Abstract

A new method of analysis employing the time-dependent response of long-period-grating (LPG) fiber-optic sensors is introduced. The current kinetic approach allows analysis of the time-dependent wavelength shift of the sensor, in contrast to previous studies, in which the LPG sensing element has been operated in an equilibrium mode and modeled with Langmuir adsorption behavior. A detailed kinetic model presented is based on diffusion of the analyte through the outer protective membrane coating into the affinity coating, which is bound to the fiber cladding. A simpler phenomenological approach presented is based on measurement of the slope of the time-dependent response of the LPG sensor. We demonstrate the principles of the kinetic methods by employing a commercial Cu+2 sensor with a carboxymethylcellulose sensing element. The detailed mathematical model fits the time-dependent behavior well and provides a means of calibrating the concentration-dependent time response. In the current approach, copper concentrations below parts per 106 are reliably analyzed. The kinetic model allows early-time measurement for low concentrations of the analyte, where equilibration times are long. This kinetic model should be generally applicable to other affinity-coated LPG fiber-optic sensors.

© 2005 Optical Society of America

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  1. L. W. Qu, R. B. Martin, W. J. Huang, K. F. Fu, D. Zweifel, Y. Lin, Y. P. Sun, C. E. Bunker, B. A. Harruff, J. R. Gord, L. F. Allard, “Interactions of functionalized carbon nanotubes with tethered pyrenes in solution,” J. Chem. Phys. 117, 8089–8094 (2002).
    [CrossRef]
  2. B. A. Harruff, C. E. Bunker, “Spectral properties of AOT-protected CdS nanoparticles: quantum yield enhancement by photolysis,” Langmuir 19, 893–897 (2003).
    [CrossRef]
  3. K. T. V. Grattan, T. Sun, “Fiber optic sensor technology: an overview,” Sens. Actuators 82, 40–61 (2000).
    [CrossRef]
  4. A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan, J. E. Sipe, “Long-period fiber gratings as band-rejection filters,” J. Lightwave Technol. 14, 58–65 (1996).
    [CrossRef]
  5. V. Bhatia, A. M. Vengsarkar, “Optical fiber long-period grating sensors,” Opt. Lett. 21, 692–694 (1996).
    [CrossRef] [PubMed]
  6. B. A. L. Gwandu, X. Shu, T. P. D. Allsop, “Simultaneous refractive index and temperature measurement using cascaded long-period grating in double-cladding fibre,” Electron. Lett. 38, 695–696 (2002).
    [CrossRef]
  7. C. C. Ye, S. W. James, R. P. Tatam, “Simultaneous temperature and bend sensing with long-period fiber gratings,” Opt. Lett. 25, 1007–1009 (2000).
    [CrossRef]
  8. H. J. Patrick, “Self-aligning, bipolar bend transducer based on long period grating written in eccentric core fibre,” Electron. Lett. 36, 1763–1764 (2000).
    [CrossRef]
  9. Y. Liu, L. Zhang, J. A. R. Williams, I. Bennion, “Optical bend sensor based on measurement of resonance mode splitting of long-period fiber grating,” IEEE Photon. Technol. Lett. 12, 531–533 (2000).
    [CrossRef]
  10. H. J. Patrick, S. T. Vohra, C. C. Chang, “Long period fibre gratings for structural bend sensing,” Electron. Lett. 34, 1773–1775 (1998).
    [CrossRef]
  11. S. R. M. Kueh, R. S. Parnas, S. G. Advani, “A methodology for using long-period gratings and mold-filling simulations to minimize the intrusiveness of flow sensors in liquid composite molding,” Compos. Sci. Technol. 62, 311–327 (2002).
    [CrossRef]
  12. Y. Liu, L. Zhang, J. A. R. Williams, I. Bennion, “Bend sensing by measuring the resonance splitting of long-period fiber gratings,” Opt. Commun. 193, 69–72 (2001).
    [CrossRef]
  13. Y.-G. Han, B. H. Lee, W.-T. Han, U.-C. Paek, Y. Chung, “Fibre-optic sensing applications of a pair of long-period fibre gratings,” Meas. Sci. Technol. 12, 778–781 (2001).
    [CrossRef]
  14. L. A. Wang, C. Y. Lin, G. W. Chern, “A torsion sensor made of a corrugated long period fibre grating,” Meas. Sci. Technol. 12, 793–799 (2001).
    [CrossRef]
  15. R. Falciai, A. G. Mignani, A. Vannini, “Long period gratings as solution concentration sensors,” Sens. Actuators B 74, 74–77 (2001).
    [CrossRef]
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    [CrossRef]
  17. K. Goswami, J. Prohaska, A. Menon, E. Mendoza, R. Lieberman, “Evanescent wave sensor for detecting volatile organic compounds,” in Chemical, Biochemical, and Environmental Fiber Sensors X, Proc. SPIE3540, 115–122 (1998).
    [CrossRef]
  18. J. A. Greene, M. E. Jones, T. A. Tran, K. A. Murphy, P. M. Schindler, V. Bhatia, R. G. May, D. Sherrer, R. O. Claus, “Grating-based optical fiber-based corrosion sensors,” in Smart Sensing Processing and Instrumentation, Proc. SPIE2718, 170–174 (1996).
  19. J. Elster, J. Greene, M. Jones, T. Bailey, S. Lenahan, W. Velander, R. Van Tassel, W. Hodges, “Optical fiber-based chemical sensors for detection of corrosion precursors and byproducts,” in Chemical, Biochemical, and Environmental Fiber Sensors X, Proc. SPIE3540, 251–257 (1998).
    [CrossRef]
  20. X. Shu, D. Huang, “Highly sensitive chemical sensor based on the measurement of the separation of dual resonant peaks in a 100-μm-period fiber grating,” Opt. Commun. 171, 65–69 (1999).
    [CrossRef]
  21. T. Allsop, L. Zhang, I. Bennion, “Detection of organic aromatic compounds in paraffin by a long-period fiber grating optical sensor with optimized sensitivity,” Opt. Commun. 191, 181–190 (2001).
    [CrossRef]
  22. T. A. Tran, V. Bhatia, T. D’Alberto, K. A. Murphy, R. O. Claus, “Real-time immunoassays using fiber-optic long-period grating sensors,” in Biomedical Sensing, Imaging, and Tracking Technologies I, Proc. SPIE2676, 165–170 (1996).
    [CrossRef]
  23. D. Appell, “Fiber sensing—clad fiber detects biological agents fast,” Laser Focus World 34, 26–27 (1998).
  24. D. C. Harris, Quantitative Chemical Analysis,6th ed. (Freeman, San Francisco, Calif., 2003).
  25. J. H. Espenson, Chemical Kinetics and Reaction Mechanisms, 2nd ed. (McGraw-Hill, New York, 1995).
  26. J. Bard, L. R. Faulkner, Electrochemical Methods: Fundamentals and Applications (Wiley, New York, 2001).

