Abstract

In recent years, fiber Bragg grating (FBG), for the well-known advantages over other fiber optic sensors, has attracted more attention in ultrasonic inspection for structure health monitoring (SHM). Spectrum shift of FBG to ultrasonic wave is caused by the refractive index profile changing along the FBG, which can be attributed to nonuniform perturbation caused by strain-optic and geometric effects of ultrasonic wave. Response of FBG to the above two effects was analyzed firstly by the V-I transmission matrix model, showing high computing efficiency. Based on this model, spectra response of FBG under changing ultrasonic frequencies was simulated and discussed. In experiment, the system was able to detect a wideband ultrasonic wave ranging from 15 to 1380 kHz. These results would provide a guideline for an FBG-based acoustic detection system design in a specific ultrasonic frequency.

© 2012 Optical Society of America

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References

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  1. D. Clorennec, C. Prada, and D. Royer, “Laser ultrasonic inspection of plates using zero-group velocity lamb modes,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 57, 1125–1132 (2010).
    [CrossRef]
  2. C. J. Lane, A. K. Dunhill, B. W. Drinkwater, and P. D. Wilcox, “The inspection of anisotropic single-crystal components using a 2-D ultrasonic array,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 57, 2742–2752 (2010).
    [CrossRef]
  3. N. E. Fisher, D. J. Webb, C. N. Pannell, D. A. Jackson, L. R. Gavrilov, J. W. Hand, L. Zhang, and I. Bennion, “Ultrasonic field and temperature sensor based on short in-fibre Bragg gratings,” Electron. Lett. 34, 1139–1140 (1998).
    [CrossRef]
  4. G. Wild and S. Hinckley, “Acousto-ultrasonic optical fiber sensors: overview and state-of-the-art,” IEEE Sens. J. 8, 1184–1193 (2008).
    [CrossRef]
  5. S. Campopiano, A. Cutolo, A. Cusano, M. Giordano, G. Parente, G. Lanza, and A. Laudati, “Underwater acoustic sensors based on fiber Bragg gratings,” Sensors 9, 4446–4454 (2009).
    [CrossRef]
  6. A. Rosenthal, D. Razansky, and V. Ntziachristos, “High-sensitivity compact ultrasonic detector based on a pi-phase-shifted fiber Bragg grating,” Opt. Lett. 36, 1833–1835 (2011).
    [CrossRef]
  7. C. Betz, G. Thursby, B. Culshaw, and W. J. Staszewski, “Acousto-ultrasonic sensing using fiber Bragg gratings,” Smart Materials and Structures 12, 122–128 (2003).
    [CrossRef]
  8. H. P. Loock, W. S. Hopkins, C. M. Blair, R. Resendes, J. Saari, and N. R. Trefiak, “Recording the sound of musical instruments with FBGs: the photonic pickup,” Appl. Opt. 48, 2735–2741 (2009).
    [CrossRef]
  9. H. Tsuda, “Fiber Bragg grating vibration-sensing system, insensitive to Bragg wavelength and employing fiber ring laser,” Opt. Lett. 35, 2349–2351 (2010).
    [CrossRef]
  10. P. Fomitchov and S. Krishnaswamy, “Response of a fiber Bragg grating ultrasonic sensor,” Opt. Eng. 42, 956–963 (2003).
    [CrossRef]
  11. A. Minardo, A. Cusano, R. Bernini, L. Zeni, and M. Giordano, “Response of fiber Bragg grating to longitudinal ultrasonic waves,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 52, 304–312 (2005).
    [CrossRef]
  12. J. Capmany, M. A. Muriel, S. Sales, J. J. Rubio, and D. Pastor, “Microwave V-I transmission matrix formalism for the analysis of photonic circuits: application to fiber Bragg gratings,” J. Lightwave Technol. 21, 3125–3134 (2003).
    [CrossRef]
  13. M. McCall, “On the application of coupled mode theory for modeling fiber Bragg gratings,” J. Lightwave Technol. 18, 236–242 (2000).
    [CrossRef]
  14. Z. X. Li, L. Pei, C. H. Qi, W. J. Peng, T. G. Ning, R. F. Zhao, and S. Gao, “Fiber grating Fabry-Perot cavity studied by V-I transmission matrix method,” Acta Phys. Sin. 59, 8615–8624 (2010).
  15. D. C. Betz, W. J. Staszewski, G. Thursby, and B. Culshaw, “Structural damage identification using multifunctional Bragg grating sensors: II damage detection results and analysis,” Smart Materials and Structures 15, 1313–1322 (2006).
    [CrossRef]

