Abstract

We demonstrate a fiber-optic 3D vector displacement sensor based on the monitoring of Bragg reflection from an eccentric grating inscribed in a depressed-cladding fiber using the femtosecond laser side-illumination and phase-mask technique. The compact sensing probe consists of a short section of depressed cladding fiber (DCF) containing eccentrically positioned fiber Bragg gratings. The eccentric grating breaks the cylindrical symmetry of the fiber cross-section and further has bending orientation-dependence. The generated fundamental resonance is strongly sensitive to bending of the fiber, and the direction of the bending plane can be determined from its responses. When integrated with axis strain monitoring, the sensor achieves a 3D vector displacement measurement via simple geometric analysis.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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    [Crossref]
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    [Crossref]
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    [Crossref]
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2017 (2)

K. M. Yang, J. He, C. Liao, Y. Wang, S. Liu, K. Guo, J. Zhou, Z. Li, Z. Tan, and Y. Wang, “Femtosecond Laser Inscription of Fiber Bragg Grating in Twin-core Few-mode Fiber for Directional Bend Sensing,” J. Lightwave Technol. 35(21), 4670–4676 (2017).
[Crossref]

Q. Rong, T. Guo, W. Bao, Z. Shao, G. D. Peng, and X. Qiao, “Highly sensitive fiber-optic accelerometer by grating inscription in specific core dip fiber,” Sci. Rep. 7(1), 11856 (2017).
[Crossref] [PubMed]

2016 (3)

D. Feng, X. Qiao, and J. Albert, “Off-axis ultraviolet-written fiber Bragg gratings for directional bending measurements,” Opt. Lett. 41(6), 1201–1204 (2016).
[Crossref] [PubMed]

J. Kong, X. W. Ouyang, A. Zhou, and L. B. Yuan, “Highly Sensitive Directional Bending Sensor Based on Eccentric Core Fiber Mach–Zehnder Modal Interferometer,” IEEE Sens. J. 16(18), 6899–6902 (2016).
[Crossref]

K. Chah, D. Kinet, and C. Caucheteur, “Negative axial strain sensitivity in gold-coated eccentric fiber Bragg gratings,” Sci. Rep. 6(1), 38042 (2016).
[Crossref] [PubMed]

2015 (3)

W. J. Bao, X. G. Qiao, Q. Z. Rong, N. F. Hu, H. Z. Yang, Z. Y. Feng, and M. L. Hu, “Sensing Characteristics for a Fiber Bragg Grating Inscribed Over a Fiber Core and Cladding,” IEEE Photonics Technol. Lett. 27(7), 709–712 (2015).
[Crossref]

C. Waltermann, A. Doering, M. Köhring, M. Angelmahr, and W. Schade, “Cladding waveguide gratings in standard single-mode fiber for 3D shape sensing,” Opt. Lett. 40(13), 3109–3112 (2015).
[Crossref] [PubMed]

D. Feng, W. Zhou, X. Qiao, and J. Albert, “Compact Optical Fiber 3D Shape Sensor Based on a Pair of Orthogonal Tilted Fiber Bragg Gratings,” Sci. Rep. 5(1), 17415 (2015).
[Crossref] [PubMed]

2014 (1)

2012 (2)

2010 (1)

2009 (1)

X. Chen, C. Zhang, D. J. Webb, R. Suo, G. D. Peng, and K. Kalli, “Optical bend sensor for vector curvature measurement based on Bragg grating in eccentric core polymer optical fibre,” Proc. SPIE 7503, 750327 (2009).
[Crossref]

2007 (1)

R. T. Schermer and J. H. Cole, “Improved Bend Loss Formula Verified for Optical Fiber by Simulation and Experiment,” IEEE J. Quantum Electron. 43(10), 899–909 (2007).
[Crossref]

2006 (1)

2005 (1)

2004 (1)

2003 (2)

