Abstract

The theoretical model of etched fiber Bragg grating (FBG) backward cladding-mode resonances for ambient refractive index sensing is presented. The dependent behaviors of the mode resonances have been analyzed in the etching process and the ambient refractive index changed. The analysis is based on the classical coupling-mode theory while considering interactions among multiple modes and developed on a three-layer step-index fiber geometry. Experimental data match the theoretical model wonderfully. This model not only describes the relationship between the FBG backward cladding-mode resonances and the ambient index but also is valuable for the design of a flexible highly sensitive ambient index sensor.

© 2007 Optical Society of America

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  1. N. Chen, B. Yun, and Y. Cui, "Cladding mode resonances of etch-eroded fiber Bragg grating for ambient refractive index sensing," Appl. Phys. Lett. 88, 133902 (2006).
    [CrossRef]
  2. W. Liang, Y. Huang, Y. Xu, R. K. Lee, and A. Yariv, "Highly sensitive fiber Bragg grating refractive index sensors," Appl. Phys. Lett. 86, 151122 (2005).
    [CrossRef]
  3. A. Iadicicco, S. Campopiano, A. Cutolo, M. Giordano, and A. Cusano, "Refractive index sensor based on microstructured fiber Bragg grating," IEEE Photon. Technol. Lett. 17, 1250-1252 (2005).
    [CrossRef]
  4. A. Iadicicco, A. Cusano, A. Cutolo, R. Bernini, and M. Giordano, "Thinned fiber Bragg gratings as high sensitivity refractive index sensor," IEEE Photon. Technol. Lett. 16, 1149-1151 (2004).
    [CrossRef]
  5. K. Zhou, X. Chen, L. Zhang, and I. Bennion, "High-sensitivity optical chemsensor based on etched D-fibre Bragg gratings," Electron. Lett. 40, 232-234 (2004).
    [CrossRef]
  6. K. Schroeder, W. Ecke, R. Mueller, R. Willsch, and A. Andreev, "A fibre Bragg grating refractometer," Meas. Sci. Technol. 12, 757-764 (2001).
    [CrossRef]
  7. H. J. Patrick, A. D. Kersey, and F. Bucholtz, "Analysis of the response of long period fiber gratings to external index of refraction," J. Lightwave Technol. 16, 1606-1612 (1998).
    [CrossRef]
  8. K. S. Chiang, Y. Liu, M. Ng, and X. Dong, "Analysis of etched long-period fibre grating and its response to external refractive index," Electron. Lett. 36, 966-967 (2000).
    [CrossRef]
  9. X. Shu, L. Zhang, and I. Bennion, "Sensitivity characteristics of long-period fiber gratings," J. Lightwave Technol. 20, 255-266 (2002).
    [CrossRef]
  10. A. D. Kersey, M. A. Davis, H. J. Patrick, M. LeBlanc, K. P. Koo, C. G. Askins, M. A. Putnam, and E. J. Friebele, "Fiber grating sensors," J. Lightwave Technol. 15, 1442-1463 (1997).
    [CrossRef]
  11. T. Erdogan, "Cladding-mode resonances in short- and long-period fiber grating filters," J. Opt. Soc. Am. A 14, 1760-1773 (1997).
    [CrossRef]
  12. T. Erdogan, "Errata: cladding-mode resonances in short- and long-period fiber grating filters," J. Opt. Soc. Am. A 17, 2113-2113 (2000).
    [CrossRef]
  13. C. Y. H. Tsao, D. N. Payne, and W. A. Gambling, "Modal characteristics of three-layered optical fiber waveguides: a modified approach," J. Opt. Soc. Am. A 6, 555-563 (1989).
    [CrossRef]

2006 (1)

N. Chen, B. Yun, and Y. Cui, "Cladding mode resonances of etch-eroded fiber Bragg grating for ambient refractive index sensing," Appl. Phys. Lett. 88, 133902 (2006).
[CrossRef]

2005 (2)