2011 (1)

2010 (4)

H. Tsuda, “Fiber Bragg grating vibration-sensing system, insensitive to Bragg wavelength and employing fiber ring laser,” Opt. Lett. 35, 2349–2351 (2010).
[CrossRef]

D. Clorennec, C. Prada, and D. Royer, “Laser ultrasonic inspection of plates using zero-group velocity lamb modes,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 57, 1125–1132 (2010).
[CrossRef]

C. J. Lane, A. K. Dunhill, B. W. Drinkwater, and P. D. Wilcox, “The inspection of anisotropic single-crystal components using a 2-D ultrasonic array,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 57, 2742–2752 (2010).
[CrossRef]

Z. X. Li, L. Pei, C. H. Qi, W. J. Peng, T. G. Ning, R. F. Zhao, and S. Gao, “Fiber grating Fabry-Perot cavity studied by V-I transmission matrix method,” Acta Phys. Sin. 59, 8615–8624 (2010).

2009 (2)

H. P. Loock, W. S. Hopkins, C. M. Blair, R. Resendes, J. Saari, and N. R. Trefiak, “Recording the sound of musical instruments with FBGs: the photonic pickup,” Appl. Opt. 48, 2735–2741 (2009).
[CrossRef]

S. Campopiano, A. Cutolo, A. Cusano, M. Giordano, G. Parente, G. Lanza, and A. Laudati, “Underwater acoustic sensors based on fiber Bragg gratings,” Sensors 9, 4446–4454 (2009).
[CrossRef]

2008 (1)

G. Wild and S. Hinckley, “Acousto-ultrasonic optical fiber sensors: overview and state-of-the-art,” IEEE Sens. J. 8, 1184–1193 (2008).
[CrossRef]

2006 (1)

D. C. Betz, W. J. Staszewski, G. Thursby, and B. Culshaw, “Structural damage identification using multifunctional Bragg grating sensors: II damage detection results and analysis,” Smart Materials and Structures 15, 1313–1322 (2006).
[CrossRef]

2005 (1)

A. Minardo, A. Cusano, R. Bernini, L. Zeni, and M. Giordano, “Response of fiber Bragg grating to longitudinal ultrasonic waves,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 52, 304–312 (2005).
[CrossRef]

2003 (3)

J. Capmany, M. A. Muriel, S. Sales, J. J. Rubio, and D. Pastor, “Microwave V-I transmission matrix formalism for the analysis of photonic circuits: application to fiber Bragg gratings,” J. Lightwave Technol. 21, 3125–3134 (2003).
[CrossRef]

P. Fomitchov and S. Krishnaswamy, “Response of a fiber Bragg grating ultrasonic sensor,” Opt. Eng. 42, 956–963 (2003).
[CrossRef]

C. Betz, G. Thursby, B. Culshaw, and W. J. Staszewski, “Acousto-ultrasonic sensing using fiber Bragg gratings,” Smart Materials and Structures 12, 122–128 (2003).
[CrossRef]

2000 (1)

1998 (1)

N. E. Fisher, D. J. Webb, C. N. Pannell, D. A. Jackson, L. R. Gavrilov, J. W. Hand, L. Zhang, and I. Bennion, “Ultrasonic field and temperature sensor based on short in-fibre Bragg gratings,” Electron. Lett. 34, 1139–1140 (1998).
[CrossRef]

Bennion, I.

N. E. Fisher, D. J. Webb, C. N. Pannell, D. A. Jackson, L. R. Gavrilov, J. W. Hand, L. Zhang, and I. Bennion, “Ultrasonic field and temperature sensor based on short in-fibre Bragg gratings,” Electron. Lett. 34, 1139–1140 (1998).
[CrossRef]

Bernini, R.

A. Minardo, A. Cusano, R. Bernini, L. Zeni, and M. Giordano, “Response of fiber Bragg grating to longitudinal ultrasonic waves,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 52, 304–312 (2005).
[CrossRef]

Betz, C.

C. Betz, G. Thursby, B. Culshaw, and W. J. Staszewski, “Acousto-ultrasonic sensing using fiber Bragg gratings,” Smart Materials and Structures 12, 122–128 (2003).
[CrossRef]

Betz, D. C.