2003 (1)

B. A. Harruff, C. E. Bunker, “Spectral properties of AOT-protected CdS nanoparticles: quantum yield enhancement by photolysis,” Langmuir 19, 893–897 (2003).
[CrossRef]

2002 (3)

S. R. M. Kueh, R. S. Parnas, S. G. Advani, “A methodology for using long-period gratings and mold-filling simulations to minimize the intrusiveness of flow sensors in liquid composite molding,” Compos. Sci. Technol. 62, 311–327 (2002).
[CrossRef]

B. A. L. Gwandu, X. Shu, T. P. D. Allsop, “Simultaneous refractive index and temperature measurement using cascaded long-period grating in double-cladding fibre,” Electron. Lett. 38, 695–696 (2002).
[CrossRef]

L. W. Qu, R. B. Martin, W. J. Huang, K. F. Fu, D. Zweifel, Y. Lin, Y. P. Sun, C. E. Bunker, B. A. Harruff, J. R. Gord, L. F. Allard, “Interactions of functionalized carbon nanotubes with tethered pyrenes in solution,” J. Chem. Phys. 117, 8089–8094 (2002).
[CrossRef]

2001 (5)

T. Allsop, L. Zhang, I. Bennion, “Detection of organic aromatic compounds in paraffin by a long-period fiber grating optical sensor with optimized sensitivity,” Opt. Commun. 191, 181–190 (2001).
[CrossRef]

Y. Liu, L. Zhang, J. A. R. Williams, I. Bennion, “Bend sensing by measuring the resonance splitting of long-period fiber gratings,” Opt. Commun. 193, 69–72 (2001).
[CrossRef]

Y.-G. Han, B. H. Lee, W.-T. Han, U.-C. Paek, Y. Chung, “Fibre-optic sensing applications of a pair of long-period fibre gratings,” Meas. Sci. Technol. 12, 778–781 (2001).
[CrossRef]

L. A. Wang, C. Y. Lin, G. W. Chern, “A torsion sensor made of a corrugated long period fibre grating,” Meas. Sci. Technol. 12, 793–799 (2001).
[CrossRef]

R. Falciai, A. G. Mignani, A. Vannini, “Long period gratings as solution concentration sensors,” Sens. Actuators B 74, 74–77 (2001).
[CrossRef]

2000 (4)

K. T. V. Grattan, T. Sun, “Fiber optic sensor technology: an overview,” Sens. Actuators 82, 40–61 (2000).
[CrossRef]

H. J. Patrick, “Self-aligning, bipolar bend transducer based on long period grating written in eccentric core fibre,” Electron. Lett. 36, 1763–1764 (2000).
[CrossRef]

Y. Liu, L. Zhang, J. A. R. Williams, I. Bennion, “Optical bend sensor based on measurement of resonance mode splitting of long-period fiber grating,” IEEE Photon. Technol. Lett. 12, 531–533 (2000).
[CrossRef]

C. C. Ye, S. W. James, R. P. Tatam, “Simultaneous temperature and bend sensing with long-period fiber gratings,” Opt. Lett. 25, 1007–1009 (2000).
[CrossRef]

1999 (1)

X. Shu, D. Huang, “Highly sensitive chemical sensor based on the measurement of the separation of dual resonant peaks in a 100-μm-period fiber grating,” Opt. Commun. 171, 65–69 (1999).
[CrossRef]

1998 (3)

D. Appell, “Fiber sensing—clad fiber detects biological agents fast,” Laser Focus World 34, 26–27 (1998).

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

H. J. Patrick, S. T. Vohra, C. C. Chang, “Long period fibre gratings for structural bend sensing,” Electron. Lett. 34, 1773–1775 (1998).
[CrossRef]

1996 (2)

A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan, J. E. Sipe, “Long-period fiber gratings as band-rejection filters,” J. Lightwave Technol. 14, 58–65 (1996).
[CrossRef]

V. Bhatia, A. M. Vengsarkar, “Optical fiber long-period grating sensors,” Opt. Lett. 21, 692–694 (1996).
[CrossRef] [PubMed]

Advani, S. G.

S. R. M. Kueh, R. S. Parnas, S. G. Advani, “A methodology for using long-period gratings and mold-filling simulations to minimize the intrusiveness of flow sensors in liquid composite molding,” Compos. Sci. Technol. 62, 311–327 (2002).
[CrossRef]

Allard, L. F.

L. W. Qu, R. B. Martin, W. J. Huang, K. F. Fu, D. Zweifel, Y. Lin, Y. P. Sun, C. E. Bunker, B. A. Harruff, J. R. Gord, L. F. Allard, “Interactions of functionalized carbon nanotubes with tethered pyrenes in solution,” J. Chem. Phys. 117, 8089–8094 (2002).
[CrossRef]

Allsop, T.

T. Allsop, L. Zhang, I. Bennion, “Detection of organic aromatic compounds in paraffin by a long-period fiber grating optical sensor with optimized sensitivity,” Opt. Commun. 191, 181–190 (2001).
[CrossRef]

Allsop, T. P. D.

B. A. L. Gwandu, X. Shu, T. P. D. Allsop, “Simultaneous refractive index and temperature measurement using cascaded long-period grating in double-cladding fibre,” Electron. Lett. 38, 695–696 (2002).
[CrossRef]

Appell, D.