G. M. H. Flockhart, W. N. MacPherson, J. S. Barton, J. D. C. Jones, L. Zhang, and I. Bennion, “Two-axis bend measurement with Bragg gratings in multicore optical fiber,” Opt. Lett. 28(6), 387–389 (2003).
[Crossref] [PubMed]

A. Mehta, W. Mohammed, and E. G. Johnson, “Multimode interference-based fiber-optic displacement sensor,” IEEE Photonics Technol. Lett. 15(8), 1129–1131 (2003).
[Crossref]

2001 (1)

X. Y. Dong, Y. Liu, Z. G. Liu, and X. Y. Dong, “Simultaneous displacement and temperature measurement with cantilever-based fiber Bragg grating sensor,” Opt. Commun. 192(3-6), 213–217 (2001).
[Crossref]

1998 (1)

1997 (2)

L. Dong, L. Reekie, J. L. Cruz, J. E. Caplen, J. P. de Sandro, and D. N. Payne, “Optical fibers with depressed claddings for suppression of coupling into cladding modes in fiber Bragg gratings,” IEEE Photonics Technol. Lett. 9(1), 64–66 (1997).
[Crossref]

L. Faustini and G. Martini, “Bend Loss in Single-Mode Fibers,” J. Lightwave Technol. 15(4), 671–679 (1997).
[Crossref]

1980 (1)

1976 (2)

1975 (1)

M. Heiblum and J. H. Harris, “Analysis of curved optical waveguides by conformal transformation,” IEEE J. Quantum Electron. 11(5), 313 (1975).

Albert, J.

Angelmahr, M.

Bao, W.

Q. Rong, T. Guo, W. Bao, Z. Shao, G. D. Peng, and X. Qiao, “Highly sensitive fiber-optic accelerometer by grating inscription in specific core dip fiber,” Sci. Rep. 7(1), 11856 (2017).
[Crossref] [PubMed]

Bao, W. J.

W. J. Bao, X. G. Qiao, Q. Z. Rong, N. F. Hu, H. Z. Yang, Z. Y. Feng, and M. L. Hu, “Sensing Characteristics for a Fiber Bragg Grating Inscribed Over a Fiber Core and Cladding,” IEEE Photonics Technol. Lett. 27(7), 709–712 (2015).
[Crossref]

Barton, J. S.

Bennion, I.

Block, U. L.

Caplen, J. E.

L. Dong, L. Reekie, J. L. Cruz, J. E. Caplen, J. P. de Sandro, and D. N. Payne, “Optical fibers with depressed claddings for suppression of coupling into cladding modes in fiber Bragg gratings,” IEEE Photonics Technol. Lett. 9(1), 64–66 (1997).
[Crossref]

Caucheteur, C.

K. Chah, D. Kinet, and C. Caucheteur, “Negative axial strain sensitivity in gold-coated eccentric fiber Bragg gratings,” Sci. Rep. 6(1), 38042 (2016).
[Crossref] [PubMed]

K. Chah, V. Voisin, D. Kinet, and C. Caucheteur, “Surface plasmon resonance in eccentric femtosecond-laser-induced fiber Bragg gratings,” Opt. Lett. 39(24), 6887–6890 (2014).
[Crossref] [PubMed]

Chah, K.

K. Chah, D. Kinet, and C. Caucheteur, “Negative axial strain sensitivity in gold-coated eccentric fiber Bragg gratings,” Sci. Rep. 6(1), 38042 (2016).
[Crossref] [PubMed]

K. Chah, V. Voisin, D. Kinet, and C. Caucheteur, “Surface plasmon resonance in eccentric femtosecond-laser-induced fiber Bragg gratings,” Opt. Lett. 39(24), 6887–6890 (2014).
[Crossref] [PubMed]

Chen, C. K.

Chen, X.