D. C. Betz, W. J. Staszewski, G. Thursby, and B. Culshaw, “Structural damage identification using multifunctional Bragg grating sensors: II damage detection results and analysis,” Smart Materials and Structures 15, 1313–1322 (2006).
[CrossRef]

Blair, C. M.

Campopiano, S.

S. Campopiano, A. Cutolo, A. Cusano, M. Giordano, G. Parente, G. Lanza, and A. Laudati, “Underwater acoustic sensors based on fiber Bragg gratings,” Sensors 9, 4446–4454 (2009).
[CrossRef]

Capmany, J.

Clorennec, D.

D. Clorennec, C. Prada, and D. Royer, “Laser ultrasonic inspection of plates using zero-group velocity lamb modes,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 57, 1125–1132 (2010).
[CrossRef]

Culshaw, B.

D. C. Betz, W. J. Staszewski, G. Thursby, and B. Culshaw, “Structural damage identification using multifunctional Bragg grating sensors: II damage detection results and analysis,” Smart Materials and Structures 15, 1313–1322 (2006).
[CrossRef]

C. Betz, G. Thursby, B. Culshaw, and W. J. Staszewski, “Acousto-ultrasonic sensing using fiber Bragg gratings,” Smart Materials and Structures 12, 122–128 (2003).
[CrossRef]

Cusano, A.

S. Campopiano, A. Cutolo, A. Cusano, M. Giordano, G. Parente, G. Lanza, and A. Laudati, “Underwater acoustic sensors based on fiber Bragg gratings,” Sensors 9, 4446–4454 (2009).
[CrossRef]

A. Minardo, A. Cusano, R. Bernini, L. Zeni, and M. Giordano, “Response of fiber Bragg grating to longitudinal ultrasonic waves,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 52, 304–312 (2005).
[CrossRef]

Cutolo, A.

S. Campopiano, A. Cutolo, A. Cusano, M. Giordano, G. Parente, G. Lanza, and A. Laudati, “Underwater acoustic sensors based on fiber Bragg gratings,” Sensors 9, 4446–4454 (2009).
[CrossRef]

Drinkwater, B. W.

C. J. Lane, A. K. Dunhill, B. W. Drinkwater, and P. D. Wilcox, “The inspection of anisotropic single-crystal components using a 2-D ultrasonic array,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 57, 2742–2752 (2010).
[CrossRef]

Dunhill, A. K.

C. J. Lane, A. K. Dunhill, B. W. Drinkwater, and P. D. Wilcox, “The inspection of anisotropic single-crystal components using a 2-D ultrasonic array,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 57, 2742–2752 (2010).
[CrossRef]

Fisher, N. E.

N. E. Fisher, D. J. Webb, C. N. Pannell, D. A. Jackson, L. R. Gavrilov, J. W. Hand, L. Zhang, and I. Bennion, “Ultrasonic field and temperature sensor based on short in-fibre Bragg gratings,” Electron. Lett. 34, 1139–1140 (1998).
[CrossRef]

Fomitchov, P.

P. Fomitchov and S. Krishnaswamy, “Response of a fiber Bragg grating ultrasonic sensor,” Opt. Eng. 42, 956–963 (2003).
[CrossRef]

Gao, S.

Z. X. Li, L. Pei, C. H. Qi, W. J. Peng, T. G. Ning, R. F. Zhao, and S. Gao, “Fiber grating Fabry-Perot cavity studied by V-I transmission matrix method,” Acta Phys. Sin. 59, 8615–8624 (2010).

Gavrilov, L. R.

N. E. Fisher, D. J. Webb, C. N. Pannell, D. A. Jackson, L. R. Gavrilov, J. W. Hand, L. Zhang, and I. Bennion, “Ultrasonic field and temperature sensor based on short in-fibre Bragg gratings,” Electron. Lett. 34, 1139–1140 (1998).
[CrossRef]

Giordano, M.

S. Campopiano, A. Cutolo, A. Cusano, M. Giordano, G. Parente, G. Lanza, and A. Laudati, “Underwater acoustic sensors based on fiber Bragg gratings,” Sensors 9, 4446–4454 (2009).
[CrossRef]

A. Minardo, A. Cusano, R. Bernini, L. Zeni, and M. Giordano, “Response of fiber Bragg grating to longitudinal ultrasonic waves,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 52, 304–312 (2005).
[CrossRef]

Hand, J. W.

