Abstract

For a fiber Bragg grating (FBG) surface-bonded to a substrate subjected to tension, the FBG reflective wavelength spectrum measured using an optical spectrum analyzer is different in either the location of the center wavelength or the spectral shape from that calculated using the transfer matrix (T-matrix) method. We show that the difference in the two wavelength spectra is caused by the adhesive layer used to bond the FBG to the substrate and a birefringence effect within the strained FBG. In the former case, the adhesive reduces the strain transferred from the substrate to the FBG and, therefore, causes the T-matrix method to overestimate the shift in the center wavelength. In the latter case, a birefringence effect is induced within the FBG because only the lower part of the FBG is bonded to the stressed substrate. As a result, both the peak power and the full width at half-maximum of the experimental spectrum differ from that predicted by the T-matrix method, in which the effects of birefringence are ignored. However, it is shown that when the strain transmission loss and birefringence effect are compensated using a strain transmission correction factor and a modified T-matrix formulation based on a discretized value of the refractive index, respectively, a good agreement is obtained between the calculated spectrum and that measured experimentally.

© 2010 Optical Society of America

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References

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  1. M. LeBlanc, S. Y. Huang, M. Ohn, and R. M. Measures, “Tunable chirping of a fiber Bragg grating using a tapered cantilever beam,” Electron. Lett. 30, 2163–2165 (1994).
    [CrossRef]
  2. J. L. Cruz, A. Diez, M. V. Andres, A. Segura, B. Ortega, and L. Dong, “Fiber Bragg gratings tuned and chirped using magnetic field,” Electron. Lett. 33, 235–236 (1997).
    [CrossRef]
  3. M. Pacheco, A. Mendez, L. A. Zenteno, and F. Mendoza-Santoyo, “Chirping optical fiber Bragg gratings using tapered-thickness piezoelectric ceramic,” Electron. Lett. 34, 2348–2349 (1998).
    [CrossRef]
  4. A. Othonos and K. Kalli, Fiber Bragg Gratings: Fundamentals and Applications in Telecommunications and Sensing(Artech, 1999).
  5. C. C. Cheng, Y. L. Lo, B. S. Pun, E. M. Chang, and W. Y. Li “An investigation of bonding layer characteristics of a substrate-bonded fiber Bragg grating,” J. Lightwave Technol. 23, 3907–3915 (2005).
    [CrossRef]
  6. W. Y. Li, C. C. Cheng, and Y. L. Lo, “Investigation of strain transmission of surface-bonded FBGs used as strain sensors,” Sens. Actuators A 149, 201–207 (2009).
    [CrossRef]
  7. D. S. Li, H. N. Li, L. Ren, and G. B. Song, “Strain transferring analysis of fiber Bragg grating sensors,” Opt. Eng. 45, 024402 (2006).
    [CrossRef]
  8. S. Huang, M. LeBlanc, M. M. Ohn, and R. M. Measures, “Bragg intragrating structural sensing,” Appl. Opt. 34, 5003–5009 (1995).
    [CrossRef] [PubMed]
  9. T. Erdogan, “Fiber grating spectra,” J. Lightwave Technol. 15, 1277–1294 (1997).
    [CrossRef]
  10. P. Torres and L. C. G. Valente, “Spectral response of locally pressed fiber Bragg grating,” Opt. Commun. 208, 285–291(2002).
    [CrossRef]
  11. A. T. Alavie, R. Maaskant, R. Stubbe, A. Othonos, M. Ohn, B. Sahlgren, and R. M. Measures, “Characteristics of fiber grating sensors and their relation to manufacturing techniques,” Proc. SPIE 2444, 528–535(1995).
    [CrossRef]
  12. C. C. Cheng, Y. L. Lo, W. Y. Li, C. T. Kuo, and H. C. Cheng, “Estimations of fiber Bragg grating parameters and strain gauge factor using optical spectrum and strain distribution information,” Appl. Opt. 46, 4555–4562(2007).
    [CrossRef] [PubMed]
  13. R. Maaskant, T. Alavie, R. M. Measures, G. Tadros, S. H. Rizkalla, and A. Guha-Thakurta, “Fiber-optic Bragg grating sensors for bridge monitoring,” Cem. Concr. Compos. 19, 21–33 (1997).
    [CrossRef]
  14. M. Prabhugoud and K. Peters, “Finite element model for embedded fiber Bragg grating sensor,” Smart Mater. Struct. 15, 550–562 (2006).
    [CrossRef]

