Abstract

This paper presents an experiment and analysis on the factors affecting nonlinear evolution of Bragg wavelength with change in temperature in typical bare and embedded fiber Bragg grating-based (FBG) temperature sensors. The purpose of the study was to find the constants in the function required to evaluate temperature from Bragg wavelength shift. The temperature sensitivity of bare FBGs was found to increase with temperature elevation, and is different for FBGs written in different fiber types. The average temperature sensitivity increased by about 20% when the bare FBG temperature was elevated from 25°C to 525°C. The average temperature sensitivity of the embedded FBG sensor, investigated in the temperature range of 30°C–90°C, was a factor of 2–3 times larger than for bare FBG, depending on its fastened length with the substrate. Analytically, it is shown that the nonuniform behavior of temperature sensitivity in bare FBGs is the result of both the thermal expansion effect of the fiber and the temperature derivatives of the effective refractive index. The strain transfer and temperature coefficients of thermal expansion of the substrate affect the nonuniform behavior of temperature sensitivity in embedded FBG sensors.

© 2013 Optical Society of America

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  1. A. D. Kersey, M. A. Davis, H. J. Patrick, M. LeBlance, K. P. Koo, C. G. Askins, M. A. Putnam, and E. J. Friebele, “Fiber grating sensors,” J. Lightwave Technol. 15, 1442–1463 (1997).
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  23. N. H. Ky, H. G. Limberger, R. P. Salathe, F. Cochet, and L. Dong, “UV-irradiation-induced stress and index changes during the growth of type-I and type-IIA fiber gratings,” Opt. Commun. 225, 313–318 (2003).
    [CrossRef]
  24. J. Kumar, R. Mahakud, O. Prakash, and S. K. Dixit, “Study on hydrofluoric acid-based clad etching and chemical sensing characteristics of fiber Bragg gratings of different reflectivity fabricated under different UV exposure times,” Opt. Eng. 52, 054402 (2013).
    [CrossRef]
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2013 (1)

J. Kumar, R. Mahakud, O. Prakash, and S. K. Dixit, “Study on hydrofluoric acid-based clad etching and chemical sensing characteristics of fiber Bragg gratings of different reflectivity fabricated under different UV exposure times,” Opt. Eng. 52, 054402 (2013).
[CrossRef]

2012 (2)

S. J. Mihailov, “Fiber Bragg grating sensors for harsh environments,” Sensors 12, 1898–1918 (2012).
[CrossRef]

G. J. de Villiers, J. Treurnicht, and R. T. Dobson, “In-core high temperature measurement using fiber-Bragg gratings for nuclear reactors,” Appl. Therm. Eng. 38, 143–150 (2012).
[CrossRef]

2011 (2)

S.-C. Her and C.-Y. Huang, “Effect of coating on the strain transfer of optical fiber sensors,” Sensors 11, 6926–6941 (2011).
[CrossRef]

V. de Oliveira, M. Muller, and H. J. Kalinowski, “Bragg gratings in standard non-hydrogenated fibres for high-temperature sensing,” Appl. Opt. 50, E55–E58 (2011).
[CrossRef]

2007 (1)

2006 (2)

O. Prakash, R. Mahakud, S. K. Dixit, and U. Nundy, “Effect of the spatial coherence of ultraviolet radiation (255 nm) on the fabrication efficiency of phase mask-based fiber Bragg gratings,” Opt. Commun. 263, 65–70 (2006).
[CrossRef]

X. Zhang, Z. Wu, and B. Zhang, “Strain dependence of fiber Bragg grating sensors at low temperature,” Opt. Eng. 45, 054401 (2006).
[CrossRef]

2004 (3)

2003 (1)

N. H. Ky, H. G. Limberger, R. P. Salathe, F. Cochet, and L. Dong, “UV-irradiation-induced stress and index changes during the growth of type-I and type-IIA fiber gratings,” Opt. Commun. 225, 313–318 (2003).
[CrossRef]

2002 (1)

O. V. Butov, K. M. Golant, and I. V. Nikolin, “Ultra-thermo resistant Bragg gratings written in nitrogen-doped silica fibres,” Electron. Lett. 38, 523–525 (2002).
[CrossRef]

