Abstract

We report that, for an evanescent-wave (EW) based fiber-optic sensor, the less skewed tunnelling rays and a small number of very steep guided rays experience total internal reflection (TIR) at one end-face of the air-clad fiber segment. As a result, they demonstrate nine times greater efficiency in collecting EW-power than rays that do not exhibit end-face-TIR. This tunneling ray group originates from a launching ring that is seven times wider than that of end-face-TIR capable guided rays, enabling it to dominate the overall detected EW-power level. Strongly supporting this conclusion is the counter-intuitive experimental observation that the detected power at one end of the fiber abruptly drops 91% when the back reflection at the opposite end is eliminated, while an isotropic light source is placed at the core-cladding interface between these two ends. The mechanism of non-propagating ray excitation accounts for this high efficiency. We also indicate that many highly skewed tunnelling rays are naturally isolated from the external world because, outside the fiber core, they are accessible only via their EW fields even at the fiber end-faces. The findings reported here have significant implications for the design of future high-performance EW-based fiber sensing devices for the analysis of surface-event.

© 2009 Optical Society of America

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References

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  1. A. W. Snyder, "Leaky-ray theory of optical waveguides of circular cross-section," Appl. Phys. 4, 273-298 (1974).
    [CrossRef]
  2. A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman and Hall Ltd., London, 1983).
  3. Y. Xu, N. B. Jones, and J. C. Fothergill, "Theoretical analysis of the evanescent-wave absorption coefficient for multimode fiber-optic evanescent-wave absorption sensors," J. Mod. Opt. 46, 2007-2014 (1999).
    [CrossRef]
  4. N. Issa, "High Numerical Aperture in Multimode Microstructured Optical Fibers," Appl. Opt. 43,6191-6197 (2004).
    [CrossRef] [PubMed]
  5. M. Åslund, S. D. Jackson, J. Canning, A. Teixeira, and K. Lyytikäinen-Digweed, "The influence of skew rays on angular losses in air-clad fibers," Opt. Commun. 262, 77-81 (2006).
    [CrossRef]
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  11. T. Yoshimura and Y. Koyamada, "Influence of tunnelling rays to baseband frequency response of step-index plastic optical fibers," Electron. Commun. Jpn. 88, 12-17 (2005).
    [CrossRef]
  12. C. R. Taitt, T. P. Anderson, and F. S. Ligler, "Evanescent-wave fluorescence biosensors," Biosens. Bioelectron. 20, 2470-2487 (2005).
    [CrossRef] [PubMed]
  13. J. Ma and W. J. Bock, "Reshaping sample fluid droplet: Towards combined performance enhancement of evanescent-wave fiber-optic fluorometer," Opt. Lett. 32, 8-10 (2007).
    [CrossRef]
  14. G. Keiser, Optical Fiber Communications (McGraw-Hill Higher Education, third edition, 2000), Chap. 5.
  15. P. DiVita and U. Rossi, "Realistic evaluation of coupling loss between different optical fibers," J. Opt. Commun. 1, 26-32 (1980).
    [CrossRef]
  16. P. DiVita and U. Rossi, "Evaluation of splice losses induced by mismatch in fiber parameters," Opt. Quantum Electron. 13, 91-94 (1981).
    [CrossRef]

2008 (2)

2007 (2)

2006 (1)

M. Åslund, S. D. Jackson, J. Canning, A. Teixeira, and K. Lyytikäinen-Digweed, "The influence of skew rays on angular losses in air-clad fibers," Opt. Commun. 262, 77-81 (2006).
[CrossRef]

2005 (2)

T. Yoshimura and Y. Koyamada, "Influence of tunnelling rays to baseband frequency response of step-index plastic optical fibers," Electron. Commun. Jpn. 88, 12-17 (2005).
[CrossRef]

C. R. Taitt, T. P. Anderson, and F. S. Ligler, "Evanescent-wave fluorescence biosensors," Biosens. Bioelectron. 20, 2470-2487 (2005).
[CrossRef] [PubMed]

2004 (2)

2002 (1)

1999 (1)

Y. Xu, N. B. Jones, and J. C. Fothergill, "Theoretical analysis of the evanescent-wave absorption coefficient for multimode fiber-optic evanescent-wave absorption sensors," J. Mod. Opt. 46, 2007-2014 (1999).
[CrossRef]

1981 (1)

P. DiVita and U. Rossi, "Evaluation of splice losses induced by mismatch in fiber parameters," Opt. Quantum Electron. 13, 91-94 (1981).
[CrossRef]

1980 (1)

P. DiVita and U. Rossi, "Realistic evaluation of coupling loss between different optical fibers," J. Opt. Commun. 1, 26-32 (1980).
[CrossRef]

1974 (1)

A. W. Snyder, "Leaky-ray theory of optical waveguides of circular cross-section," Appl. Phys. 4, 273-298 (1974).
[CrossRef]

Amezcua, R.