2009 (1)

W. Y. Li, C. C. Cheng, and Y. L. Lo, “Investigation of strain transmission of surface-bonded FBGs used as strain sensors,” Sens. Actuators A 149, 201–207 (2009).
[CrossRef]

2007 (1)

2006 (2)

M. Prabhugoud and K. Peters, “Finite element model for embedded fiber Bragg grating sensor,” Smart Mater. Struct. 15, 550–562 (2006).
[CrossRef]

D. S. Li, H. N. Li, L. Ren, and G. B. Song, “Strain transferring analysis of fiber Bragg grating sensors,” Opt. Eng. 45, 024402 (2006).
[CrossRef]

2005 (1)

2002 (1)

P. Torres and L. C. G. Valente, “Spectral response of locally pressed fiber Bragg grating,” Opt. Commun. 208, 285–291(2002).
[CrossRef]

1998 (1)

M. Pacheco, A. Mendez, L. A. Zenteno, and F. Mendoza-Santoyo, “Chirping optical fiber Bragg gratings using tapered-thickness piezoelectric ceramic,” Electron. Lett. 34, 2348–2349 (1998).
[CrossRef]

1997 (3)

J. L. Cruz, A. Diez, M. V. Andres, A. Segura, B. Ortega, and L. Dong, “Fiber Bragg gratings tuned and chirped using magnetic field,” Electron. Lett. 33, 235–236 (1997).
[CrossRef]

T. Erdogan, “Fiber grating spectra,” J. Lightwave Technol. 15, 1277–1294 (1997).
[CrossRef]

R. Maaskant, T. Alavie, R. M. Measures, G. Tadros, S. H. Rizkalla, and A. Guha-Thakurta, “Fiber-optic Bragg grating sensors for bridge monitoring,” Cem. Concr. Compos. 19, 21–33 (1997).
[CrossRef]

1995 (2)

A. T. Alavie, R. Maaskant, R. Stubbe, A. Othonos, M. Ohn, B. Sahlgren, and R. M. Measures, “Characteristics of fiber grating sensors and their relation to manufacturing techniques,” Proc. SPIE 2444, 528–535(1995).
[CrossRef]

S. Huang, M. LeBlanc, M. M. Ohn, and R. M. Measures, “Bragg intragrating structural sensing,” Appl. Opt. 34, 5003–5009 (1995).
[CrossRef] [PubMed]

1994 (1)

M. LeBlanc, S. Y. Huang, M. Ohn, and R. M. Measures, “Tunable chirping of a fiber Bragg grating using a tapered cantilever beam,” Electron. Lett. 30, 2163–2165 (1994).
[CrossRef]

Alavie, A. T.

A. T. Alavie, R. Maaskant, R. Stubbe, A. Othonos, M. Ohn, B. Sahlgren, and R. M. Measures, “Characteristics of fiber grating sensors and their relation to manufacturing techniques,” Proc. SPIE 2444, 528–535(1995).
[CrossRef]

Alavie, T.

R. Maaskant, T. Alavie, R. M. Measures, G. Tadros, S. H. Rizkalla, and A. Guha-Thakurta, “Fiber-optic Bragg grating sensors for bridge monitoring,” Cem. Concr. Compos. 19, 21–33 (1997).
[CrossRef]

Andres, M. V.

J. L. Cruz, A. Diez, M. V. Andres, A. Segura, B. Ortega, and L. Dong, “Fiber Bragg gratings tuned and chirped using magnetic field,” Electron. Lett. 33, 235–236 (1997).
[CrossRef]

Chang, E. M.

Cheng, C. C.

Cheng, H. C.

Cruz, J. L.