1999 (1)

1998 (2)

L. Yuan and L. Zhou, “Sensitivity coefficient evaluation of an embedded fiber-optic strain sensor,” Sens. Actuators A 69, 5–11 (1998).
[CrossRef]

M. B. Reid and M. Ozcan, “Temperature dependence of fiber optic Bragg gratings at low temperatures,” Opt. Eng. 37, 237–240 (1998).
[CrossRef]

1997 (2)

A. D. Kersey, M. A. Davis, H. J. Patrick, M. LeBlance, K. P. Koo, C. G. Askins, M. A. Putnam, and E. J. Friebele, “Fiber grating sensors,” J. Lightwave Technol. 15, 1442–1463 (1997).
[CrossRef]

G. Ghosh, “Sellmeier coefficients and dispersion of thermo-optic coefficients for some optical glasses,” Appl. Opt. 36, 1540–1546 (1997).
[CrossRef]

1996 (1)

1994 (2)

T. Erdogan, V. Mizrahi, P. J. Lemaire, and D. Monroe, “Decay of ultraviolet induced fiber Bragg gratings,” J. Appl. Phys. 76, 73–80 (1994).
[CrossRef]

G. Ghosh, M. Endo, and T. Iwasaki, “Temperature-dependent Sellmeier coefficients and chromatic dispersions for some optical-fiber glasses,” J. Lightwave Technol. 12, 1338–1342 (1994).
[CrossRef]

1991 (1)

J. Matsuoka, N. Kitamura, S. Fujinaga, T. Kitaoka, and H. Yamashita, “Temperature dependence of refractive index of SiO2 glass,” J. Non-Cryst. Solids 135, 86–89 (1991).
[CrossRef]

1969 (1)

1941 (1)

F. C. Nix and D. MacNair, “The thermal expansion of pure metals: copper, gold, aluminum, nickel, and iron”, Phys. Rev. 60, 597–605 (1941).
[CrossRef]

Askins, C. G.

A. D. Kersey, M. A. Davis, H. J. Patrick, M. LeBlance, K. P. Koo, C. G. Askins, M. A. Putnam, and E. J. Friebele, “Fiber grating sensors,” J. Lightwave Technol. 15, 1442–1463 (1997).
[CrossRef]

Bartelt, H.

Barton, J. S.

Bennion, I.

Butov, O. V.

O. V. Butov, K. M. Golant, and I. V. Nikolin, “Ultra-thermo resistant Bragg gratings written in nitrogen-doped silica fibres,” Electron. Lett. 38, 523–525 (2002).
[CrossRef]

Chisholm, K. E.

Chojetzki, C.

Cochet, F.

N. H. Ky, H. G. Limberger, R. P. Salathe, F. Cochet, and L. Dong, “UV-irradiation-induced stress and index changes during the growth of type-I and type-IIA fiber gratings,” Opt. Commun. 225, 313–318 (2003).
[CrossRef]

Davis, M. A.

A. D. Kersey, M. A. Davis, H. J. Patrick, M. LeBlance, K. P. Koo, C. G. Askins, M. A. Putnam, and E. J. Friebele, “Fiber grating sensors,” J. Lightwave Technol. 15, 1442–1463 (1997).
[CrossRef]

de Oliveira, V.

de Villiers, G. J.

G. J. de Villiers, J. Treurnicht, and R. T. Dobson, “In-core high temperature measurement using fiber-Bragg gratings for nuclear reactors,” Appl. Therm. Eng. 38, 143–150 (2012).
[CrossRef]

Dixit, S. K.

J. Kumar, R. Mahakud, O. Prakash, and S. K. Dixit, “Study on hydrofluoric acid-based clad etching and chemical sensing characteristics of fiber Bragg gratings of different reflectivity fabricated under different UV exposure times,” Opt. Eng. 52, 054402 (2013).
[CrossRef]

O. Prakash, R. Mahakud, S. K. Dixit, and U. Nundy, “Effect of the spatial coherence of ultraviolet radiation (255 nm) on the fabrication efficiency of phase mask-based fiber Bragg gratings,” Opt. Commun. 263, 65–70 (2006).
[CrossRef]

Dobson, R. T.