Anderson, T. P.

C. R. Taitt, T. P. Anderson, and F. S. Ligler, "Evanescent-wave fluorescence biosensors," Biosens. Bioelectron. 20, 2470-2487 (2005).
[CrossRef] [PubMed]

Åslund, M.

M. Åslund, S. D. Jackson, J. Canning, A. Teixeira, and K. Lyytikäinen-Digweed, "The influence of skew rays on angular losses in air-clad fibers," Opt. Commun. 262, 77-81 (2006).
[CrossRef]

Bian, B.

Bock, W. J.

Broderick, N. G. R.

Canning, J.

M. Åslund, S. D. Jackson, J. Canning, A. Teixeira, and K. Lyytikäinen-Digweed, "The influence of skew rays on angular losses in air-clad fibers," Opt. Commun. 262, 77-81 (2006).
[CrossRef]

DiVita, P.

P. DiVita and U. Rossi, "Evaluation of splice losses induced by mismatch in fiber parameters," Opt. Quantum Electron. 13, 91-94 (1981).
[CrossRef]

P. DiVita and U. Rossi, "Realistic evaluation of coupling loss between different optical fibers," J. Opt. Commun. 1, 26-32 (1980).
[CrossRef]

Flanagan, J. C.

Fothergill, J. C.

Y. Xu, N. B. Jones, and J. C. Fothergill, "Theoretical analysis of the evanescent-wave absorption coefficient for multimode fiber-optic evanescent-wave absorption sensors," J. Mod. Opt. 46, 2007-2014 (1999).
[CrossRef]

Hayes, J. R.

Issa, N.

Jackson, S. D.

M. Åslund, S. D. Jackson, J. Canning, A. Teixeira, and K. Lyytikäinen-Digweed, "The influence of skew rays on angular losses in air-clad fibers," Opt. Commun. 262, 77-81 (2006).
[CrossRef]

Jones, N. B.

Y. Xu, N. B. Jones, and J. C. Fothergill, "Theoretical analysis of the evanescent-wave absorption coefficient for multimode fiber-optic evanescent-wave absorption sensors," J. Mod. Opt. 46, 2007-2014 (1999).
[CrossRef]

Koyamada, Y.

T. Yoshimura and Y. Koyamada, "Influence of tunnelling rays to baseband frequency response of step-index plastic optical fibers," Electron. Commun. Jpn. 88, 12-17 (2005).
[CrossRef]

Ligler, F. S.

C. R. Taitt, T. P. Anderson, and F. S. Ligler, "Evanescent-wave fluorescence biosensors," Biosens. Bioelectron. 20, 2470-2487 (2005).
[CrossRef] [PubMed]

Lu, J.

Lyytikäinen-Digweed, K.

M. Åslund, S. D. Jackson, J. Canning, A. Teixeira, and K. Lyytikäinen-Digweed, "The influence of skew rays on angular losses in air-clad fibers," Opt. Commun. 262, 77-81 (2006).
[CrossRef]

Ma, J.

Monro, T.

Padden, W.

Poladian, L.

Poletti, F.

Richardson, D. J.

Rossi, U.

P. DiVita and U. Rossi, "Evaluation of splice losses induced by mismatch in fiber parameters," Opt. Quantum Electron. 13, 91-94 (1981).
[CrossRef]

P. DiVita and U. Rossi, "Realistic evaluation of coupling loss between different optical fibers," J. Opt. Commun. 1, 26-32 (1980).
[CrossRef]

Shi, Y.

Snyder, A. W.

A. W. Snyder, "Leaky-ray theory of optical waveguides of circular cross-section," Appl. Phys. 4, 273-298 (1974).
[CrossRef]

Taitt, C. R.

C. R. Taitt, T. P. Anderson, and F. S. Ligler, "Evanescent-wave fluorescence biosensors," Biosens. Bioelectron. 20, 2470-2487 (2005).
[CrossRef] [PubMed]

Teixeira, A.

M. Åslund, S. D. Jackson, J. Canning, A. Teixeira, and K. Lyytikäinen-Digweed, "The influence of skew rays on angular losses in air-clad fibers," Opt. Commun. 262, 77-81 (2006).
[CrossRef]

Xu, Y.

Y. Xu, N. B. Jones, and J. C. Fothergill, "Theoretical analysis of the evanescent-wave absorption coefficient for multimode fiber-optic evanescent-wave absorption sensors," J. Mod. Opt. 46, 2007-2014 (1999).
[CrossRef]

Yoshimura, T.