J. L. Cruz, A. Diez, M. V. Andres, A. Segura, B. Ortega, and L. Dong, “Fiber Bragg gratings tuned and chirped using magnetic field,” Electron. Lett. 33, 235–236 (1997).
[CrossRef]

Diez, A.

J. L. Cruz, A. Diez, M. V. Andres, A. Segura, B. Ortega, and L. Dong, “Fiber Bragg gratings tuned and chirped using magnetic field,” Electron. Lett. 33, 235–236 (1997).
[CrossRef]

Dong, L.

J. L. Cruz, A. Diez, M. V. Andres, A. Segura, B. Ortega, and L. Dong, “Fiber Bragg gratings tuned and chirped using magnetic field,” Electron. Lett. 33, 235–236 (1997).
[CrossRef]

Erdogan, T.

T. Erdogan, “Fiber grating spectra,” J. Lightwave Technol. 15, 1277–1294 (1997).
[CrossRef]

Guha-Thakurta, A.

R. Maaskant, T. Alavie, R. M. Measures, G. Tadros, S. H. Rizkalla, and A. Guha-Thakurta, “Fiber-optic Bragg grating sensors for bridge monitoring,” Cem. Concr. Compos. 19, 21–33 (1997).
[CrossRef]

Huang, S.

Huang, S. Y.

M. LeBlanc, S. Y. Huang, M. Ohn, and R. M. Measures, “Tunable chirping of a fiber Bragg grating using a tapered cantilever beam,” Electron. Lett. 30, 2163–2165 (1994).
[CrossRef]

Kalli, K.

A. Othonos and K. Kalli, Fiber Bragg Gratings: Fundamentals and Applications in Telecommunications and Sensing(Artech, 1999).

Kuo, C. T.

LeBlanc, M.

S. Huang, M. LeBlanc, M. M. Ohn, and R. M. Measures, “Bragg intragrating structural sensing,” Appl. Opt. 34, 5003–5009 (1995).
[CrossRef] [PubMed]

M. LeBlanc, S. Y. Huang, M. Ohn, and R. M. Measures, “Tunable chirping of a fiber Bragg grating using a tapered cantilever beam,” Electron. Lett. 30, 2163–2165 (1994).
[CrossRef]

Li, D. S.

D. S. Li, H. N. Li, L. Ren, and G. B. Song, “Strain transferring analysis of fiber Bragg grating sensors,” Opt. Eng. 45, 024402 (2006).
[CrossRef]

Li, H. N.

D. S. Li, H. N. Li, L. Ren, and G. B. Song, “Strain transferring analysis of fiber Bragg grating sensors,” Opt. Eng. 45, 024402 (2006).
[CrossRef]

Li, W. Y.

Lo, Y. L.

Maaskant, R.

R. Maaskant, T. Alavie, R. M. Measures, G. Tadros, S. H. Rizkalla, and A. Guha-Thakurta, “Fiber-optic Bragg grating sensors for bridge monitoring,” Cem. Concr. Compos. 19, 21–33 (1997).
[CrossRef]

A. T. Alavie, R. Maaskant, R. Stubbe, A. Othonos, M. Ohn, B. Sahlgren, and R. M. Measures, “Characteristics of fiber grating sensors and their relation to manufacturing techniques,” Proc. SPIE 2444, 528–535(1995).
[CrossRef]

Measures, R. M.

R. Maaskant, T. Alavie, R. M. Measures, G. Tadros, S. H. Rizkalla, and A. Guha-Thakurta, “Fiber-optic Bragg grating sensors for bridge monitoring,” Cem. Concr. Compos. 19, 21–33 (1997).
[CrossRef]

S. Huang, M. LeBlanc, M. M. Ohn, and R. M. Measures, “Bragg intragrating structural sensing,” Appl. Opt. 34, 5003–5009 (1995).
[CrossRef] [PubMed]

A. T. Alavie, R. Maaskant, R. Stubbe, A. Othonos, M. Ohn, B. Sahlgren, and R. M. Measures, “Characteristics of fiber grating sensors and their relation to manufacturing techniques,” Proc. SPIE 2444, 528–535(1995).
[CrossRef]

M. LeBlanc, S. Y. Huang, M. Ohn, and R. M. Measures, “Tunable chirping of a fiber Bragg grating using a tapered cantilever beam,” Electron. Lett. 30, 2163–2165 (1994).
[CrossRef]

Mendez, A.