G. J. de Villiers, J. Treurnicht, and R. T. Dobson, “In-core high temperature measurement using fiber-Bragg gratings for nuclear reactors,” Appl. Therm. Eng. 38, 143–150 (2012).
[CrossRef]

Dong, L.

N. H. Ky, H. G. Limberger, R. P. Salathe, F. Cochet, and L. Dong, “UV-irradiation-induced stress and index changes during the growth of type-I and type-IIA fiber gratings,” Opt. Commun. 225, 313–318 (2003).
[CrossRef]

Endo, M.

G. Ghosh, M. Endo, and T. Iwasaki, “Temperature-dependent Sellmeier coefficients and chromatic dispersions for some optical-fiber glasses,” J. Lightwave Technol. 12, 1338–1342 (1994).
[CrossRef]

Erdogan, T.

T. Erdogan, V. Mizrahi, P. J. Lemaire, and D. Monroe, “Decay of ultraviolet induced fiber Bragg gratings,” J. Appl. Phys. 76, 73–80 (1994).
[CrossRef]

Flockhart, M. H.

Foote, P. D.

Friebele, E. J.

A. D. Kersey, M. A. Davis, H. J. Patrick, M. LeBlance, K. P. Koo, C. G. Askins, M. A. Putnam, and E. J. Friebele, “Fiber grating sensors,” J. Lightwave Technol. 15, 1442–1463 (1997).
[CrossRef]

Fujinaga, S.

J. Matsuoka, N. Kitamura, S. Fujinaga, T. Kitaoka, and H. Yamashita, “Temperature dependence of refractive index of SiO2 glass,” J. Non-Cryst. Solids 135, 86–89 (1991).
[CrossRef]

Ghosh, G.

G. Ghosh, “Sellmeier coefficients and dispersion of thermo-optic coefficients for some optical glasses,” Appl. Opt. 36, 1540–1546 (1997).
[CrossRef]

G. Ghosh, M. Endo, and T. Iwasaki, “Temperature-dependent Sellmeier coefficients and chromatic dispersions for some optical-fiber glasses,” J. Lightwave Technol. 12, 1338–1342 (1994).
[CrossRef]

Golant, K. M.

O. V. Butov, K. M. Golant, and I. V. Nikolin, “Ultra-thermo resistant Bragg gratings written in nitrogen-doped silica fibres,” Electron. Lett. 38, 523–525 (2002).
[CrossRef]

Gordon, A.

Grattan, K. T. V.

Grobnic, D.

D. Grobnic, J. Stephen, C. Mihailov, W. Smelser, and D. Huimin, “Sapphire fibre Bragg grating sensor made using femtosecond laser radiation for ultrahigh temperature applications,” IEEE Photon. Technol. Lett. 16, 2505–2507 (2004).
[CrossRef]

Gupta, S.

He, J.

Her, S.-C.

S.-C. Her and C.-Y. Huang, “Effect of coating on the strain transfer of optical fiber sensors,” Sensors 11, 6926–6941 (2011).
[CrossRef]

Huang, C.-Y.

S.-C. Her and C.-Y. Huang, “Effect of coating on the strain transfer of optical fiber sensors,” Sensors 11, 6926–6941 (2011).
[CrossRef]

Huimin, D.

D. Grobnic, J. Stephen, C. Mihailov, W. Smelser, and D. Huimin, “Sapphire fibre Bragg grating sensor made using femtosecond laser radiation for ultrahigh temperature applications,” IEEE Photon. Technol. Lett. 16, 2505–2507 (2004).
[CrossRef]

Iwasaki, T.

G. Ghosh, M. Endo, and T. Iwasaki, “Temperature-dependent Sellmeier coefficients and chromatic dispersions for some optical-fiber glasses,” J. Lightwave Technol. 12, 1338–1342 (1994).
[CrossRef]

Jones, J. D. C.

Jung, J.

Kalinowski, H. J.

Kashyap, R.