D. Appell, “Fiber sensing—clad fiber detects biological agents fast,” Laser Focus World 34, 26–27 (1998).

Bailey, T.

J. Elster, J. Greene, M. Jones, T. Bailey, S. Lenahan, W. Velander, R. Van Tassel, W. Hodges, “Optical fiber-based chemical sensors for detection of corrosion precursors and byproducts,” in Chemical, Biochemical, and Environmental Fiber Sensors X, Proc. SPIE3540, 251–257 (1998).
[CrossRef]

Bard, J.

J. Bard, L. R. Faulkner, Electrochemical Methods: Fundamentals and Applications (Wiley, New York, 2001).

Bennion, I.

T. Allsop, L. Zhang, I. Bennion, “Detection of organic aromatic compounds in paraffin by a long-period fiber grating optical sensor with optimized sensitivity,” Opt. Commun. 191, 181–190 (2001).
[CrossRef]

Y. Liu, L. Zhang, J. A. R. Williams, I. Bennion, “Bend sensing by measuring the resonance splitting of long-period fiber gratings,” Opt. Commun. 193, 69–72 (2001).
[CrossRef]

Y. Liu, L. Zhang, J. A. R. Williams, I. Bennion, “Optical bend sensor based on measurement of resonance mode splitting of long-period fiber grating,” IEEE Photon. Technol. Lett. 12, 531–533 (2000).
[CrossRef]

Bhatia, V.

V. Bhatia, A. M. Vengsarkar, “Optical fiber long-period grating sensors,” Opt. Lett. 21, 692–694 (1996).
[CrossRef] [PubMed]

A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan, J. E. Sipe, “Long-period fiber gratings as band-rejection filters,” J. Lightwave Technol. 14, 58–65 (1996).
[CrossRef]

T. A. Tran, V. Bhatia, T. D’Alberto, K. A. Murphy, R. O. Claus, “Real-time immunoassays using fiber-optic long-period grating sensors,” in Biomedical Sensing, Imaging, and Tracking Technologies I, Proc. SPIE2676, 165–170 (1996).
[CrossRef]

J. A. Greene, M. E. Jones, T. A. Tran, K. A. Murphy, P. M. Schindler, V. Bhatia, R. G. May, D. Sherrer, R. O. Claus, “Grating-based optical fiber-based corrosion sensors,” in Smart Sensing Processing and Instrumentation, Proc. SPIE2718, 170–174 (1996).

Bucholtz, F.

Bunker, C. E.

B. A. Harruff, C. E. Bunker, “Spectral properties of AOT-protected CdS nanoparticles: quantum yield enhancement by photolysis,” Langmuir 19, 893–897 (2003).
[CrossRef]

L. W. Qu, R. B. Martin, W. J. Huang, K. F. Fu, D. Zweifel, Y. Lin, Y. P. Sun, C. E. Bunker, B. A. Harruff, J. R. Gord, L. F. Allard, “Interactions of functionalized carbon nanotubes with tethered pyrenes in solution,” J. Chem. Phys. 117, 8089–8094 (2002).
[CrossRef]

Chang, C. C.

H. J. Patrick, S. T. Vohra, C. C. Chang, “Long period fibre gratings for structural bend sensing,” Electron. Lett. 34, 1773–1775 (1998).
[CrossRef]

Chern, G. W.

L. A. Wang, C. Y. Lin, G. W. Chern, “A torsion sensor made of a corrugated long period fibre grating,” Meas. Sci. Technol. 12, 793–799 (2001).
[CrossRef]

Chung, Y.

Y.-G. Han, B. H. Lee, W.-T. Han, U.-C. Paek, Y. Chung, “Fibre-optic sensing applications of a pair of long-period fibre gratings,” Meas. Sci. Technol. 12, 778–781 (2001).
[CrossRef]

Claus, R. O.

T. A. Tran, V. Bhatia, T. D’Alberto, K. A. Murphy, R. O. Claus, “Real-time immunoassays using fiber-optic long-period grating sensors,” in Biomedical Sensing, Imaging, and Tracking Technologies I, Proc. SPIE2676, 165–170 (1996).
[CrossRef]

J. A. Greene, M. E. Jones, T. A. Tran, K. A. Murphy, P. M. Schindler, V. Bhatia, R. G. May, D. Sherrer, R. O. Claus, “Grating-based optical fiber-based corrosion sensors,” in Smart Sensing Processing and Instrumentation, Proc. SPIE2718, 170–174 (1996).

D’Alberto, T.

T. A. Tran, V. Bhatia, T. D’Alberto, K. A. Murphy, R. O. Claus, “Real-time immunoassays using fiber-optic long-period grating sensors,” in Biomedical Sensing, Imaging, and Tracking Technologies I, Proc. SPIE2676, 165–170 (1996).
[CrossRef]

Elster, J.

J. Elster, J. Greene, M. Jones, T. Bailey, S. Lenahan, W. Velander, R. Van Tassel, W. Hodges, “Optical fiber-based chemical sensors for detection of corrosion precursors and byproducts,” in Chemical, Biochemical, and Environmental Fiber Sensors X, Proc. SPIE3540, 251–257 (1998).
[CrossRef]

Erdogan, T.

A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan, J. E. Sipe, “Long-period fiber gratings as band-rejection filters,” J. Lightwave Technol. 14, 58–65 (1996).
[CrossRef]

Espenson, J. H.

J. H. Espenson, Chemical Kinetics and Reaction Mechanisms, 2nd ed. (McGraw-Hill, New York, 1995).

Falciai, R.

R. Falciai, A. G. Mignani, A. Vannini, “Long period gratings as solution concentration sensors,” Sens. Actuators B 74, 74–77 (2001).
[CrossRef]

Faulkner, L. R.

J. Bard, L. R. Faulkner, Electrochemical Methods: Fundamentals and Applications (Wiley, New York, 2001).

Fu, K. F.