X. Chen, C. Zhang, D. J. Webb, R. Suo, G. D. Peng, and K. Kalli, “Optical bend sensor for vector curvature measurement based on Bragg grating in eccentric core polymer optical fibre,” Proc. SPIE 7503, 750327 (2009).
[Crossref]

D. Zhao, X. Chen, K. Zhou, L. Zhang, I. Bennion, W. N. MacPherson, J. S. Barton, and J. D. C. Jones, “Bend sensors with direction recognition based on long-period gratings written in D-shaped fiber,” Appl. Opt. 43(29), 5425–5428 (2004).
[Crossref] [PubMed]

Cole, J. H.

R. T. Schermer and J. H. Cole, “Improved Bend Loss Formula Verified for Optical Fiber by Simulation and Experiment,” IEEE J. Quantum Electron. 43(10), 899–909 (2007).
[Crossref]

Cruz, J. L.

L. Dong, L. Reekie, J. L. Cruz, J. E. Caplen, J. P. de Sandro, and D. N. Payne, “Optical fibers with depressed claddings for suppression of coupling into cladding modes in fiber Bragg gratings,” IEEE Photonics Technol. Lett. 9(1), 64–66 (1997).
[Crossref]

Dangui, V.

de Sandro, J. P.

L. Dong, L. Reekie, J. L. Cruz, J. E. Caplen, J. P. de Sandro, and D. N. Payne, “Optical fibers with depressed claddings for suppression of coupling into cladding modes in fiber Bragg gratings,” IEEE Photonics Technol. Lett. 9(1), 64–66 (1997).
[Crossref]

Digonnet, M. J. F.

Doering, A.

Dong, L.

L. Dong, L. Reekie, J. L. Cruz, J. E. Caplen, J. P. de Sandro, and D. N. Payne, “Optical fibers with depressed claddings for suppression of coupling into cladding modes in fiber Bragg gratings,” IEEE Photonics Technol. Lett. 9(1), 64–66 (1997).
[Crossref]

Dong, X. Y.

X. Y. Dong, Y. Liu, Z. G. Liu, and X. Y. Dong, “Simultaneous displacement and temperature measurement with cantilever-based fiber Bragg grating sensor,” Opt. Commun. 192(3-6), 213–217 (2001).
[Crossref]

X. Y. Dong, Y. Liu, Z. G. Liu, and X. Y. Dong, “Simultaneous displacement and temperature measurement with cantilever-based fiber Bragg grating sensor,” Opt. Commun. 192(3-6), 213–217 (2001).
[Crossref]

Faustini, L.

L. Faustini and G. Martini, “Bend Loss in Single-Mode Fibers,” J. Lightwave Technol. 15(4), 671–679 (1997).
[Crossref]

Fejer, M. M.

Feng, D.

D. Feng, X. Qiao, and J. Albert, “Off-axis ultraviolet-written fiber Bragg gratings for directional bending measurements,” Opt. Lett. 41(6), 1201–1204 (2016).
[Crossref] [PubMed]

D. Feng, W. Zhou, X. Qiao, and J. Albert, “Compact Optical Fiber 3D Shape Sensor Based on a Pair of Orthogonal Tilted Fiber Bragg Gratings,” Sci. Rep. 5(1), 17415 (2015).
[Crossref] [PubMed]

Feng, Z. Y.

W. J. Bao, X. G. Qiao, Q. Z. Rong, N. F. Hu, H. Z. Yang, Z. Y. Feng, and M. L. Hu, “Sensing Characteristics for a Fiber Bragg Grating Inscribed Over a Fiber Core and Cladding,” IEEE Photonics Technol. Lett. 27(7), 709–712 (2015).
[Crossref]

Q. Z. Rong, X. G. Qiao, J. Zhang, R. H. Wang, M. L. Hu, and Z. Y. Feng, “Simultaneous Measurement for Displacement and Temperature Using Fiber Bragg Grating Cladding Mode Based on Core Diameter Mismatch,” J. Lightwave Technol. 30(11), 1645–1650 (2012).
[Crossref]

Flockhart, G. M. H.

Gao, S.

Geng, P.

Grobnic, D.

Guo, K.

Guo, T.