R. Kashyap, Fiber Bragg Gratings (Academic, 1999).

Kersey, A. D.

A. D. Kersey, M. A. Davis, H. J. Patrick, M. LeBlance, K. P. Koo, C. G. Askins, M. A. Putnam, and E. J. Friebele, “Fiber grating sensors,” J. Lightwave Technol. 15, 1442–1463 (1997).
[CrossRef]

Kim, N. S.

Kitamura, N.

J. Matsuoka, N. Kitamura, S. Fujinaga, T. Kitaoka, and H. Yamashita, “Temperature dependence of refractive index of SiO2 glass,” J. Non-Cryst. Solids 135, 86–89 (1991).
[CrossRef]

Kitaoka, T.

J. Matsuoka, N. Kitamura, S. Fujinaga, T. Kitaoka, and H. Yamashita, “Temperature dependence of refractive index of SiO2 glass,” J. Non-Cryst. Solids 135, 86–89 (1991).
[CrossRef]

Koo, K. P.

A. D. Kersey, M. A. Davis, H. J. Patrick, M. LeBlance, K. P. Koo, C. G. Askins, M. A. Putnam, and E. J. Friebele, “Fiber grating sensors,” J. Lightwave Technol. 15, 1442–1463 (1997).
[CrossRef]

Kumar, J.

J. Kumar, R. Mahakud, O. Prakash, and S. K. Dixit, “Study on hydrofluoric acid-based clad etching and chemical sensing characteristics of fiber Bragg gratings of different reflectivity fabricated under different UV exposure times,” Opt. Eng. 52, 054402 (2013).
[CrossRef]

Ky, N. H.

N. H. Ky, H. G. Limberger, R. P. Salathe, F. Cochet, and L. Dong, “UV-irradiation-induced stress and index changes during the growth of type-I and type-IIA fiber gratings,” Opt. Commun. 225, 313–318 (2003).
[CrossRef]

Latka, I.

LeBlance, M.

A. D. Kersey, M. A. Davis, H. J. Patrick, M. LeBlance, K. P. Koo, C. G. Askins, M. A. Putnam, and E. J. Friebele, “Fiber grating sensors,” J. Lightwave Technol. 15, 1442–1463 (1997).
[CrossRef]

Lee, B.

Lemaire, P. J.

T. Erdogan, V. Mizrahi, P. J. Lemaire, and D. Monroe, “Decay of ultraviolet induced fiber Bragg gratings,” J. Appl. Phys. 76, 73–80 (1994).
[CrossRef]

Limberger, H. G.

N. H. Ky, H. G. Limberger, R. P. Salathe, F. Cochet, and L. Dong, “UV-irradiation-induced stress and index changes during the growth of type-I and type-IIA fiber gratings,” Opt. Commun. 225, 313–318 (2003).
[CrossRef]

MacNair, D.

F. C. Nix and D. MacNair, “The thermal expansion of pure metals: copper, gold, aluminum, nickel, and iron”, Phys. Rev. 60, 597–605 (1941).
[CrossRef]

MacPherson, W. N.

Mahakud, R.

J. Kumar, R. Mahakud, O. Prakash, and S. K. Dixit, “Study on hydrofluoric acid-based clad etching and chemical sensing characteristics of fiber Bragg gratings of different reflectivity fabricated under different UV exposure times,” Opt. Eng. 52, 054402 (2013).
[CrossRef]

O. Prakash, R. Mahakud, S. K. Dixit, and U. Nundy, “Effect of the spatial coherence of ultraviolet radiation (255 nm) on the fabrication efficiency of phase mask-based fiber Bragg gratings,” Opt. Commun. 263, 65–70 (2006).
[CrossRef]

Maier, R. J.

Matsuoka, J.

J. Matsuoka, N. Kitamura, S. Fujinaga, T. Kitaoka, and H. Yamashita, “Temperature dependence of refractive index of SiO2 glass,” J. Non-Cryst. Solids 135, 86–89 (1991).
[CrossRef]

Mihailov, C.