L. W. Qu, R. B. Martin, W. J. Huang, K. F. Fu, D. Zweifel, Y. Lin, Y. P. Sun, C. E. Bunker, B. A. Harruff, J. R. Gord, L. F. Allard, “Interactions of functionalized carbon nanotubes with tethered pyrenes in solution,” J. Chem. Phys. 117, 8089–8094 (2002).
[CrossRef]

Gord, J. R.

L. W. Qu, R. B. Martin, W. J. Huang, K. F. Fu, D. Zweifel, Y. Lin, Y. P. Sun, C. E. Bunker, B. A. Harruff, J. R. Gord, L. F. Allard, “Interactions of functionalized carbon nanotubes with tethered pyrenes in solution,” J. Chem. Phys. 117, 8089–8094 (2002).
[CrossRef]

Goswami, K.

K. Goswami, J. Prohaska, A. Menon, E. Mendoza, R. Lieberman, “Evanescent wave sensor for detecting volatile organic compounds,” in Chemical, Biochemical, and Environmental Fiber Sensors X, Proc. SPIE3540, 115–122 (1998).
[CrossRef]

Grattan, K. T. V.

K. T. V. Grattan, T. Sun, “Fiber optic sensor technology: an overview,” Sens. Actuators 82, 40–61 (2000).
[CrossRef]

Greene, J.

J. Elster, J. Greene, M. Jones, T. Bailey, S. Lenahan, W. Velander, R. Van Tassel, W. Hodges, “Optical fiber-based chemical sensors for detection of corrosion precursors and byproducts,” in Chemical, Biochemical, and Environmental Fiber Sensors X, Proc. SPIE3540, 251–257 (1998).
[CrossRef]

Greene, J. A.

J. A. Greene, M. E. Jones, T. A. Tran, K. A. Murphy, P. M. Schindler, V. Bhatia, R. G. May, D. Sherrer, R. O. Claus, “Grating-based optical fiber-based corrosion sensors,” in Smart Sensing Processing and Instrumentation, Proc. SPIE2718, 170–174 (1996).

Gwandu, B. A. L.

B. A. L. Gwandu, X. Shu, T. P. D. Allsop, “Simultaneous refractive index and temperature measurement using cascaded long-period grating in double-cladding fibre,” Electron. Lett. 38, 695–696 (2002).
[CrossRef]

Han, W.-T.

Y.-G. Han, B. H. Lee, W.-T. Han, U.-C. Paek, Y. Chung, “Fibre-optic sensing applications of a pair of long-period fibre gratings,” Meas. Sci. Technol. 12, 778–781 (2001).
[CrossRef]

Han, Y.-G.

Y.-G. Han, B. H. Lee, W.-T. Han, U.-C. Paek, Y. Chung, “Fibre-optic sensing applications of a pair of long-period fibre gratings,” Meas. Sci. Technol. 12, 778–781 (2001).
[CrossRef]

Harris, D. C.

D. C. Harris, Quantitative Chemical Analysis,6th ed. (Freeman, San Francisco, Calif., 2003).

Harruff, B. A.

B. A. Harruff, C. E. Bunker, “Spectral properties of AOT-protected CdS nanoparticles: quantum yield enhancement by photolysis,” Langmuir 19, 893–897 (2003).
[CrossRef]

L. W. Qu, R. B. Martin, W. J. Huang, K. F. Fu, D. Zweifel, Y. Lin, Y. P. Sun, C. E. Bunker, B. A. Harruff, J. R. Gord, L. F. Allard, “Interactions of functionalized carbon nanotubes with tethered pyrenes in solution,” J. Chem. Phys. 117, 8089–8094 (2002).
[CrossRef]

Hodges, W.

J. Elster, J. Greene, M. Jones, T. Bailey, S. Lenahan, W. Velander, R. Van Tassel, W. Hodges, “Optical fiber-based chemical sensors for detection of corrosion precursors and byproducts,” in Chemical, Biochemical, and Environmental Fiber Sensors X, Proc. SPIE3540, 251–257 (1998).
[CrossRef]

Huang, D.

X. Shu, D. Huang, “Highly sensitive chemical sensor based on the measurement of the separation of dual resonant peaks in a 100-μm-period fiber grating,” Opt. Commun. 171, 65–69 (1999).
[CrossRef]

Huang, W. J.

L. W. Qu, R. B. Martin, W. J. Huang, K. F. Fu, D. Zweifel, Y. Lin, Y. P. Sun, C. E. Bunker, B. A. Harruff, J. R. Gord, L. F. Allard, “Interactions of functionalized carbon nanotubes with tethered pyrenes in solution,” J. Chem. Phys. 117, 8089–8094 (2002).
[CrossRef]

James, S. W.

Jones, M.

J. Elster, J. Greene, M. Jones, T. Bailey, S. Lenahan, W. Velander, R. Van Tassel, W. Hodges, “Optical fiber-based chemical sensors for detection of corrosion precursors and byproducts,” in Chemical, Biochemical, and Environmental Fiber Sensors X, Proc. SPIE3540, 251–257 (1998).
[CrossRef]

Jones, M. E.

J. A. Greene, M. E. Jones, T. A. Tran, K. A. Murphy, P. M. Schindler, V. Bhatia, R. G. May, D. Sherrer, R. O. Claus, “Grating-based optical fiber-based corrosion sensors,” in Smart Sensing Processing and Instrumentation, Proc. SPIE2718, 170–174 (1996).

Judkins, J. B.

A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan, J. E. Sipe, “Long-period fiber gratings as band-rejection filters,” J. Lightwave Technol. 14, 58–65 (1996).
[CrossRef]

Kersey, A. D.

Kueh, S. R. M.

S. R. M. Kueh, R. S. Parnas, S. G. Advani, “A methodology for using long-period gratings and mold-filling simulations to minimize the intrusiveness of flow sensors in liquid composite molding,” Compos. Sci. Technol. 62, 311–327 (2002).
[CrossRef]

Lee, B. H.

Y.-G. Han, B. H. Lee, W.-T. Han, U.-C. Paek, Y. Chung, “Fibre-optic sensing applications of a pair of long-period fibre gratings,” Meas. Sci. Technol. 12, 778–781 (2001).
[CrossRef]

Lemaire, P. J.