M. Pacheco, A. Mendez, L. A. Zenteno, and F. Mendoza-Santoyo, “Chirping optical fiber Bragg gratings using tapered-thickness piezoelectric ceramic,” Electron. Lett. 34, 2348–2349 (1998).
[CrossRef]

Mendoza-Santoyo, F.

M. Pacheco, A. Mendez, L. A. Zenteno, and F. Mendoza-Santoyo, “Chirping optical fiber Bragg gratings using tapered-thickness piezoelectric ceramic,” Electron. Lett. 34, 2348–2349 (1998).
[CrossRef]

Ohn, M.

A. T. Alavie, R. Maaskant, R. Stubbe, A. Othonos, M. Ohn, B. Sahlgren, and R. M. Measures, “Characteristics of fiber grating sensors and their relation to manufacturing techniques,” Proc. SPIE 2444, 528–535(1995).
[CrossRef]

M. LeBlanc, S. Y. Huang, M. Ohn, and R. M. Measures, “Tunable chirping of a fiber Bragg grating using a tapered cantilever beam,” Electron. Lett. 30, 2163–2165 (1994).
[CrossRef]

Ohn, M. M.

Ortega, B.

J. L. Cruz, A. Diez, M. V. Andres, A. Segura, B. Ortega, and L. Dong, “Fiber Bragg gratings tuned and chirped using magnetic field,” Electron. Lett. 33, 235–236 (1997).
[CrossRef]

Othonos, A.

A. T. Alavie, R. Maaskant, R. Stubbe, A. Othonos, M. Ohn, B. Sahlgren, and R. M. Measures, “Characteristics of fiber grating sensors and their relation to manufacturing techniques,” Proc. SPIE 2444, 528–535(1995).
[CrossRef]

A. Othonos and K. Kalli, Fiber Bragg Gratings: Fundamentals and Applications in Telecommunications and Sensing(Artech, 1999).

Pacheco, M.

M. Pacheco, A. Mendez, L. A. Zenteno, and F. Mendoza-Santoyo, “Chirping optical fiber Bragg gratings using tapered-thickness piezoelectric ceramic,” Electron. Lett. 34, 2348–2349 (1998).
[CrossRef]

Peters, K.

M. Prabhugoud and K. Peters, “Finite element model for embedded fiber Bragg grating sensor,” Smart Mater. Struct. 15, 550–562 (2006).
[CrossRef]

Prabhugoud, M.

M. Prabhugoud and K. Peters, “Finite element model for embedded fiber Bragg grating sensor,” Smart Mater. Struct. 15, 550–562 (2006).
[CrossRef]

Pun, B. S.

Ren, L.

D. S. Li, H. N. Li, L. Ren, and G. B. Song, “Strain transferring analysis of fiber Bragg grating sensors,” Opt. Eng. 45, 024402 (2006).
[CrossRef]

Rizkalla, S. H.

R. Maaskant, T. Alavie, R. M. Measures, G. Tadros, S. H. Rizkalla, and A. Guha-Thakurta, “Fiber-optic Bragg grating sensors for bridge monitoring,” Cem. Concr. Compos. 19, 21–33 (1997).
[CrossRef]

Sahlgren, B.

A. T. Alavie, R. Maaskant, R. Stubbe, A. Othonos, M. Ohn, B. Sahlgren, and R. M. Measures, “Characteristics of fiber grating sensors and their relation to manufacturing techniques,” Proc. SPIE 2444, 528–535(1995).
[CrossRef]

Segura, A.

J. L. Cruz, A. Diez, M. V. Andres, A. Segura, B. Ortega, and L. Dong, “Fiber Bragg gratings tuned and chirped using magnetic field,” Electron. Lett. 33, 235–236 (1997).
[CrossRef]

Song, G. B.

