1008–1013 (1987).
[CrossRef]

Jackson, D. A.

D. A. Jackson, J. D. C. Jones, “Fiber Optic Sensors,” Opt. Acta 33, 1469–1503 (1986).
[CrossRef]

Jones, J. D. C.

D. A. Jackson, J. D. C. Jones, “Fiber Optic Sensors,” Opt. Acta 33, 1469–1503 (1986).
[CrossRef]

Martinelli, M.

M. Martinelli, “The Dynamic Behavior of a Single-Mode Optical Fiber Strain Gage,” IEEE J. Quantum Electron. 18, 666–670 (1982).
[CrossRef]

Namihira, Y.

Y. Namihira, Y. Horiuchi, H. Wakabayashi, “Dynamic Polarisation Fluctuation Characteristics of Optical Fibre Submarine Cable Coupling under Periodic Variable Tension,” Electron. Lett. 23, 1201–1202 (1987).
[CrossRef]

Ohtsuka, Y.

Y. Ohtsuka, M. Tsukada, Y. Imai, “Correlation Processing of Fluctuating Optical Waves Guided in an Externally Perturbed Birefringent Single-Mode Fiber by Optical Heterodyne Interferometry,” IEEE/OSA J. Lightwave Technol. LT-6, 191–196 (1988).
[CrossRef]

Y. Imai, Y. Ohtsuka, “Retardation Characteristics of a Bent Birefringent Fiber and Its Application to Fiber-Optic Sensing Techniques Using Polarization Mode Interference,” IEEE/OSA J. Lightwave Technol. LT-5, 1008–1013 (1987).
[CrossRef]

Okamoto, K.

M. P. Varnham, A. J. Barlow, D. N. Payne, K. Okamoto, “Polarimetric Strain Gauge Using High Birefringence Fiber,” Electron. Lett. 19, 699–700 (1983).
[CrossRef]

Payne, D. N.

M. P. Varnham, A. J. Barlow, D. N. Payne, K. Okamoto, “Polarimetric Strain Gauge Using High Birefringence Fiber,” Electron. Lett. 19, 699–700 (1983).
[CrossRef]

Rowe, H. E.

H. E. Rowe, Signals and Noise in Communication Systems (D. Van Nostrand, Princeton, 1965), Chap. IV.

Swinney, H. L.

H. Z. Cummins, H. L. Swinney, “Light Beating Spectroscopy,” Prog. Optics 8, 133–200 (1970).
[CrossRef]

Tsukada, M.

Y. Ohtsuka, M. Tsukada, Y. Imai, “Correlation Processing of Fluctuating Optical Waves Guided in an Externally Perturbed Birefringent Single-Mode Fiber by Optical Heterodyne Interferometry,” IEEE/OSA J. Lightwave Technol. LT-6, 191–196 (1988).
[CrossRef]

Varnham, M. P.

M. P. Varnham, A. J. Barlow, D. N. Payne, K. Okamoto, “Polarimetric Strain Gauge Using High Birefringence Fiber,” Electron. Lett. 19, 699–700 (1983).
[CrossRef]

Wakabayashi, H.

Y. Namihira, Y. Horiuchi, H. Wakabayashi, “Dynamic Polarisation Fluctuation Characteristics of Optical Fibre Submarine Cable Coupling under Periodic Variable Tension,” Electron. Lett. 23, 1201–1202 (1987).
[CrossRef]

Electron. Lett. (2)

Y. Namihira, Y. Horiuchi, H. Wakabayashi, “Dynamic Polarisation Fluctuation Characteristics of Optical Fibre Submarine Cable Coupling under Periodic Variable Tension,” Electron. Lett. 23, 1201–1202 (1987).
[CrossRef]

M. P. Varnham, A. J. Barlow, D. N. Payne, K. Okamoto, “Polarimetric Strain Gauge Using High Birefringence Fiber,” Electron. Lett. 19, 699–700 (1983).
[CrossRef]

IEEE J. Quantum Electron. (2)

T. G. Giallorenzi et al., “Optical Fiber Sensor Technology,” IEEE J. Quantum Electron. QE-18, 626–665 (1982).
[CrossRef]

M. Martinelli, “The Dynamic Behavior of a Single-Mode Optical Fiber Strain Gage,” IEEE J. Quantum Electron. 18, 666–670 (1982).
[CrossRef]

IEEE/OSA J. Lightwave Technol. (2)

Y. Imai, Y. Ohtsuka, “Retardation Characteristics of a Bent Birefringent Fiber and Its Application to Fiber-Optic Sensing Techniques Using Polarization Mode Interference,” IEEE/OSA J. Lightwave Technol. LT-5, 1008–1013 (1987).
[CrossRef]

Y. Ohtsuka, M. Tsukada, Y. Imai, “Correlation Processing of Fluctuating Optical Waves Guided in an Externally Perturbed Birefringent Single-Mode Fiber by Optical Heterodyne Interferometry,” IEEE/OSA J. Lightwave Technol. LT-6, 191–196 (1988).
[CrossRef]