A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan, J. E. Sipe, “Long-period fiber gratings as band-rejection filters,” J. Lightwave Technol. 14, 58–65 (1996).
[CrossRef]

Lenahan, S.

J. Elster, J. Greene, M. Jones, T. Bailey, S. Lenahan, W. Velander, R. Van Tassel, W. Hodges, “Optical fiber-based chemical sensors for detection of corrosion precursors and byproducts,” in Chemical, Biochemical, and Environmental Fiber Sensors X, Proc. SPIE3540, 251–257 (1998).
[CrossRef]

Lieberman, R.

K. Goswami, J. Prohaska, A. Menon, E. Mendoza, R. Lieberman, “Evanescent wave sensor for detecting volatile organic compounds,” in Chemical, Biochemical, and Environmental Fiber Sensors X, Proc. SPIE3540, 115–122 (1998).
[CrossRef]

Lin, C. Y.

L. A. Wang, C. Y. Lin, G. W. Chern, “A torsion sensor made of a corrugated long period fibre grating,” Meas. Sci. Technol. 12, 793–799 (2001).
[CrossRef]

Lin, Y.

L. W. Qu, R. B. Martin, W. J. Huang, K. F. Fu, D. Zweifel, Y. Lin, Y. P. Sun, C. E. Bunker, B. A. Harruff, J. R. Gord, L. F. Allard, “Interactions of functionalized carbon nanotubes with tethered pyrenes in solution,” J. Chem. Phys. 117, 8089–8094 (2002).
[CrossRef]

Liu, Y.

Y. Liu, L. Zhang, J. A. R. Williams, I. Bennion, “Bend sensing by measuring the resonance splitting of long-period fiber gratings,” Opt. Commun. 193, 69–72 (2001).
[CrossRef]

Y. Liu, L. Zhang, J. A. R. Williams, I. Bennion, “Optical bend sensor based on measurement of resonance mode splitting of long-period fiber grating,” IEEE Photon. Technol. Lett. 12, 531–533 (2000).
[CrossRef]

Martin, R. B.

L. W. Qu, R. B. Martin, W. J. Huang, K. F. Fu, D. Zweifel, Y. Lin, Y. P. Sun, C. E. Bunker, B. A. Harruff, J. R. Gord, L. F. Allard, “Interactions of functionalized carbon nanotubes with tethered pyrenes in solution,” J. Chem. Phys. 117, 8089–8094 (2002).
[CrossRef]

May, R. G.

J. A. Greene, M. E. Jones, T. A. Tran, K. A. Murphy, P. M. Schindler, V. Bhatia, R. G. May, D. Sherrer, R. O. Claus, “Grating-based optical fiber-based corrosion sensors,” in Smart Sensing Processing and Instrumentation, Proc. SPIE2718, 170–174 (1996).

Mendoza, E.

K. Goswami, J. Prohaska, A. Menon, E. Mendoza, R. Lieberman, “Evanescent wave sensor for detecting volatile organic compounds,” in Chemical, Biochemical, and Environmental Fiber Sensors X, Proc. SPIE3540, 115–122 (1998).
[CrossRef]

Menon, A.

K. Goswami, J. Prohaska, A. Menon, E. Mendoza, R. Lieberman, “Evanescent wave sensor for detecting volatile organic compounds,” in Chemical, Biochemical, and Environmental Fiber Sensors X, Proc. SPIE3540, 115–122 (1998).
[CrossRef]

Mignani, A. G.

R. Falciai, A. G. Mignani, A. Vannini, “Long period gratings as solution concentration sensors,” Sens. Actuators B 74, 74–77 (2001).
[CrossRef]

Murphy, K. A.

J. A. Greene, M. E. Jones, T. A. Tran, K. A. Murphy, P. M. Schindler, V. Bhatia, R. G. May, D. Sherrer, R. O. Claus, “Grating-based optical fiber-based corrosion sensors,” in Smart Sensing Processing and Instrumentation, Proc. SPIE2718, 170–174 (1996).

T. A. Tran, V. Bhatia, T. D’Alberto, K. A. Murphy, R. O. Claus, “Real-time immunoassays using fiber-optic long-period grating sensors,” in Biomedical Sensing, Imaging, and Tracking Technologies I, Proc. SPIE2676, 165–170 (1996).
[CrossRef]

Paek, U.-C.

Y.-G. Han, B. H. Lee, W.-T. Han, U.-C. Paek, Y. Chung, “Fibre-optic sensing applications of a pair of long-period fibre gratings,” Meas. Sci. Technol. 12, 778–781 (2001).
[CrossRef]

Parnas, R. S.

S. R. M. Kueh, R. S. Parnas, S. G. Advani, “A methodology for using long-period gratings and mold-filling simulations to minimize the intrusiveness of flow sensors in liquid composite molding,” Compos. Sci. Technol. 62, 311–327 (2002).
[CrossRef]

Patrick, H. J.

H. J. Patrick, “Self-aligning, bipolar bend transducer based on long period grating written in eccentric core fibre,” Electron. Lett. 36, 1763–1764 (2000).
[CrossRef]

H. J. Patrick, S. T. Vohra, C. C. Chang, “Long period fibre gratings for structural bend sensing,” Electron. Lett. 34, 1773–1775 (1998).
[CrossRef]

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

Prohaska, J.

K. Goswami, J. Prohaska, A. Menon, E. Mendoza, R. Lieberman, “Evanescent wave sensor for detecting volatile organic compounds,” in Chemical, Biochemical, and Environmental Fiber Sensors X, Proc. SPIE3540, 115–122 (1998).
[CrossRef]

Qu, L. W.

L. W. Qu, R. B. Martin, W. J. Huang, K. F. Fu, D. Zweifel, Y. Lin, Y. P. Sun, C. E. Bunker, B. A. Harruff, J. R. Gord, L. F. Allard, “Interactions of functionalized carbon nanotubes with tethered pyrenes in solution,” J. Chem. Phys. 117, 8089–8094 (2002).
[CrossRef]

Schindler, P. M.