D. S. Li, H. N. Li, L. Ren, and G. B. Song, “Strain transferring analysis of fiber Bragg grating sensors,” Opt. Eng. 45, 024402 (2006).
[CrossRef]

Stubbe, R.

A. T. Alavie, R. Maaskant, R. Stubbe, A. Othonos, M. Ohn, B. Sahlgren, and R. M. Measures, “Characteristics of fiber grating sensors and their relation to manufacturing techniques,” Proc. SPIE 2444, 528–535(1995).
[CrossRef]

Tadros, G.

R. Maaskant, T. Alavie, R. M. Measures, G. Tadros, S. H. Rizkalla, and A. Guha-Thakurta, “Fiber-optic Bragg grating sensors for bridge monitoring,” Cem. Concr. Compos. 19, 21–33 (1997).
[CrossRef]

Torres, P.

P. Torres and L. C. G. Valente, “Spectral response of locally pressed fiber Bragg grating,” Opt. Commun. 208, 285–291(2002).
[CrossRef]

Valente, L. C. G.

P. Torres and L. C. G. Valente, “Spectral response of locally pressed fiber Bragg grating,” Opt. Commun. 208, 285–291(2002).
[CrossRef]

Zenteno, L. A.

M. Pacheco, A. Mendez, L. A. Zenteno, and F. Mendoza-Santoyo, “Chirping optical fiber Bragg gratings using tapered-thickness piezoelectric ceramic,” Electron. Lett. 34, 2348–2349 (1998).
[CrossRef]

Appl. Opt. (2)

Cem. Concr. Compos. (1)

R. Maaskant, T. Alavie, R. M. Measures, G. Tadros, S. H. Rizkalla, and A. Guha-Thakurta, “Fiber-optic Bragg grating sensors for bridge monitoring,” Cem. Concr. Compos. 19, 21–33 (1997).
[CrossRef]

Electron. Lett. (3)

M. LeBlanc, S. Y. Huang, M. Ohn, and R. M. Measures, “Tunable chirping of a fiber Bragg grating using a tapered cantilever beam,” Electron. Lett. 30, 2163–2165 (1994).
[CrossRef]

J. L. Cruz, A. Diez, M. V. Andres, A. Segura, B. Ortega, and L. Dong, “Fiber Bragg gratings tuned and chirped using magnetic field,” Electron. Lett. 33, 235–236 (1997).
[CrossRef]

M. Pacheco, A. Mendez, L. A. Zenteno, and F. Mendoza-Santoyo, “Chirping optical fiber Bragg gratings using tapered-thickness piezoelectric ceramic,” Electron. Lett. 34, 2348–2349 (1998).
[CrossRef]

J. Lightwave Technol. (2)

Opt. Commun. (1)

P. Torres and L. C. G. Valente, “Spectral response of locally pressed fiber Bragg grating,” Opt. Commun. 208, 285–291(2002).
[CrossRef]

Opt. Eng. (1)

D. S. Li, H. N. Li, L. Ren, and G. B. Song, “Strain transferring analysis of fiber Bragg grating sensors,” Opt. Eng. 45, 024402 (2006).
[CrossRef]

Proc. SPIE (1)

A. T. Alavie, R. Maaskant, R. Stubbe, A. Othonos, M. Ohn, B. Sahlgren, and R. M. Measures, “Characteristics of fiber grating sensors and their relation to manufacturing techniques,” Proc. SPIE 2444, 528–535(1995).
[CrossRef]

Sens. Actuators A (1)

W. Y. Li, C. C. Cheng, and Y. L. Lo, “Investigation of strain transmission of surface-bonded FBGs used as strain sensors,” Sens. Actuators A 149, 201–207 (2009).
[CrossRef]

Smart Mater. Struct. (1)

M. Prabhugoud and K. Peters, “Finite element model for embedded fiber Bragg grating sensor,” Smart Mater. Struct. 15, 550–562 (2006).
[CrossRef]

Other (1)

A. Othonos and K. Kalli, Fiber Bragg Gratings: Fundamentals and Applications in Telecommunications and Sensing(Artech, 1999).