W. Liang, Y. Huang, Y. Xu, R. K. Lee, and A. Yariv, "Highly sensitive fiber Bragg grating refractive index sensors," Appl. Phys. Lett. 86, 151122 (2005).
[CrossRef]

A. Iadicicco, S. Campopiano, A. Cutolo, M. Giordano, and A. Cusano, "Refractive index sensor based on microstructured fiber Bragg grating," IEEE Photon. Technol. Lett. 17, 1250-1252 (2005).
[CrossRef]

2004 (2)

A. Iadicicco, A. Cusano, A. Cutolo, R. Bernini, and M. Giordano, "Thinned fiber Bragg gratings as high sensitivity refractive index sensor," IEEE Photon. Technol. Lett. 16, 1149-1151 (2004).
[CrossRef]

K. Zhou, X. Chen, L. Zhang, and I. Bennion, "High-sensitivity optical chemsensor based on etched D-fibre Bragg gratings," Electron. Lett. 40, 232-234 (2004).
[CrossRef]

2002 (1)

2001 (1)

K. Schroeder, W. Ecke, R. Mueller, R. Willsch, and A. Andreev, "A fibre Bragg grating refractometer," Meas. Sci. Technol. 12, 757-764 (2001).
[CrossRef]

2000 (2)

K. S. Chiang, Y. Liu, M. Ng, and X. Dong, "Analysis of etched long-period fibre grating and its response to external refractive index," Electron. Lett. 36, 966-967 (2000).
[CrossRef]

T. Erdogan, "Errata: cladding-mode resonances in short- and long-period fiber grating filters," J. Opt. Soc. Am. A 17, 2113-2113 (2000).
[CrossRef]

1998 (1)

1997 (2)

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

T. Erdogan, "Cladding-mode resonances in short- and long-period fiber grating filters," J. Opt. Soc. Am. A 14, 1760-1773 (1997).
[CrossRef]

1989 (1)

Andreev, A.

K. Schroeder, W. Ecke, R. Mueller, R. Willsch, and A. Andreev, "A fibre Bragg grating refractometer," Meas. Sci. Technol. 12, 757-764 (2001).
[CrossRef]

Askins, C. G.

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

Bennion, I.

K. Zhou, X. Chen, L. Zhang, and I. Bennion, "High-sensitivity optical chemsensor based on etched D-fibre Bragg gratings," Electron. Lett. 40, 232-234 (2004).
[CrossRef]

X. Shu, L. Zhang, and I. Bennion, "Sensitivity characteristics of long-period fiber gratings," J. Lightwave Technol. 20, 255-266 (2002).
[CrossRef]

Bernini, R.

A. Iadicicco, A. Cusano, A. Cutolo, R. Bernini, and M. Giordano, "Thinned fiber Bragg gratings as high sensitivity refractive index sensor," IEEE Photon. Technol. Lett. 16, 1149-1151 (2004).
[CrossRef]

Bucholtz, F.

Campopiano, S.

A. Iadicicco, S. Campopiano, A. Cutolo, M. Giordano, and A. Cusano, "Refractive index sensor based on microstructured fiber Bragg grating," IEEE Photon. Technol. Lett. 17, 1250-1252 (2005).
[CrossRef]

Chen, N.

N. Chen, B. Yun, and Y. Cui, "Cladding mode resonances of etch-eroded fiber Bragg grating for ambient refractive index sensing," Appl. Phys. Lett. 88, 133902 (2006).
[CrossRef]

Chen, X.

K. Zhou, X. Chen, L. Zhang, and I. Bennion, "High-sensitivity optical chemsensor based on etched D-fibre Bragg gratings," Electron. Lett. 40, 232-234 (2004).
[CrossRef]

Chiang, K. S.

K. S. Chiang, Y. Liu, M. Ng, and X. Dong, "Analysis of etched long-period fibre grating and its response to external refractive index," Electron. Lett. 36, 966-967 (2000).
[CrossRef]

Cui, Y.