N. E. Fisher, D. J. Webb, C. N. Pannell, D. A. Jackson, L. R. Gavrilov, J. W. Hand, L. Zhang, and I. Bennion, “Ultrasonic field and temperature sensor based on short in-fibre Bragg gratings,” Electron. Lett. 34, 1139–1140 (1998).
[CrossRef]

Hinckley, S.

G. Wild and S. Hinckley, “Acousto-ultrasonic optical fiber sensors: overview and state-of-the-art,” IEEE Sens. J. 8, 1184–1193 (2008).
[CrossRef]

Hopkins, W. S.

Jackson, D. A.

N. E. Fisher, D. J. Webb, C. N. Pannell, D. A. Jackson, L. R. Gavrilov, J. W. Hand, L. Zhang, and I. Bennion, “Ultrasonic field and temperature sensor based on short in-fibre Bragg gratings,” Electron. Lett. 34, 1139–1140 (1998).
[CrossRef]

Krishnaswamy, S.

P. Fomitchov and S. Krishnaswamy, “Response of a fiber Bragg grating ultrasonic sensor,” Opt. Eng. 42, 956–963 (2003).
[CrossRef]

Lane, C. J.

C. J. Lane, A. K. Dunhill, B. W. Drinkwater, and P. D. Wilcox, “The inspection of anisotropic single-crystal components using a 2-D ultrasonic array,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 57, 2742–2752 (2010).
[CrossRef]

Lanza, G.

S. Campopiano, A. Cutolo, A. Cusano, M. Giordano, G. Parente, G. Lanza, and A. Laudati, “Underwater acoustic sensors based on fiber Bragg gratings,” Sensors 9, 4446–4454 (2009).
[CrossRef]

Laudati, A.

S. Campopiano, A. Cutolo, A. Cusano, M. Giordano, G. Parente, G. Lanza, and A. Laudati, “Underwater acoustic sensors based on fiber Bragg gratings,” Sensors 9, 4446–4454 (2009).
[CrossRef]

Li, Z. X.

Z. X. Li, L. Pei, C. H. Qi, W. J. Peng, T. G. Ning, R. F. Zhao, and S. Gao, “Fiber grating Fabry-Perot cavity studied by V-I transmission matrix method,” Acta Phys. Sin. 59, 8615–8624 (2010).

Loock, H. P.

McCall, M.

Minardo, A.

A. Minardo, A. Cusano, R. Bernini, L. Zeni, and M. Giordano, “Response of fiber Bragg grating to longitudinal ultrasonic waves,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 52, 304–312 (2005).
[CrossRef]

Muriel, M. A.

Ning, T. G.

Z. X. Li, L. Pei, C. H. Qi, W. J. Peng, T. G. Ning, R. F. Zhao, and S. Gao, “Fiber grating Fabry-Perot cavity studied by V-I transmission matrix method,” Acta Phys. Sin. 59, 8615–8624 (2010).

Ntziachristos, V.

Pannell, C. N.

N. E. Fisher, D. J. Webb, C. N. Pannell, D. A. Jackson, L. R. Gavrilov, J. W. Hand, L. Zhang, and I. Bennion, “Ultrasonic field and temperature sensor based on short in-fibre Bragg gratings,” Electron. Lett. 34, 1139–1140 (1998).
[CrossRef]

Parente, G.

S. Campopiano, A. Cutolo, A. Cusano, M. Giordano, G. Parente, G. Lanza, and A. Laudati, “Underwater acoustic sensors based on fiber Bragg gratings,” Sensors 9, 4446–4454 (2009).
[CrossRef]

Pastor, D.

Pei, L.

Z. X. Li, L. Pei, C. H. Qi, W. J. Peng, T. G. Ning, R. F. Zhao, and S. Gao, “Fiber grating Fabry-Perot cavity studied by V-I transmission matrix method,” Acta Phys. Sin. 59, 8615–8624 (2010).

Peng, W. J.

Z. X. Li, L. Pei, C. H. Qi, W. J. Peng, T. G. Ning, R. F. Zhao, and S. Gao, “Fiber grating Fabry-Perot cavity studied by V-I transmission matrix method,” Acta Phys. Sin. 59, 8615–8624 (2010).

Prada, C.

D. Clorennec, C. Prada, and D. Royer, “Laser ultrasonic inspection of plates using zero-group velocity lamb modes,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 57, 1125–1132 (2010).
[CrossRef]

Qi, C. H.