Q. Rong, T. Guo, W. Bao, Z. Shao, G. D. Peng, and X. Qiao, “Highly sensitive fiber-optic accelerometer by grating inscription in specific core dip fiber,” Sci. Rep. 7(1), 11856 (2017).
[Crossref] [PubMed]

Haggans, C. W.

Harris, J. H.

M. Heiblum and J. H. Harris, “Analysis of curved optical waveguides by conformal transformation,” IEEE J. Quantum Electron. 11(5), 313 (1975).

He, J.

Heiblum, M.

M. Heiblum and J. H. Harris, “Analysis of curved optical waveguides by conformal transformation,” IEEE J. Quantum Electron. 11(5), 313 (1975).

Hu, M. L.

W. J. Bao, X. G. Qiao, Q. Z. Rong, N. F. Hu, H. Z. Yang, Z. Y. Feng, and M. L. Hu, “Sensing Characteristics for a Fiber Bragg Grating Inscribed Over a Fiber Core and Cladding,” IEEE Photonics Technol. Lett. 27(7), 709–712 (2015).
[Crossref]

Q. Z. Rong, X. G. Qiao, J. Zhang, R. H. Wang, M. L. Hu, and Z. Y. Feng, “Simultaneous Measurement for Displacement and Temperature Using Fiber Bragg Grating Cladding Mode Based on Core Diameter Mismatch,” J. Lightwave Technol. 30(11), 1645–1650 (2012).
[Crossref]

Hu, N. F.

W. J. Bao, X. G. Qiao, Q. Z. Rong, N. F. Hu, H. Z. Yang, Z. Y. Feng, and M. L. Hu, “Sensing Characteristics for a Fiber Bragg Grating Inscribed Over a Fiber Core and Cladding,” IEEE Photonics Technol. Lett. 27(7), 709–712 (2015).
[Crossref]

Johnson, E. G.

A. Mehta, W. Mohammed, and E. G. Johnson, “Multimode interference-based fiber-optic displacement sensor,” IEEE Photonics Technol. Lett. 15(8), 1129–1131 (2003).
[Crossref]

Jones, J. D. C.

Kalli, K.

X. Chen, C. Zhang, D. J. Webb, R. Suo, G. D. Peng, and K. Kalli, “Optical bend sensor for vector curvature measurement based on Bragg grating in eccentric core polymer optical fibre,” Proc. SPIE 7503, 750327 (2009).
[Crossref]

Kinet, D.

K. Chah, D. Kinet, and C. Caucheteur, “Negative axial strain sensitivity in gold-coated eccentric fiber Bragg gratings,” Sci. Rep. 6(1), 38042 (2016).
[Crossref] [PubMed]

K. Chah, V. Voisin, D. Kinet, and C. Caucheteur, “Surface plasmon resonance in eccentric femtosecond-laser-induced fiber Bragg gratings,” Opt. Lett. 39(24), 6887–6890 (2014).
[Crossref] [PubMed]

Köhring, M.

Kong, J.

J. Kong, X. W. Ouyang, A. Zhou, and L. B. Yuan, “Highly Sensitive Directional Bending Sensor Based on Eccentric Core Fiber Mach–Zehnder Modal Interferometer,” IEEE Sens. J. 16(18), 6899–6902 (2016).
[Crossref]

Laronche, A.

Li, Z.

Liao, C.

Liu, S.

Liu, Y.

X. Y. Dong, Y. Liu, Z. G. Liu, and X. Y. Dong, “Simultaneous displacement and temperature measurement with cantilever-based fiber Bragg grating sensor,” Opt. Commun. 192(3-6), 213–217 (2001).
[Crossref]

Liu, Z. G.

X. Y. Dong, Y. Liu, Z. G. Liu, and X. Y. Dong, “Simultaneous displacement and temperature measurement with cantilever-based fiber Bragg grating sensor,” Opt. Commun. 192(3-6), 213–217 (2001).
[Crossref]

MacPherson, W. N.

Marcuse, D.

Martini, G.