N. Chen, B. Yun, and Y. Cui, "Cladding mode resonances of etch-eroded fiber Bragg grating for ambient refractive index sensing," Appl. Phys. Lett. 88, 133902 (2006).
[CrossRef]

Cusano, A.

A. Iadicicco, S. Campopiano, A. Cutolo, M. Giordano, and A. Cusano, "Refractive index sensor based on microstructured fiber Bragg grating," IEEE Photon. Technol. Lett. 17, 1250-1252 (2005).
[CrossRef]

A. Iadicicco, A. Cusano, A. Cutolo, R. Bernini, and M. Giordano, "Thinned fiber Bragg gratings as high sensitivity refractive index sensor," IEEE Photon. Technol. Lett. 16, 1149-1151 (2004).
[CrossRef]

Cutolo, A.

A. Iadicicco, S. Campopiano, A. Cutolo, M. Giordano, and A. Cusano, "Refractive index sensor based on microstructured fiber Bragg grating," IEEE Photon. Technol. Lett. 17, 1250-1252 (2005).
[CrossRef]

A. Iadicicco, A. Cusano, A. Cutolo, R. Bernini, and M. Giordano, "Thinned fiber Bragg gratings as high sensitivity refractive index sensor," IEEE Photon. Technol. Lett. 16, 1149-1151 (2004).
[CrossRef]

Davis, M. A.

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

Dong, X.

K. S. Chiang, Y. Liu, M. Ng, and X. Dong, "Analysis of etched long-period fibre grating and its response to external refractive index," Electron. Lett. 36, 966-967 (2000).
[CrossRef]

Ecke, W.

K. Schroeder, W. Ecke, R. Mueller, R. Willsch, and A. Andreev, "A fibre Bragg grating refractometer," Meas. Sci. Technol. 12, 757-764 (2001).
[CrossRef]

Erdogan, T.

Friebele, E. J.

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

Gambling, W. A.

Giordano, M.

A. Iadicicco, S. Campopiano, A. Cutolo, M. Giordano, and A. Cusano, "Refractive index sensor based on microstructured fiber Bragg grating," IEEE Photon. Technol. Lett. 17, 1250-1252 (2005).
[CrossRef]

A. Iadicicco, A. Cusano, A. Cutolo, R. Bernini, and M. Giordano, "Thinned fiber Bragg gratings as high sensitivity refractive index sensor," IEEE Photon. Technol. Lett. 16, 1149-1151 (2004).
[CrossRef]

Huang, Y.

W. Liang, Y. Huang, Y. Xu, R. K. Lee, and A. Yariv, "Highly sensitive fiber Bragg grating refractive index sensors," Appl. Phys. Lett. 86, 151122 (2005).
[CrossRef]

Iadicicco, A.

A. Iadicicco, S. Campopiano, A. Cutolo, M. Giordano, and A. Cusano, "Refractive index sensor based on microstructured fiber Bragg grating," IEEE Photon. Technol. Lett. 17, 1250-1252 (2005).
[CrossRef]

A. Iadicicco, A. Cusano, A. Cutolo, R. Bernini, and M. Giordano, "Thinned fiber Bragg gratings as high sensitivity refractive index sensor," IEEE Photon. Technol. Lett. 16, 1149-1151 (2004).
[CrossRef]

Kersey, A. D.

H. J. Patrick, A. D. Kersey, and F. Bucholtz, "Analysis of the response of long period fiber gratings to external index of refraction," J. Lightwave Technol. 16, 1606-1612 (1998).
[CrossRef]

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

Koo, K. P.

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

LeBlanc, M.

A. D. Kersey, M. A. Davis, H. J. Patrick, M. LeBlanc, 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, R. K.

W. Liang, Y. Huang, Y. Xu, R. K. Lee, and A. Yariv, "Highly sensitive fiber Bragg grating refractive index sensors," Appl. Phys. Lett. 86, 151122 (2005).
[CrossRef]

Liang, W.