J. A. Greene, M. E. Jones, T. A. Tran, K. A. Murphy, P. M. Schindler, V. Bhatia, R. G. May, D. Sherrer, R. O. Claus, “Grating-based optical fiber-based corrosion sensors,” in Smart Sensing Processing and Instrumentation, Proc. SPIE2718, 170–174 (1996).

Sherrer, D.

J. A. Greene, M. E. Jones, T. A. Tran, K. A. Murphy, P. M. Schindler, V. Bhatia, R. G. May, D. Sherrer, R. O. Claus, “Grating-based optical fiber-based corrosion sensors,” in Smart Sensing Processing and Instrumentation, Proc. SPIE2718, 170–174 (1996).

Shu, X.

B. A. L. Gwandu, X. Shu, T. P. D. Allsop, “Simultaneous refractive index and temperature measurement using cascaded long-period grating in double-cladding fibre,” Electron. Lett. 38, 695–696 (2002).
[CrossRef]

X. Shu, D. Huang, “Highly sensitive chemical sensor based on the measurement of the separation of dual resonant peaks in a 100-μm-period fiber grating,” Opt. Commun. 171, 65–69 (1999).
[CrossRef]

Sipe, J. E.

A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan, J. E. Sipe, “Long-period fiber gratings as band-rejection filters,” J. Lightwave Technol. 14, 58–65 (1996).
[CrossRef]

Sun, T.

K. T. V. Grattan, T. Sun, “Fiber optic sensor technology: an overview,” Sens. Actuators 82, 40–61 (2000).
[CrossRef]

Sun, Y. P.

L. W. Qu, R. B. Martin, W. J. Huang, K. F. Fu, D. Zweifel, Y. Lin, Y. P. Sun, C. E. Bunker, B. A. Harruff, J. R. Gord, L. F. Allard, “Interactions of functionalized carbon nanotubes with tethered pyrenes in solution,” J. Chem. Phys. 117, 8089–8094 (2002).
[CrossRef]

Tatam, R. P.

Tran, T. A.

T. A. Tran, V. Bhatia, T. D’Alberto, K. A. Murphy, R. O. Claus, “Real-time immunoassays using fiber-optic long-period grating sensors,” in Biomedical Sensing, Imaging, and Tracking Technologies I, Proc. SPIE2676, 165–170 (1996).
[CrossRef]

J. A. Greene, M. E. Jones, T. A. Tran, K. A. Murphy, P. M. Schindler, V. Bhatia, R. G. May, D. Sherrer, R. O. Claus, “Grating-based optical fiber-based corrosion sensors,” in Smart Sensing Processing and Instrumentation, Proc. SPIE2718, 170–174 (1996).

Van Tassel, R.

J. Elster, J. Greene, M. Jones, T. Bailey, S. Lenahan, W. Velander, R. Van Tassel, W. Hodges, “Optical fiber-based chemical sensors for detection of corrosion precursors and byproducts,” in Chemical, Biochemical, and Environmental Fiber Sensors X, Proc. SPIE3540, 251–257 (1998).
[CrossRef]

Vannini, A.

R. Falciai, A. G. Mignani, A. Vannini, “Long period gratings as solution concentration sensors,” Sens. Actuators B 74, 74–77 (2001).
[CrossRef]

Velander, W.

J. Elster, J. Greene, M. Jones, T. Bailey, S. Lenahan, W. Velander, R. Van Tassel, W. Hodges, “Optical fiber-based chemical sensors for detection of corrosion precursors and byproducts,” in Chemical, Biochemical, and Environmental Fiber Sensors X, Proc. SPIE3540, 251–257 (1998).
[CrossRef]

Vengsarkar, A. M.

V. Bhatia, A. M. Vengsarkar, “Optical fiber long-period grating sensors,” Opt. Lett. 21, 692–694 (1996).
[CrossRef] [PubMed]

A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan, J. E. Sipe, “Long-period fiber gratings as band-rejection filters,” J. Lightwave Technol. 14, 58–65 (1996).
[CrossRef]

Vohra, S. T.

H. J. Patrick, S. T. Vohra, C. C. Chang, “Long period fibre gratings for structural bend sensing,” Electron. Lett. 34, 1773–1775 (1998).
[CrossRef]

Wang, L. A.

L. A. Wang, C. Y. Lin, G. W. Chern, “A torsion sensor made of a corrugated long period fibre grating,” Meas. Sci. Technol. 12, 793–799 (2001).
[CrossRef]

Williams, J. A. R.

Y. Liu, L. Zhang, J. A. R. Williams, I. Bennion, “Bend sensing by measuring the resonance splitting of long-period fiber gratings,” Opt. Commun. 193, 69–72 (2001).
[CrossRef]

Y. Liu, L. Zhang, J. A. R. Williams, I. Bennion, “Optical bend sensor based on measurement of resonance mode splitting of long-period fiber grating,” IEEE Photon. Technol. Lett. 12, 531–533 (2000).
[CrossRef]

Ye, C. C.

Zhang, L.

T. Allsop, L. Zhang, I. Bennion, “Detection of organic aromatic compounds in paraffin by a long-period fiber grating optical sensor with optimized sensitivity,” Opt. Commun. 191, 181–190 (2001).
[CrossRef]

Y. Liu, L. Zhang, J. A. R. Williams, I. Bennion, “Bend sensing by measuring the resonance splitting of long-period fiber gratings,” Opt. Commun. 193, 69–72 (2001).
[CrossRef]

Y. Liu, L. Zhang, J. A. R. Williams, I. Bennion, “Optical bend sensor based on measurement of resonance mode splitting of long-period fiber grating,” IEEE Photon. Technol. Lett. 12, 531–533 (2000).
[CrossRef]

Zweifel, D.