L. Faustini and G. Martini, “Bend Loss in Single-Mode Fibers,” J. Lightwave Technol. 15(4), 671–679 (1997).
[Crossref]

Mehta, A.

A. Mehta, W. Mohammed, and E. G. Johnson, “Multimode interference-based fiber-optic displacement sensor,” IEEE Photonics Technol. Lett. 15(8), 1129–1131 (2003).
[Crossref]

Mihailov, S.

Mohammed, W.

A. Mehta, W. Mohammed, and E. G. Johnson, “Multimode interference-based fiber-optic displacement sensor,” IEEE Photonics Technol. Lett. 15(8), 1129–1131 (2003).
[Crossref]

Ouyang, X. W.

J. Kong, X. W. Ouyang, A. Zhou, and L. B. Yuan, “Highly Sensitive Directional Bending Sensor Based on Eccentric Core Fiber Mach–Zehnder Modal Interferometer,” IEEE Sens. J. 16(18), 6899–6902 (2016).
[Crossref]

Payne, D. N.

L. Dong, L. Reekie, J. L. Cruz, J. E. Caplen, J. P. de Sandro, and D. N. Payne, “Optical fibers with depressed claddings for suppression of coupling into cladding modes in fiber Bragg gratings,” IEEE Photonics Technol. Lett. 9(1), 64–66 (1997).
[Crossref]

Peng, G. D.

Q. Rong, T. Guo, W. Bao, Z. Shao, G. D. Peng, and X. Qiao, “Highly sensitive fiber-optic accelerometer by grating inscription in specific core dip fiber,” Sci. Rep. 7(1), 11856 (2017).
[Crossref] [PubMed]

X. Chen, C. Zhang, D. J. Webb, R. Suo, G. D. Peng, and K. Kalli, “Optical bend sensor for vector curvature measurement based on Bragg grating in eccentric core polymer optical fibre,” Proc. SPIE 7503, 750327 (2009).
[Crossref]

Qiao, X.

Q. Rong, T. Guo, W. Bao, Z. Shao, G. D. Peng, and X. Qiao, “Highly sensitive fiber-optic accelerometer by grating inscription in specific core dip fiber,” Sci. Rep. 7(1), 11856 (2017).
[Crossref] [PubMed]

D. Feng, X. Qiao, and J. Albert, “Off-axis ultraviolet-written fiber Bragg gratings for directional bending measurements,” Opt. Lett. 41(6), 1201–1204 (2016).
[Crossref] [PubMed]

D. Feng, W. Zhou, X. Qiao, and J. Albert, “Compact Optical Fiber 3D Shape Sensor Based on a Pair of Orthogonal Tilted Fiber Bragg Gratings,” Sci. Rep. 5(1), 17415 (2015).
[Crossref] [PubMed]

Qiao, X. G.

W. J. Bao, X. G. Qiao, Q. Z. Rong, N. F. Hu, H. Z. Yang, Z. Y. Feng, and M. L. Hu, “Sensing Characteristics for a Fiber Bragg Grating Inscribed Over a Fiber Core and Cladding,” IEEE Photonics Technol. Lett. 27(7), 709–712 (2015).
[Crossref]

Q. Z. Rong, X. G. Qiao, J. Zhang, R. H. Wang, M. L. Hu, and Z. Y. Feng, “Simultaneous Measurement for Displacement and Temperature Using Fiber Bragg Grating Cladding Mode Based on Core Diameter Mismatch,” J. Lightwave Technol. 30(11), 1645–1650 (2012).
[Crossref]

Reekie, L.

L. Dong, L. Reekie, J. L. Cruz, J. E. Caplen, J. P. de Sandro, and D. N. Payne, “Optical fibers with depressed claddings for suppression of coupling into cladding modes in fiber Bragg gratings,” IEEE Photonics Technol. Lett. 9(1), 64–66 (1997).
[Crossref]

Rong, Q.