W. Liang, Y. Huang, Y. Xu, R. K. Lee, and A. Yariv, "Highly sensitive fiber Bragg grating refractive index sensors," Appl. Phys. Lett. 86, 151122 (2005).
[CrossRef]

Liu, Y.

K. S. Chiang, Y. Liu, M. Ng, and X. Dong, "Analysis of etched long-period fibre grating and its response to external refractive index," Electron. Lett. 36, 966-967 (2000).
[CrossRef]

Mueller, R.

K. Schroeder, W. Ecke, R. Mueller, R. Willsch, and A. Andreev, "A fibre Bragg grating refractometer," Meas. Sci. Technol. 12, 757-764 (2001).
[CrossRef]

Ng, M.

K. S. Chiang, Y. Liu, M. Ng, and X. Dong, "Analysis of etched long-period fibre grating and its response to external refractive index," Electron. Lett. 36, 966-967 (2000).
[CrossRef]

Patrick, H. J.

H. J. Patrick, A. D. Kersey, and F. Bucholtz, "Analysis of the response of long period fiber gratings to external index of refraction," J. Lightwave Technol. 16, 1606-1612 (1998).
[CrossRef]

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

Payne, D. N.

Putnam, M. A.

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

Schroeder, K.

K. Schroeder, W. Ecke, R. Mueller, R. Willsch, and A. Andreev, "A fibre Bragg grating refractometer," Meas. Sci. Technol. 12, 757-764 (2001).
[CrossRef]

Shu, X.

Tsao, C. Y. H.

Willsch, R.

K. Schroeder, W. Ecke, R. Mueller, R. Willsch, and A. Andreev, "A fibre Bragg grating refractometer," Meas. Sci. Technol. 12, 757-764 (2001).
[CrossRef]

Xu, Y.

W. Liang, Y. Huang, Y. Xu, R. K. Lee, and A. Yariv, "Highly sensitive fiber Bragg grating refractive index sensors," Appl. Phys. Lett. 86, 151122 (2005).
[CrossRef]

Yariv, A.

W. Liang, Y. Huang, Y. Xu, R. K. Lee, and A. Yariv, "Highly sensitive fiber Bragg grating refractive index sensors," Appl. Phys. Lett. 86, 151122 (2005).
[CrossRef]

Yun, B.

N. Chen, B. Yun, and Y. Cui, "Cladding mode resonances of etch-eroded fiber Bragg grating for ambient refractive index sensing," Appl. Phys. Lett. 88, 133902 (2006).
[CrossRef]

Zhang, L.

K. Zhou, X. Chen, L. Zhang, and I. Bennion, "High-sensitivity optical chemsensor based on etched D-fibre Bragg gratings," Electron. Lett. 40, 232-234 (2004).
[CrossRef]

X. Shu, L. Zhang, and I. Bennion, "Sensitivity characteristics of long-period fiber gratings," J. Lightwave Technol. 20, 255-266 (2002).
[CrossRef]

Zhou, K.

K. Zhou, X. Chen, L. Zhang, and I. Bennion, "High-sensitivity optical chemsensor based on etched D-fibre Bragg gratings," Electron. Lett. 40, 232-234 (2004).
[CrossRef]

Appl. Phys. Lett. (2)

N. Chen, B. Yun, and Y. Cui, "Cladding mode resonances of etch-eroded fiber Bragg grating for ambient refractive index sensing," Appl. Phys. Lett. 88, 133902 (2006).
[CrossRef]

W. Liang, Y. Huang, Y. Xu, R. K. Lee, and A. Yariv, "Highly sensitive fiber Bragg grating refractive index sensors," Appl. Phys. Lett. 86, 151122 (2005).
[CrossRef]

Electron. Lett. (2)

K. S. Chiang, Y. Liu, M. Ng, and X. Dong, "Analysis of etched long-period fibre grating and its response to external refractive index," Electron. Lett. 36, 966-967 (2000).
[CrossRef]

K. Zhou, X. Chen, L. Zhang, and I. Bennion, "High-sensitivity optical chemsensor based on etched D-fibre Bragg gratings," Electron. Lett. 40, 232-234 (2004).
[CrossRef]