L. W. Qu, R. B. Martin, W. J. Huang, K. F. Fu, D. Zweifel, Y. Lin, Y. P. Sun, C. E. Bunker, B. A. Harruff, J. R. Gord, L. F. Allard, “Interactions of functionalized carbon nanotubes with tethered pyrenes in solution,” J. Chem. Phys. 117, 8089–8094 (2002).
[CrossRef]

Compos. Sci. Technol. (1)

S. R. M. Kueh, R. S. Parnas, S. G. Advani, “A methodology for using long-period gratings and mold-filling simulations to minimize the intrusiveness of flow sensors in liquid composite molding,” Compos. Sci. Technol. 62, 311–327 (2002).
[CrossRef]

Electron. Lett. (3)

H. J. Patrick, “Self-aligning, bipolar bend transducer based on long period grating written in eccentric core fibre,” Electron. Lett. 36, 1763–1764 (2000).
[CrossRef]

H. J. Patrick, S. T. Vohra, C. C. Chang, “Long period fibre gratings for structural bend sensing,” Electron. Lett. 34, 1773–1775 (1998).
[CrossRef]

B. A. L. Gwandu, X. Shu, T. P. D. Allsop, “Simultaneous refractive index and temperature measurement using cascaded long-period grating in double-cladding fibre,” Electron. Lett. 38, 695–696 (2002).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

Y. Liu, L. Zhang, J. A. R. Williams, I. Bennion, “Optical bend sensor based on measurement of resonance mode splitting of long-period fiber grating,” IEEE Photon. Technol. Lett. 12, 531–533 (2000).
[CrossRef]

J. Chem. Phys. (1)

L. W. Qu, R. B. Martin, W. J. Huang, K. F. Fu, D. Zweifel, Y. Lin, Y. P. Sun, C. E. Bunker, B. A. Harruff, J. R. Gord, L. F. Allard, “Interactions of functionalized carbon nanotubes with tethered pyrenes in solution,” J. Chem. Phys. 117, 8089–8094 (2002).
[CrossRef]

J. Lightwave Technol. (2)

A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan, J. E. Sipe, “Long-period fiber gratings as band-rejection filters,” J. Lightwave Technol. 14, 58–65 (1996).
[CrossRef]

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

Langmuir (1)

B. A. Harruff, C. E. Bunker, “Spectral properties of AOT-protected CdS nanoparticles: quantum yield enhancement by photolysis,” Langmuir 19, 893–897 (2003).
[CrossRef]

Laser Focus World (1)

D. Appell, “Fiber sensing—clad fiber detects biological agents fast,” Laser Focus World 34, 26–27 (1998).

Meas. Sci. Technol. (2)

Y.-G. Han, B. H. Lee, W.-T. Han, U.-C. Paek, Y. Chung, “Fibre-optic sensing applications of a pair of long-period fibre gratings,” Meas. Sci. Technol. 12, 778–781 (2001).
[CrossRef]

L. A. Wang, C. Y. Lin, G. W. Chern, “A torsion sensor made of a corrugated long period fibre grating,” Meas. Sci. Technol. 12, 793–799 (2001).
[CrossRef]

Opt. Commun. (3)

Y. Liu, L. Zhang, J. A. R. Williams, I. Bennion, “Bend sensing by measuring the resonance splitting of long-period fiber gratings,” Opt. Commun. 193, 69–72 (2001).
[CrossRef]

X. Shu, D. Huang, “Highly sensitive chemical sensor based on the measurement of the separation of dual resonant peaks in a 100-μm-period fiber grating,” Opt. Commun. 171, 65–69 (1999).
[CrossRef]

T. Allsop, L. Zhang, I. Bennion, “Detection of organic aromatic compounds in paraffin by a long-period fiber grating optical sensor with optimized sensitivity,” Opt. Commun. 191, 181–190 (2001).
[CrossRef]

Opt. Lett. (2)

Sens. Actuators (1)

K. T. V. Grattan, T. Sun, “Fiber optic sensor technology: an overview,” Sens. Actuators 82, 40–61 (2000).
[CrossRef]

Sens. Actuators B (1)

R. Falciai, A. G. Mignani, A. Vannini, “Long period gratings as solution concentration sensors,” Sens. Actuators B 74, 74–77 (2001).
[CrossRef]

Other (7)

K. Goswami, J. Prohaska, A. Menon, E. Mendoza, R. Lieberman, “Evanescent wave sensor for detecting volatile organic compounds,” in Chemical, Biochemical, and Environmental Fiber Sensors X, Proc. SPIE3540, 115–122 (1998).
[CrossRef]

J. A. Greene, M. E. Jones, T. A. Tran, K. A. Murphy, P. M. Schindler, V. Bhatia, R. G. May, D. Sherrer, R. O. Claus, “Grating-based optical fiber-based corrosion sensors,” in Smart Sensing Processing and Instrumentation, Proc. SPIE2718, 170–174 (1996).

J. Elster, J. Greene, M. Jones, T. Bailey, S. Lenahan, W. Velander, R. Van Tassel, W. Hodges, “Optical fiber-based chemical sensors for detection of corrosion precursors and byproducts,” in Chemical, Biochemical, and Environmental Fiber Sensors X, Proc. SPIE3540, 251–257 (1998).
[CrossRef]

T. A. Tran, V. Bhatia, T. D’Alberto, K. A. Murphy, R. O. Claus, “Real-time immunoassays using fiber-optic long-period grating sensors,” in Biomedical Sensing, Imaging, and Tracking Technologies I, Proc. SPIE2676, 165–170 (1996).
[CrossRef]

D. C. Harris, Quantitative Chemical Analysis,6th ed. (Freeman, San Francisco, Calif., 2003).

J. H. Espenson, Chemical Kinetics and Reaction Mechanisms, 2nd ed. (McGraw-Hill, New York, 1995).

J. Bard, L. R. Faulkner, Electrochemical Methods: Fundamentals and Applications (Wiley, New York, 2001).

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Figures (7)

Fig. 1
Fig. 1

Schematic representation of the LPG fiber-optic sensor. The affinity coating on the cladding collapses on exposure to Cu+2 solution.

Fig. 2
Fig. 2

Wavelength shift of the spectral-loss element versus the local refractive index for a bare LPG. Line, linear least-squares fit.

