Abstract

An empirical “guided-mode refraction model” has been invoked to explain the optical attenuation of radiation in an exposed core optical fiber sensor subject to heterogeneous (surface) crystal growth. Based on Fresnel reflectance values at the internal fiber–crystal and crystal–solution interfaces, the model predictions agree with experimental observations of radial loss of radiation from the fiber core through the crystals as well as attenuation of guided radiation as a function of the radiation launch angle into the fiber.

© 2010 Optical Society of America

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References

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  1. O. S. Wolfbeis, Anal. Chem. 80, 4269 (2008).
    [CrossRef] [PubMed]
  2. R. Philip-Chandy, P. J. Scully, and D. Thomas, Sens. Act. B 71, 19 (2000).
    [CrossRef]
  3. M. Boerkamp, D. W. Lamb, P. G. Lye, C. M. Fellows, A. Al-Hamzah, and A. D. Wallace, Ind. Eng. Chem. Res. 49, 4682 (2010).
    [CrossRef]
  4. D. E. Grey, American Institute of Physics Handbook, 3rd ed. (McGraw-Hill, 1972).
  5. N. J. Harrick, Internal Reflection Spectroscopy (Wiley, 1967).
  6. E. Hecht, Optics (Addison Wesley, 2002).
  7. D. E. McCarthy, Appl. Opt. 6, 1896 (1967).
    [CrossRef] [PubMed]

2010 (1)

M. Boerkamp, D. W. Lamb, P. G. Lye, C. M. Fellows, A. Al-Hamzah, and A. D. Wallace, Ind. Eng. Chem. Res. 49, 4682 (2010).
[CrossRef]

2008 (1)

O. S. Wolfbeis, Anal. Chem. 80, 4269 (2008).
[CrossRef] [PubMed]

2000 (1)

R. Philip-Chandy, P. J. Scully, and D. Thomas, Sens. Act. B 71, 19 (2000).
[CrossRef]

1967 (1)

Al-Hamzah, A.

M. Boerkamp, D. W. Lamb, P. G. Lye, C. M. Fellows, A. Al-Hamzah, and A. D. Wallace, Ind. Eng. Chem. Res. 49, 4682 (2010).
[CrossRef]

Boerkamp, M.

M. Boerkamp, D. W. Lamb, P. G. Lye, C. M. Fellows, A. Al-Hamzah, and A. D. Wallace, Ind. Eng. Chem. Res. 49, 4682 (2010).
[CrossRef]

Fellows, C. M.

M. Boerkamp, D. W. Lamb, P. G. Lye, C. M. Fellows, A. Al-Hamzah, and A. D. Wallace, Ind. Eng. Chem. Res. 49, 4682 (2010).
[CrossRef]

Grey, D. E.

D. E. Grey, American Institute of Physics Handbook, 3rd ed. (McGraw-Hill, 1972).

Harrick, N. J.

N. J. Harrick, Internal Reflection Spectroscopy (Wiley, 1967).

Hecht, E.

E. Hecht, Optics (Addison Wesley, 2002).

Lamb, D. W.

M. Boerkamp, D. W. Lamb, P. G. Lye, C. M. Fellows, A. Al-Hamzah, and A. D. Wallace, Ind. Eng. Chem. Res. 49, 4682 (2010).
[CrossRef]

Lye, P. G.

M. Boerkamp, D. W. Lamb, P. G. Lye, C. M. Fellows, A. Al-Hamzah, and A. D. Wallace, Ind. Eng. Chem. Res. 49, 4682 (2010).
[CrossRef]

McCarthy, D. E.

Philip-Chandy, R.

R. Philip-Chandy, P. J. Scully, and D. Thomas, Sens. Act. B 71, 19 (2000).
[CrossRef]

Scully, P. J.

R. Philip-Chandy, P. J. Scully, and D. Thomas, Sens. Act. B 71, 19 (2000).
[CrossRef]

Thomas, D.

R. Philip-Chandy, P. J. Scully, and D. Thomas, Sens. Act. B 71, 19 (2000).
[CrossRef]

Wallace, A. D.

M. Boerkamp, D. W. Lamb, P. G. Lye, C. M. Fellows, A. Al-Hamzah, and A. D. Wallace, Ind. Eng. Chem. Res. 49, 4682 (2010).
[CrossRef]

Wolfbeis, O. S.

O. S. Wolfbeis, Anal. Chem. 80, 4269 (2008).
[CrossRef] [PubMed]

Anal. Chem. (1)

O. S. Wolfbeis, Anal. Chem. 80, 4269 (2008).
[CrossRef] [PubMed]

Appl. Opt. (1)

Ind. Eng. Chem. Res. (1)

M. Boerkamp, D. W. Lamb, P. G. Lye, C. M. Fellows, A. Al-Hamzah, and A. D. Wallace, Ind. Eng. Chem. Res. 49, 4682 (2010).
[CrossRef]

Sens. Act. B (1)

R. Philip-Chandy, P. J. Scully, and D. Thomas, Sens. Act. B 71, 19 (2000).
[CrossRef]

Other (3)

D. E. Grey, American Institute of Physics Handbook, 3rd ed. (McGraw-Hill, 1972).

N. J. Harrick, Internal Reflection Spectroscopy (Wiley, 1967).

E. Hecht, Optics (Addison Wesley, 2002).

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Figures (5)

Fig. 1
Fig. 1

Schematic diagram of the guided-mode refraction model illustrating the primary pathway of rays entering and exiting a crystal in contact with the silica fiber core (not to scale). Angles are given relative to the indicated normal (dashed line).

Fig. 2
Fig. 2

Schematic diagram illustrating the removal of cladding (thick black line) from 1 / 4 , 1 / 2 , and 3 / 4 of the circumference (“circumf.”) of a silica core fiber for exposure to surface crystal growth. Note the overlapping radiation field for the 3 / 4 exposed circumference. “Sensor head” indicates the relative location of the radial power detector (not to scale).

Fig. 3
Fig. 3

The measured power of refracted rays ( P refracted ) as a function of the optical output ( P output ) of a 600 μm core diam eter, silica optical fiber during the calcium carbonate crystal growth. Exposed core length = 1 cm . Data represent different proportions of the circumference ( 1 / 4 , 1 / 2 , 3 / 4 , and whole) of exposed core, according to Fig. 2.

Fig. 4
Fig. 4

Wavelength-dependent attenuation profiles of a 600 μm diameter silica optical fiber with exposed core length = 6 cm . A white light source is used.

Fig. 5
Fig. 5

Measured and calculated attenuation of guided radiation (He–Ne laser) as functions of launch angle. Measured val ues acquired after 70 min of crystal formation on a 200 μm diameter silica optical fiber with exposed core length = 6 cm .

Equations (2)

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Attenuation = 10 log 10 ( P P 0 ) ,
P refracted = β · P output ,

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