D. Grobnic, J. Stephen, C. Mihailov, W. Smelser, and D. Huimin, “Sapphire fibre Bragg grating sensor made using femtosecond laser radiation for ultrahigh temperature applications,” IEEE Photon. Technol. Lett. 16, 2505–2507 (2004).
[CrossRef]

Mihailov, S. J.

S. J. Mihailov, “Fiber Bragg grating sensors for harsh environments,” Sensors 12, 1898–1918 (2012).
[CrossRef]

Mizrahi, V.

T. Erdogan, V. Mizrahi, P. J. Lemaire, and D. Monroe, “Decay of ultraviolet induced fiber Bragg gratings,” J. Appl. Phys. 76, 73–80 (1994).
[CrossRef]

Mizunami, T.

Monroe, D.

T. Erdogan, V. Mizrahi, P. J. Lemaire, and D. Monroe, “Decay of ultraviolet induced fiber Bragg gratings,” J. Appl. Phys. 76, 73–80 (1994).
[CrossRef]

Muller, M.

Nam, H.

Neu, J. T.

Nikolin, I. V.

O. V. Butov, K. M. Golant, and I. V. Nikolin, “Ultra-thermo resistant Bragg gratings written in nitrogen-doped silica fibres,” Electron. Lett. 38, 523–525 (2002).
[CrossRef]

Nix, F. C.

F. C. Nix and D. MacNair, “The thermal expansion of pure metals: copper, gold, aluminum, nickel, and iron”, Phys. Rev. 60, 597–605 (1941).
[CrossRef]

Nundy, U.

O. Prakash, R. Mahakud, S. K. Dixit, and U. Nundy, “Effect of the spatial coherence of ultraviolet radiation (255 nm) on the fabrication efficiency of phase mask-based fiber Bragg gratings,” Opt. Commun. 263, 65–70 (2006).
[CrossRef]

Oh Byun, J.

Ozcan, M.

M. B. Reid and M. Ozcan, “Temperature dependence of fiber optic Bragg gratings at low temperatures,” Opt. Eng. 37, 237–240 (1998).
[CrossRef]

Patrick, H. J.

A. D. Kersey, M. A. Davis, H. J. Patrick, M. LeBlance, K. P. Koo, C. G. Askins, M. A. Putnam, and E. J. Friebele, “Fiber grating sensors,” J. Lightwave Technol. 15, 1442–1463 (1997).
[CrossRef]

Prakash, O.

J. Kumar, R. Mahakud, O. Prakash, and S. K. Dixit, “Study on hydrofluoric acid-based clad etching and chemical sensing characteristics of fiber Bragg gratings of different reflectivity fabricated under different UV exposure times,” Opt. Eng. 52, 054402 (2013).
[CrossRef]

O. Prakash, R. Mahakud, S. K. Dixit, and U. Nundy, “Effect of the spatial coherence of ultraviolet radiation (255 nm) on the fabrication efficiency of phase mask-based fiber Bragg gratings,” Opt. Commun. 263, 65–70 (2006).
[CrossRef]

Putnam, M. A.

A. D. Kersey, M. A. Davis, H. J. Patrick, M. LeBlance, K. P. Koo, C. G. Askins, M. A. Putnam, and E. J. Friebele, “Fiber grating sensors,” J. Lightwave Technol. 15, 1442–1463 (1997).
[CrossRef]

Read, I.

Reid, M. B.

M. B. Reid and M. Ozcan, “Temperature dependence of fiber optic Bragg gratings at low temperatures,” Opt. Eng. 37, 237–240 (1998).
[CrossRef]

Rothhardt, M.

Salathe, R. P.

N. H. Ky, H. G. Limberger, R. P. Salathe, F. Cochet, and L. Dong, “UV-irradiation-induced stress and index changes during the growth of type-I and type-IIA fiber gratings,” Opt. Commun. 225, 313–318 (2003).
[CrossRef]

Schuster, K.

Shen, Y.

Shimomura, T.

Smelser, W.

D. Grobnic, J. Stephen, C. Mihailov, W. Smelser, and D. Huimin, “Sapphire fibre Bragg grating sensor made using femtosecond laser radiation for ultrahigh temperature applications,” IEEE Photon. Technol. Lett. 16, 2505–2507 (2004).
[CrossRef]

Stephen, J.