Fig. 3
Fig. 3

Fiber-sensor responses versus time for a series of different Cu+2 concentrations in aqueous solution.

Fig. 4
Fig. 4

Fiber-sensor responses plotted as normalized wavelength shift versus normalized time for concentrations depicted in Fig. 3.

Fig. 5
Fig. 5

Fit of kinetic model (solid curve) to fiber-sensor response (dotted curve) for 100-μM Cu+2 solution.

Fig. 6
Fig. 6

LPG calibration curve with kf1′ plotted as a function of formal Cu+2 concentration in aqueous solution. The main figure covers the entire concentration range used in this study. The dotted curve is arbitrary and serves only to highlight the position of kf1′ values. The inset figure is an expansion of the lower concentration range in which linear behavior is observed. Solid line is obtained from a linear least-squares fit of low-concentration data.

Fig. 7
Fig. 7

LPG calibration curve with the initial slope of the spectral-loss-element response plotted as a function of Cu+2 concentration in aqueous solution. Dotted curve is arbitrary and used to highlight the position of slope values. Solid line is obtained from a linear least-squares fit of low-concentration data.

Tables (1)

Tables Icon

Table 1 Measured Rate Constants for the Coated Fiber

Equations (45)

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t n = t / t linear ,
λ n = λ / λ linear .
Cu + 2 ( aq ) + ( 1 - θ s ) Cu + 2 ( s ) ,
Cu + 2 ( s ) + ( 1 - θ m ) Cu + 2 ( m ) ,
d [ Cu + 2 ( aq ) ] / d t = 0
d θ s / d t = k f 1 [ Cu + 2 ( aq ) ] ( 1 - θ s ) - k r θ s - k f 2 θ s ( 1 - θ m ) .
d θ s / d t = k f l ( 1 - θ s ) - k r θ s - k f 2 θ s ( 1 - θ m ) ,
k f l = k f 1 [ Cu + 2 ( aq ) ] .
d θ s / d t = k t ( k * - θ s ) - k f 2 θ s ( 1 - θ m ) ,
d θ m / d t = k f 2 θ s ( 1 - θ m ) .
d θ s / d t = k t ( k * - θ s ) - d θ m / d t .
d θ m / d t = k f 2 ( 1 - θ m ) { k * [ ln ( 1 - θ m ) ] + k f 1 t - θ m } .
d λ / d t = λ max ( k f 2 ( 1 - λ / λ max ) { k * [ ln ( 1 - λ / λ max ) ] + k f 1 t - λ / λ max } ) ,
θ m = λ / λ max .
t = ( 1 / k f 1 ) ( { L / [ k f 2 ( 1 - λ / λ max ) ] } + λ / λ max - k * [ ln ( 1 - λ / λ max ) ] ) .
θ s * = k * - θ s ,
θ m * = 1 - θ m ,
d θ s * / d t = - d θ s / d t ,
d θ m * / d t = - d θ m / d t .
- d θ m * / d t = d θ m / d t = k f 2 ( k * - θ s * ) θ m * ,
( - d θ m * / d t ) ( 1 / k f 2 θ m * ) = k * - θ s * ,
θ s * = k * + ( 1 / k f 2 θ m * ) ( d θ m * / d t ) = k * + ( 1 / k f 2 ) [ d ( ln θ m * ) / d t ] .
d θ s / d t = - d θ s * / d t = k t θ s * + d θ m * / d t = k t [ k * + ( 1 / k f 2 θ m * ) ( d θ m * / d t ) ] + d θ m * / d t = k f 1 + [ ( k t / k f 2 θ m * ) + 1 ] d θ m * / d t
k t k * = ( k f 1 / k t ) k t = k f 1 .
a = k t / k f 2 ,
- d θ s * / d t = k f 1 + [ ( a + θ m * ) / θ m * ] d θ m * / d t .
θ m * = e p .
ln θ m * = p ,             ln ( 1 - θ m ) = p ,             d θ m * / d t = e p d p / d t .
[ ( a + θ m * ) / θ m * ] d θ m * / d t = [ ( a + e p ) / e p ] e p d p / d t = ( a + e p ) d p / d t = d ( a p + e p ) / d t .
- d θ s * / d t = k f 1 + d ( a p + e p ) / d t ,
d θ s * / d t + d ( a p + e p ) / d t = - k f 1 ,
d ( θ s * + a p + e p ) / d t = - k f 1 .
θ s * + a p + e p = - k f 1 t + Q ,
k * - θ s + ( k t / k f 2 ) [ ln ( 1 - θ m ) ] + ( 1 - θ m ) = - k f 1 t - Q .
θ s = ( k t / k f 2 ) [ ln ( 1 - θ m ) ] + k f 1 t - θ m .
θ s = k * [ ln ( 1 - θ m ) ] + k f 1 t - θ m ,
k * = k t / k f 2 .
d θ m / d t = k f 2 ( 1 - θ m ) { k * [ ln ( 1 - θ m ) ] + k f 1 t - θ m } .
d λ / d t = λ max ( k f 2 ( 1 - λ / λ max ) { k * [ ln ( 1 - λ / λ max ) ] + k f 1 t - λ / λ max } ) .
t = f ( θ m ) = k a + k b θ m + k c θ m 2 + k d θ m 3 + k e θ m 4 ,
t = f ( λ / λ max ) = k a + k b ( λ / λ max ) + k c ( λ / λ max ) 2 + k d ( λ / λ max ) 3 + k e ( λ / λ max ) 4 .
d t / d ( λ / λ max ) = k b + 2 k c ( λ / λ max ) + 3 k d ( λ / λ max ) 2 + 4 k e ( λ / λ max ) 3 = 1 / L ,
d ( λ / λ max ) / d t = L .
L / [ k f 2 ( 1 - λ / λ max ) ] = k * [ ln ( 1 - λ / λ max ) ] + k f 1 t - λ / λ max .
t = ( 1 / k f 1 ) ( { L / [ k f 2 ( 1 - λ / λ max ) ] } + λ / λ max - k * [ ln ( 1 - λ / λ max ) ] ) .

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