Z. X. Li, L. Pei, C. H. Qi, W. J. Peng, T. G. Ning, R. F. Zhao, and S. Gao, “Fiber grating Fabry-Perot cavity studied by V-I transmission matrix method,” Acta Phys. Sin. 59, 8615–8624 (2010).

Razansky, D.

Resendes, R.

Rosenthal, A.

Royer, D.

D. Clorennec, C. Prada, and D. Royer, “Laser ultrasonic inspection of plates using zero-group velocity lamb modes,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 57, 1125–1132 (2010).
[CrossRef]

Rubio, J. J.

Saari, J.

Sales, S.

Staszewski, W. J.

D. C. Betz, W. J. Staszewski, G. Thursby, and B. Culshaw, “Structural damage identification using multifunctional Bragg grating sensors: II damage detection results and analysis,” Smart Materials and Structures 15, 1313–1322 (2006).
[CrossRef]

C. Betz, G. Thursby, B. Culshaw, and W. J. Staszewski, “Acousto-ultrasonic sensing using fiber Bragg gratings,” Smart Materials and Structures 12, 122–128 (2003).
[CrossRef]

Thursby, G.

D. C. Betz, W. J. Staszewski, G. Thursby, and B. Culshaw, “Structural damage identification using multifunctional Bragg grating sensors: II damage detection results and analysis,” Smart Materials and Structures 15, 1313–1322 (2006).
[CrossRef]

C. Betz, G. Thursby, B. Culshaw, and W. J. Staszewski, “Acousto-ultrasonic sensing using fiber Bragg gratings,” Smart Materials and Structures 12, 122–128 (2003).
[CrossRef]

Trefiak, N. R.

Tsuda, H.

Webb, D. J.

N. E. Fisher, D. J. Webb, C. N. Pannell, D. A. Jackson, L. R. Gavrilov, J. W. Hand, L. Zhang, and I. Bennion, “Ultrasonic field and temperature sensor based on short in-fibre Bragg gratings,” Electron. Lett. 34, 1139–1140 (1998).
[CrossRef]

Wilcox, P. D.

C. J. Lane, A. K. Dunhill, B. W. Drinkwater, and P. D. Wilcox, “The inspection of anisotropic single-crystal components using a 2-D ultrasonic array,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 57, 2742–2752 (2010).
[CrossRef]

Wild, G.

G. Wild and S. Hinckley, “Acousto-ultrasonic optical fiber sensors: overview and state-of-the-art,” IEEE Sens. J. 8, 1184–1193 (2008).
[CrossRef]

Zeni, L.

A. Minardo, A. Cusano, R. Bernini, L. Zeni, and M. Giordano, “Response of fiber Bragg grating to longitudinal ultrasonic waves,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 52, 304–312 (2005).
[CrossRef]

Zhang, L.

N. E. Fisher, D. J. Webb, C. N. Pannell, D. A. Jackson, L. R. Gavrilov, J. W. Hand, L. Zhang, and I. Bennion, “Ultrasonic field and temperature sensor based on short in-fibre Bragg gratings,” Electron. Lett. 34, 1139–1140 (1998).
[CrossRef]

Zhao, R. F.

Z. X. Li, L. Pei, C. H. Qi, W. J. Peng, T. G. Ning, R. F. Zhao, and S. Gao, “Fiber grating Fabry-Perot cavity studied by V-I transmission matrix method,” Acta Phys. Sin. 59, 8615–8624 (2010).

Acta Phys. Sin. (1)

Z. X. Li, L. Pei, C. H. Qi, W. J. Peng, T. G. Ning, R. F. Zhao, and S. Gao, “Fiber grating Fabry-Perot cavity studied by V-I transmission matrix method,” Acta Phys. Sin. 59, 8615–8624 (2010).

Appl. Opt. (1)

Electron. Lett. (1)

N. E. Fisher, D. J. Webb, C. N. Pannell, D. A. Jackson, L. R. Gavrilov, J. W. Hand, L. Zhang, and I. Bennion, “Ultrasonic field and temperature sensor based on short in-fibre Bragg gratings,” Electron. Lett. 34, 1139–1140 (1998).
[CrossRef]

IEEE Sens. J. (1)

G. Wild and S. Hinckley, “Acousto-ultrasonic optical fiber sensors: overview and state-of-the-art,” IEEE Sens. J. 8, 1184–1193 (2008).
[CrossRef]

IEEE Trans. Ultrason. Ferroelectr. Freq. Control (3)