D. Grobnic, J. Stephen, C. Mihailov, W. Smelser, and D. Huimin, “Sapphire fibre Bragg grating sensor made using femtosecond laser radiation for ultrahigh temperature applications,” IEEE Photon. Technol. Lett. 16, 2505–2507 (2004).
[CrossRef]

Sun, T.

Treurnicht, J.

G. J. de Villiers, J. Treurnicht, and R. T. Dobson, “In-core high temperature measurement using fiber-Bragg gratings for nuclear reactors,” Appl. Therm. Eng. 38, 143–150 (2012).
[CrossRef]

Unger, S.

Wray, J. H.

Wu, Z.

X. Zhang, Z. Wu, and B. Zhang, “Strain dependence of fiber Bragg grating sensors at low temperature,” Opt. Eng. 45, 054401 (2006).
[CrossRef]

Yamao, T.

Yamashita, H.

J. Matsuoka, N. Kitamura, S. Fujinaga, T. Kitaoka, and H. Yamashita, “Temperature dependence of refractive index of SiO2 glass,” J. Non-Cryst. Solids 135, 86–89 (1991).
[CrossRef]

Yuan, L.

L. Yuan and L. Zhou, “Sensitivity coefficient evaluation of an embedded fiber-optic strain sensor,” Sens. Actuators A 69, 5–11 (1998).
[CrossRef]

Zhang, B.

X. Zhang, Z. Wu, and B. Zhang, “Strain dependence of fiber Bragg grating sensors at low temperature,” Opt. Eng. 45, 054401 (2006).
[CrossRef]

Zhang, L.

Zhang, X.

X. Zhang, Z. Wu, and B. Zhang, “Strain dependence of fiber Bragg grating sensors at low temperature,” Opt. Eng. 45, 054401 (2006).
[CrossRef]

Zhou, L.

L. Yuan and L. Zhou, “Sensitivity coefficient evaluation of an embedded fiber-optic strain sensor,” Sens. Actuators A 69, 5–11 (1998).
[CrossRef]

Appl. Opt. (6)

Appl. Therm. Eng. (1)

G. J. de Villiers, J. Treurnicht, and R. T. Dobson, “In-core high temperature measurement using fiber-Bragg gratings for nuclear reactors,” Appl. Therm. Eng. 38, 143–150 (2012).
[CrossRef]

Electron. Lett. (1)

O. V. Butov, K. M. Golant, and I. V. Nikolin, “Ultra-thermo resistant Bragg gratings written in nitrogen-doped silica fibres,” Electron. Lett. 38, 523–525 (2002).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

D. Grobnic, J. Stephen, C. Mihailov, W. Smelser, and D. Huimin, “Sapphire fibre Bragg grating sensor made using femtosecond laser radiation for ultrahigh temperature applications,” IEEE Photon. Technol. Lett. 16, 2505–2507 (2004).
[CrossRef]

J. Appl. Phys. (1)

T. Erdogan, V. Mizrahi, P. J. Lemaire, and D. Monroe, “Decay of ultraviolet induced fiber Bragg gratings,” J. Appl. Phys. 76, 73–80 (1994).
[CrossRef]

J. Lightwave Technol. (2)

A. D. Kersey, M. A. Davis, H. J. Patrick, M. LeBlance, K. P. Koo, C. G. Askins, M. A. Putnam, and E. J. Friebele, “Fiber grating sensors,” J. Lightwave Technol. 15, 1442–1463 (1997).
[CrossRef]

G. Ghosh, M. Endo, and T. Iwasaki, “Temperature-dependent Sellmeier coefficients and chromatic dispersions for some optical-fiber glasses,” J. Lightwave Technol. 12, 1338–1342 (1994).
[CrossRef]

J. Non-Cryst. Solids (1)

J. Matsuoka, N. Kitamura, S. Fujinaga, T. Kitaoka, and H. Yamashita, “Temperature dependence of refractive index of SiO2 glass,” J. Non-Cryst. Solids 135, 86–89 (1991).
[CrossRef]