Opt. Acta (1)

D. A. Jackson, J. D. C. Jones, “Fiber Optic Sensors,” Opt. Acta 33, 1469–1503 (1986).
[CrossRef]

Opt. Lett. (1)

Prog. Optics (1)

H. Z. Cummins, H. L. Swinney, “Light Beating Spectroscopy,” Prog. Optics 8, 133–200 (1970).
[CrossRef]

Other (1)

H. E. Rowe, Signals and Noise in Communication Systems (D. Van Nostrand, Princeton, 1965), Chap. IV.

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Figures (11)

Fig. 1
Fig. 1

Conceptual heterodyne detection scheme. Each component of the orthogonal modes leaving from the test fiber consists of the excited and cross coupled modes.

Fig. 2
Fig. 2

Schematic representation of the photocurrent power spectrum.

Fig. 3
Fig. 3

Overall view of the constructed fiber-optic correlation processing system.

Fig. 4
Fig. 4

Test fiber coiled around a cylindrical PZT to produce axial vibration.

Fig. 5
Fig. 5

Test fiber squeezed between a circular plate of PZT and an acrylic plate to give the lateral vibration.

Fig. 6
Fig. 6

Phase-modulated beat-photocurrent signal.

Fig. 7
Fig. 7

Power spectrum of a Gaussian signal to drive the PZT cylinder.

Fig. 8
Fig. 8

Power spectrum and auto-correlation function for the complex amplitude of the excited mode A s (t).

Fig. 9
Fig. 9

Theoretically computed power spectrum and auto-correlation function for the Gaussian axial vibration.

Fig. 10
Fig. 10

Power spectra and auto-correlation functions of the complex amplitude A s (t) and the coupled mode A fs (t).

Fig. 11
Fig. 11

Cross power spectrum between the complex amplitudes of the two excited modes A s (t) and A f (t).

Equations (10)

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E s ( t ) = A s ( t ) exp ( - 2 π i ν 1 t ) + A f s ( t ) exp ( - 2 π i ν 2 t ) E f ( t ) = A f ( t ) exp ( - 2 π i ν 2 t ) + A f s ( t ) exp ( - 2 π i ν 1 t ) } ,
j s ( t ) = e η E LO ( t ) + E s ( t ) 2 = e η { P ( t ) + 2 Re [ A s ( t ) A L O * exp ( - 2 π i Δ ν 1 t ) ] + 2 Re [ A f s ( t ) A LO * exp ( - 2 π i Δ ν 2 t ) ] + 2 Re [ A s ( t ) A f s * ( t ) exp ( - 2 π i Δ ν 3 t ) ] } ,
P ( t ) = A LO 2 + A s ( t ) 2 + A f s ( t ) 2 ,
Δ ν 1 = ν 1 - ν LO Δ ν 2 = ν 2 - ν LO Δ ν 3 = ν 1 - ν 2 } .
R j ( τ ) = e 2 η E ( t ) 2 δ ( τ ) + e 2 η 2 E ( t ) 2 E ( t + τ ) 2 = e j ( t ) δ ( τ ) + j ( t ) j ( t + τ ) ,
R j s ( τ ) = e 2 η P ( t ) δ ( τ ) + e 2 η { P ( t ) P ( t + τ ) + A LO 2 Re [ A s * ( t ) A s ( t + τ ) exp ( - 2 π i Δ ν 1 τ ) ] + A LO 2 Re [ A f s * ( t ) A f s ( t + τ ) exp ( - 2 π i Δ ν 2 τ ) ] + Re [ B * ( t ) B ( t + τ ) exp ( - 2 π i Δ ν 3 τ ) ] } ,
S j s ( ν ) = - R j s ( τ ) exp ( 2 π i ν τ ) d τ = e 2 η P ( t ) + e 2 η 2 [ Φ P ( ν ) + A LO 2 { Φ A s ( ν - Δ ν 1 ) + Φ A s ( - ν - Δ ν 1 ) } + A LO 2 { Φ A f s ( ν - Δ ν 2 ) + Φ A f s ( - ν - Δ ν 2 ) } + { Φ B ( ν - Δ ν 3 ) + Φ B ( - ν - Δ ν 3 ) } ] ,
Φ P ( ν ) = - P ( t ) P ( t + τ ) exp ( 2 π i ν τ ) d τ Φ A s ( ν ) = - A s * ( t ) A s ( t + τ ) exp ( 2 π i ν τ ) d τ Φ A f s ( ν ) = - A f s * ( t ) A f s ( t + τ ) exp ( 2 π i ν τ ) d τ Φ B ( ν ) = - B * ( t ) B ( t + τ ) exp ( 2 π i ν τ ) d τ } .
C A s ( τ ) = A s * ( t ) A s ( t + τ ) = K exp [ - σ 2 { 1 - C θ ( τ ) / C θ ( 0 ) } ] ,
σ 2 = ln ( C A s ( ) / C A s ( 0 ) .

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