D. Clorennec, C. Prada, and D. Royer, “Laser ultrasonic inspection of plates using zero-group velocity lamb modes,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 57, 1125–1132 (2010).
[CrossRef]

C. J. Lane, A. K. Dunhill, B. W. Drinkwater, and P. D. Wilcox, “The inspection of anisotropic single-crystal components using a 2-D ultrasonic array,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 57, 2742–2752 (2010).
[CrossRef]

A. Minardo, A. Cusano, R. Bernini, L. Zeni, and M. Giordano, “Response of fiber Bragg grating to longitudinal ultrasonic waves,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 52, 304–312 (2005).
[CrossRef]

J. Lightwave Technol. (2)

Opt. Eng. (1)

P. Fomitchov and S. Krishnaswamy, “Response of a fiber Bragg grating ultrasonic sensor,” Opt. Eng. 42, 956–963 (2003).
[CrossRef]

Opt. Lett. (2)

Sensors (1)

S. Campopiano, A. Cutolo, A. Cusano, M. Giordano, G. Parente, G. Lanza, and A. Laudati, “Underwater acoustic sensors based on fiber Bragg gratings,” Sensors 9, 4446–4454 (2009).
[CrossRef]

Smart Materials and Structures (2)

C. Betz, G. Thursby, B. Culshaw, and W. J. Staszewski, “Acousto-ultrasonic sensing using fiber Bragg gratings,” Smart Materials and Structures 12, 122–128 (2003).
[CrossRef]

D. C. Betz, W. J. Staszewski, G. Thursby, and B. Culshaw, “Structural damage identification using multifunctional Bragg grating sensors: II damage detection results and analysis,” Smart Materials and Structures 15, 1313–1322 (2006).
[CrossRef]

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Figures (10)

Fig. 1.
Fig. 1.

Light propagates through adjacent layers within one period of fiber grating.

Fig. 2.
Fig. 2.

Error between reflection spectrum solved by V-I transmission matrix method and traditional transmission matrix method.

Fig. 3.
Fig. 3.

The refractive index distribution of FBG before ultrasonic wave interacting with.

Fig. 4.
Fig. 4.

Schematic diagram of the FBG composed of multilayers after interacting with ultrasonic wave.

Fig. 5.
Fig. 5.

Reflected spectrum shift of FBG under strain-optic and geometric effects.

Fig. 6.
Fig. 6.

Original FBG spectra (dotted lines) and spectra under influences of ultrasonic waves (solid lines) calculated for (a) λUS/L=0.1; (b) λUS/L=1; (c) λUS/L=10; (d) λUS/L=100.

Fig. 7.
Fig. 7.

Maximum amplitude change of reflectivity at FWHM ΔRF versus the ratio λUS/L.

Fig. 8.
Fig. 8.

Schematic diagram of the acoustic emission and detection scheme (left) and the spectrum of FBG used in the experiment (right).

Fig. 9.
Fig. 9.

The PZT excitation waveform (solid line) and the FBG response (dotted line).

Fig. 10.
Fig. 10.

Normalized optical signal strength plotted with respect to the ratio λUS/L, with L being the FBG length.

Equations (11)

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

[Em,iEm,r]=A[Em+1,iEm+1,r].
Vm=Em,i+Em,r,Im=1Ω(Em,iEm,r),
VIP=[cosϕjΩsinϕjsinϕΩcosϕ],ϕ=2πnλl,
n(z)=N+dn+dnsin(2πz/Λ),n(z)N+dn+4πdnsin(2πz/Λ),
n(z,t)=n(z)+Δn(z,t)=π4n(z)+(1π4)(N+dn),12N3[εUS(1σ)p12σεUSp11]·εUScos(kUSzwUSt),
z=z+εUSλUS2πsin(2πλUSzwUSt).
l(z,t)=l+Δl(z,t)=Λ2[1+εUScos(kUSzwUSt)].
VIm=[cosϕjΩsinϕjsinϕΩcosϕ]×[cosϕ^jΩ^sinϕ^jsinϕ^Ω^cosϕ^],ϕ=2πnmλlm,Ω=120πnm,ϕ^=2πn^mλl^m,Ω^=120πn^m.
VI=[ABCD]=m=1MVIm.
R=|r|2=(A+B/Ω^CΩDΩ/Ω^A+B/Ω^+CΩ+DΩ/Ω^)2,
λUS=ν/f,

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