Q. Rong, T. Guo, W. Bao, Z. Shao, G. D. Peng, and X. Qiao, “Highly sensitive fiber-optic accelerometer by grating inscription in specific core dip fiber,” Sci. Rep. 7(1), 11856 (2017).
[Crossref] [PubMed]

Rong, Q. Z.

W. J. Bao, X. G. Qiao, Q. Z. Rong, N. F. Hu, H. Z. Yang, Z. Y. Feng, and M. L. Hu, “Sensing Characteristics for a Fiber Bragg Grating Inscribed Over a Fiber Core and Cladding,” IEEE Photonics Technol. Lett. 27(7), 709–712 (2015).
[Crossref]

Q. Z. Rong, X. G. Qiao, J. Zhang, R. H. Wang, M. L. Hu, and Z. Y. Feng, “Simultaneous Measurement for Displacement and Temperature Using Fiber Bragg Grating Cladding Mode Based on Core Diameter Mismatch,” J. Lightwave Technol. 30(11), 1645–1650 (2012).
[Crossref]

Schade, W.

Schermer, R. T.

R. T. Schermer and J. H. Cole, “Improved Bend Loss Formula Verified for Optical Fiber by Simulation and Experiment,” IEEE J. Quantum Electron. 43(10), 899–909 (2007).
[Crossref]

Shao, L. Y.

Shao, Z.

Q. Rong, T. Guo, W. Bao, Z. Shao, G. D. Peng, and X. Qiao, “Highly sensitive fiber-optic accelerometer by grating inscription in specific core dip fiber,” Sci. Rep. 7(1), 11856 (2017).
[Crossref] [PubMed]

Singh, H.

Smelser, C.

Smith, A. M.

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X. Chen, C. Zhang, D. J. Webb, R. Suo, G. D. Peng, and K. Kalli, “Optical bend sensor for vector curvature measurement based on Bragg grating in eccentric core polymer optical fibre,” Proc. SPIE 7503, 750327 (2009).
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Figures (9)

Fig. 1
Fig. 1 (a) Schematic of the eccentric grating. (b) Photomicrograph of the DCF cross section and the position illustration for normal inscription (white dash). (b) Diffraction patterns of the laser after passing through the fiber core for normal inscription (upper) and off-axis inscription (below).
Fig. 2
Fig. 2 Reflection spectra of the normal FBG (blue) and eccentric FBG (red).
Fig. 3
Fig. 3 (a) Schematic of a circularly bent fiber. (b) Refractive index profile distribution of an undisturbed (black line) and a bent fiber (red).
Fig. 4
Fig. 4 The E-field distribution of straight fiber versus different bending condition: (a) bending toward FBG side; (b) unbent; (c) bending backward FBG side. (d) The reflection spectra corresponding to different bending condition: blue (a); red (b); yellow (c).
Fig. 5
Fig. 5 Schematic of an axially stretched fiber.
Fig. 6
Fig. 6 (a) Schematic diagram of the displacement measurement. (b) Vector decomposition in circular cylindrical coordinates.
Fig. 7
Fig. 7 (a) Reflection spectra versus different 2D-plane displacements. (b) Reflection spectra versus a certain 2D-plane displacement in different directions.
Fig. 8
Fig. 8 The fundamental mode intensity changes versus different 2D-plane displacements (0-360°) with amplitude of 0.05 mm, 0.08 mm, and 0.11 mm.
Fig. 9
Fig. 9 The fundamental mode wavelength shift and reflection spectra (insert) versus different axis displacements.

Equations (6)

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n m =(n+Δn)(1+ x R )
Δn=( n 3 2 )( p 12 ν p 12 ν p 11 ) x R
R eff = R 1( n 2 2 )( p 12 ν p 12 ν p 11 ) x R
n m =n(1+ x R eff )
Δ n eff =( n eff 3 2 )( p 12 ν p 12 ν p 11 ) ΔL L =( n eff 3 2 )( p 12 ν p 12 ν p 11 ) ΔΛ Λ
Δ λ B = λ B L [ 1( n eff 2 2 )( p 12 ν p 12 ν p 11 ) ]ΔL

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