J. Opt. Soc. Am. (1)

Opt. Commun. (2)

O. Prakash, R. Mahakud, S. K. Dixit, and U. Nundy, “Effect of the spatial coherence of ultraviolet radiation (255 nm) on the fabrication efficiency of phase mask-based fiber Bragg gratings,” Opt. Commun. 263, 65–70 (2006).
[CrossRef]

N. H. Ky, H. G. Limberger, R. P. Salathe, F. Cochet, and L. Dong, “UV-irradiation-induced stress and index changes during the growth of type-I and type-IIA fiber gratings,” Opt. Commun. 225, 313–318 (2003).
[CrossRef]

Opt. Eng. (3)

J. Kumar, R. Mahakud, O. Prakash, and S. K. Dixit, “Study on hydrofluoric acid-based clad etching and chemical sensing characteristics of fiber Bragg gratings of different reflectivity fabricated under different UV exposure times,” Opt. Eng. 52, 054402 (2013).
[CrossRef]

X. Zhang, Z. Wu, and B. Zhang, “Strain dependence of fiber Bragg grating sensors at low temperature,” Opt. Eng. 45, 054401 (2006).
[CrossRef]

M. B. Reid and M. Ozcan, “Temperature dependence of fiber optic Bragg gratings at low temperatures,” Opt. Eng. 37, 237–240 (1998).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. (1)

F. C. Nix and D. MacNair, “The thermal expansion of pure metals: copper, gold, aluminum, nickel, and iron”, Phys. Rev. 60, 597–605 (1941).
[CrossRef]

Sens. Actuators A (1)

L. Yuan and L. Zhou, “Sensitivity coefficient evaluation of an embedded fiber-optic strain sensor,” Sens. Actuators A 69, 5–11 (1998).
[CrossRef]

Sensors (2)

S.-C. Her and C.-Y. Huang, “Effect of coating on the strain transfer of optical fiber sensors,” Sensors 11, 6926–6941 (2011).
[CrossRef]

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[CrossRef]

Other (1)

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Figures (7)

Fig. 1.
Fig. 1.

Transmission spectrum of FBG written in CMS-1550-R1.

Fig. 2.
Fig. 2.

Reflection spectra of FBG at different temperatures.

Fig. 3.
Fig. 3.

(a) Bragg wavelength shift and (b) average temperature sensitivity with increase in temperature.

Fig. 4.
Fig. 4.

Bragg wavelength shift with increase in temperature for fiber (a) A (GF1), (b) B (PS1550), and average temperature sensitivity at different temperatures for fibers (c) A and (d) B.

Fig. 5.
Fig. 5.

Simulated Bragg wavelength shift versus temperature change for typical FBGs written in fibers A, B, and C (a) Bragg wavelength shift 0–6 nm and (b) Bragg wavelength shift 4–6 nm.

Fig. 6.
Fig. 6.

Simulated (a) temperature sensitivity and (b) temperature change versus Bragg wavelength shift for a dual-end-embedded FBG.

Fig. 7.
Fig. 7.

(a) Schematic of the dual-end-embedded FBG temperature sensor. (b) Bragg wavelength shift with change in temperature for different fastened lengths.

Tables (1)

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Table 1. First and Second Derivatives of Effective Refractive Index with Temperature

Equations (12)

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Δλ=λ(κT+αf)ΔT+λkεg,
neff(T)=c0+c1ΔT+c2ΔT2+c2ΔT3+,
Λ(T)=Λ0(1+αfΔT).
λ(T)λ(T0)+a1(TT0)+a2(TT0)2+a3(TT0)3+,
S(T)=dλdT=a1+2a2(TT0)+3a3(TT0)2+.
S(T)=a1+a2(TT0)+a3(TT0)2+.
T=T0+p[1+qΔλ1],
δTera3(TT0)3a1+2a2(TT0).
Δλ=b1(TT0)+b2(TT0)2,
T=T0+b12b2[1+4b2Δλb121].
εg=(αhαf)ΔT/(1+χ/L).
ξ=1/(1+χ/L).

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