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Figures (11)

Fig. 1
Fig. 1

FBG surface bonded to a cantilever: (a) top and side views, (b) cross-sectional view, and (c) experimental setup.

Fig. 2
Fig. 2

Comparison of experimental wave length spectra and spectra simulated using the traditional T-matrix method.

Fig. 3
Fig. 3

Comparison of experimental wavelength spectra and spectra simulated using the T-matrix method with a strain transmission rate of K = 50 % .

Fig. 4
Fig. 4

3D FE model of a FBG bonded on a substrate: (a) model dimensions and (b) FE mesh.

Fig. 5
Fig. 5

Strain distribution along the center plane of the cantilever for free end displacements of 2.1, 3.6, 5.1, and 8.1 mm , respectively.

Fig. 6
Fig. 6

Stress distributions in a FBG core for a substrate compressive strain of 0.67%: (a) stress in the x direction ( σ x ), (b) stress in the y direction ( σ y ), and (c) stress in the z direction ( σ z ).

Fig. 7
Fig. 7

Distribution of the refractive index in a FBG for a substrate compressive strain of 0.67% and light transmitted in the (a) horizontal direction (X polarized) and (b) vertical direction (Y polarized).

Fig. 8
Fig. 8

Simulated spectral response with and without the birefringence effect taken into account for the substrate compressive strain of 0.67%.

Fig. 9
Fig. 9

Difference in center wavelength due to the birefringence effect when the surface-bonded FBG is compressed.

Fig. 10
Fig. 10

Comparison of the experimental wavelength spectra and wavelength spectra calculated by the T-matrix method with the strain transmission rate and birefringence effects taken into account.

Fig. 11
Fig. 11

(a) Variation of index modulation with respect to center wavelength shift caused by external force and (b) comparison of experimental wavelength spectra and wavelength spectra simulated using the T-matrix method with the strain transmission rate, birefringence, and variable index modulation effect taken into account.

Tables (2)

Tables Icon

Table 1 Fiber Bragg Grating Parameters

Tables Icon

Table 2 Material Parameters and Geometric Dimensions Used in Finite Element Simulations

Equations (14)

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

[ a i + a i ] = T ( i ) [ a i + 1 + a i + 1 ] = [ T 11 ( i ) T 12 ( i ) T 21 ( i ) T 22 ( i ) ] [ a i + 1 + a i + 1 ] ,
T 11 ( i ) = T 22 ( i ) * = cosh ( γ Δ z ) i σ ^ γ sinh ( γ Δ z ) , T 12 ( i ) = T 21 ( i ) * = i κ γ sinh ( γ Δ z ) , γ = κ 2 σ ^ 2 ,
δ n eff ( z ) = δ n ¯ eff ( z ) { 1 + υ cos [ 2 π Λ z + ϕ ( z ) ] } ,
h ( z ) = δ n ¯ eff exp [ a ( z 0.5 L L ) 2 ] ,
[ a 0 + a 0 ] = T ( 1 ) · T ( 2 ) T ( m 1 ) · T ( m ) [ a m + a m ] .
Δ λ λ B = K ( 1 n 2 2 ( p 12 + p 11 ε x x ε z z + p 12 ε y y ε z z ) ) ε z z ,
Δ λ λ B = G F ε z z ,
K = ( 1 1 cosh Γ ¯ ) ( E s t s E s t s + E F t F ) ( E s A s E s A s + E F A F + E B A B ) ,
( n x n co ) = c 1 σ x + c 2 ( σ y + σ z ) ,
c 1 = n co 3 2 E ( p 11 2 μ p 12 ) ,
c 2 = n co 3 2 E [ ( 1 μ ) p 12 μ p 11 ] .
R ( λ , n x , n y ) = | a 0 + a 0 | 2 ,
R D ( λ , n x , n y ) = n = 1 N A n R n ( λ , n x , n ) + m = 1 M A m R m ( λ , n y , m ) ,
κ = π λ υ Γ δ n co ¯ exp [ a ( z 0.5 L L ) 2 ] ,

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