IEEE Photon. Technol. Lett. (2)

A. Iadicicco, S. Campopiano, A. Cutolo, M. Giordano, and A. Cusano, "Refractive index sensor based on microstructured fiber Bragg grating," IEEE Photon. Technol. Lett. 17, 1250-1252 (2005).
[CrossRef]

A. Iadicicco, A. Cusano, A. Cutolo, R. Bernini, and M. Giordano, "Thinned fiber Bragg gratings as high sensitivity refractive index sensor," IEEE Photon. Technol. Lett. 16, 1149-1151 (2004).
[CrossRef]

J. Lightwave Technol. (3)

J. Opt. Soc. Am. A (3)

Meas. Sci. Technol. (1)

K. Schroeder, W. Ecke, R. Mueller, R. Willsch, and A. Andreev, "A fibre Bragg grating refractometer," Meas. Sci. Technol. 12, 757-764 (2001).
[CrossRef]

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Figures (10)

Fig. 1
Fig. 1

Structure of an etched FBG for ambient refractive index sensing.

Fig. 2
Fig. 2

Theoretically calculated transmission spectrum of the unetched FBG.

Fig. 3
Fig. 3

(a) Transmission spectrum of FBG cladding-mode resonances after the first etching; (b) calculated transmission spectrum with a diminished cladding diameter of 66.4 μ m .

Fig. 4
Fig. 4

Evolution of the calculated cladding-mode resonance spectra with the etching process.

Fig. 5
Fig. 5

(a) Response of 13th-order cladding-mode resonances of etched FBG to the variations of the ambient refractive index under the fiber cladding diameter of 66.4 μ m ; (b) shifts of the center wavelength with the variations of the ambient refractive index correspondingly.

Fig. 6
Fig. 6

(a) Shifts of 17th-, 15th-, 13th-, 11th-, 9th-, 7th-, 5th-, 3rd-, and 1st-order cladding-mode resonances with the ambient refractive index under the fiber diameter of 66.4 μ m . (b)Shifts of 13th-, 11th-, 9th-, 7th-, 5th-, 3rd-, and 1st-order cladding-mode resonances with the ambient refractive index under the fiber diameter of 52.8 μ m . (c) Shifts of the 13th-order cladding-mode resonance with the ambient refractive index under fiber cladding diameters of 66.4 and 52.8 μ m . (d) Shifts of the ninth-order cladding-mode resonance with the ambient refractive index under fiber cladding diameters of 66.4 and 52.8 μ m .

Fig. 7
Fig. 7

Sensing characteristics comparison of the third-order cladding-mode resonance, the first-order cladding-mode resonance, and the Bragg core-mode resonance under fiber cladding diameters of 20 μ m .

Fig. 8
Fig. 8

Responses of the seventh (13th-order) and the fifth (9th-order) cladding-mode resonances to the ambient refractive index.

Fig. 9
Fig. 9

Sensing characteristics comparison of the third (fifth-order) cladding-mode resonance before and after the third etching.

Fig. 10
Fig. 10

Sensing characteristics comparison of third (fifth-order) and first (first-order) cladding-mode resonances and the Bragg core-mode resonance after the third etching.

Equations (5)

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λ FBG co = 2 n eff co Λ FBG ,
λ FBG v = ( n eff co + n eff cl , v ) Λ FBG ,
d A co d z = i κ 01 01 co co A co + i m 2 κ 01 01 co co B co exp ( i 2 δ 01 01 co co z ) + i v m 2 κ 1 v 01 cl co B v cl exp ( i 2 δ 1 v 01 cl co z ) ,
d B co d z = i κ 01 01 co co B co i m 2 κ 01 01 co co A co exp ( + i 2 δ 01 01 co co z ) ,
v [ d B v cl d z = i m 2 κ 1 v 01 cl co A co exp ( + i 2 δ 1 v 01 cl co z ) ] ,

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