T. Yoshimura and Y. Koyamada, "Influence of tunnelling rays to baseband frequency response of step-index plastic optical fibers," Electron. Commun. Jpn. 88, 12-17 (2005).
[CrossRef]

Zhang, Z.

Appl. Opt. (1)

Appl. Phys. (1)

A. W. Snyder, "Leaky-ray theory of optical waveguides of circular cross-section," Appl. Phys. 4, 273-298 (1974).
[CrossRef]

Biosens. Bioelectron. (1)

C. R. Taitt, T. P. Anderson, and F. S. Ligler, "Evanescent-wave fluorescence biosensors," Biosens. Bioelectron. 20, 2470-2487 (2005).
[CrossRef] [PubMed]

Electron. Commun. Jpn. (1)

T. Yoshimura and Y. Koyamada, "Influence of tunnelling rays to baseband frequency response of step-index plastic optical fibers," Electron. Commun. Jpn. 88, 12-17 (2005).
[CrossRef]

J. Mod. Opt. (1)

Y. Xu, N. B. Jones, and J. C. Fothergill, "Theoretical analysis of the evanescent-wave absorption coefficient for multimode fiber-optic evanescent-wave absorption sensors," J. Mod. Opt. 46, 2007-2014 (1999).
[CrossRef]

J. Opt. Commun. (1)

P. DiVita and U. Rossi, "Realistic evaluation of coupling loss between different optical fibers," J. Opt. Commun. 1, 26-32 (1980).
[CrossRef]

Opt. Commun. (1)

M. Åslund, S. D. Jackson, J. Canning, A. Teixeira, and K. Lyytikäinen-Digweed, "The influence of skew rays on angular losses in air-clad fibers," Opt. Commun. 262, 77-81 (2006).
[CrossRef]

Opt. Express (5)

Opt. Lett. (1)

Opt. Quantum Electron. (1)

P. DiVita and U. Rossi, "Evaluation of splice losses induced by mismatch in fiber parameters," Opt. Quantum Electron. 13, 91-94 (1981).
[CrossRef]

Other (2)

G. Keiser, Optical Fiber Communications (McGraw-Hill Higher Education, third edition, 2000), Chap. 5.

A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman and Hall Ltd., London, 1983).

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Figures (5)

Fig. 1.
Fig. 1.

A typical skew ray path within a step-profile fiber waveguide when end-face-TIR occurs. ρ : fiber core radius; α : incident and reflected angle; θz : angle of incident and reflected rays with fiber axial direction AH; θϕ : the angle between the ray projection onto the fiber cross-section AD and the tangent AG.

Fig. 2.
Fig. 2.

EW-based fluorescent fiber-optic sensing setup for end-face-TIR demonstration. Inset: separation between the i- and r- fibers when the optimum power is achieved. Air-, liquid- (R6G sample) and polymer-cladding segments are identified by their corresponding RIs as marked. An RI-matching gel block is introduced to eliminate any reflections at the fiber end-face. Refer to [13] for more detailed description of the operation of this sensor.

Fig. 3.
Fig. 3.

Experimental evidence of the occurrence of end-face-TIR from observing EW-power variations when the S-end-face is exposed to a low- (air, nair = 1) and a high-RI medium (RI-matching gel block ϕ24×30 mm, ngel = 1.465). Curve ①: EW fluorescent spectrum when the S-end is exposed to the air medium; curve ②: EW fluorescent spectrum when the S-end is exposed to the gel block medium. The striking 91% power drop, apparently counter-intuitive, can only be interpreted as the elimination of end-face-TIR. Refer to the text for detail.

Fig. 4.
Fig. 4.

Experimental results when the r-fiber in Fig. 2 is reversed and the experimental steps for Fig. 3 are repeated. A segment of large-core fiber with 800 μm core size is used between the spectrometer and the r-fiber to facilitate the connection. Curve ①: EW-power spectrum when the R-end is exposed to the air medium; curve ②: EW fluorescent power spectrum when the Rend is in contact with the gel block. The nearly unchanged EW fluorescent power level confirms that very highly skewed end-face-TIR tunnelling rays make no contribution to overall detectable EW-power.

Fig. 5.
Fig. 5.

Simplified model based on Fig. 2.

Equations (11)

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Guided rays : 0 < θ z < 90 ° α c
Tunnelling rays : 90 ° α c < θ z < 90 ° and α c < α < 90 °
I R = I F 0 ( R S × T R + R S R R × R S T R + R S R R R S R R × R S T R + R S R R R S R R R S R R × R S T R + ) +
+ I F 0 + ( T R + R R × R S T R + R R R S R R × R S T R + R R R S R R R S R R × R S T R + )
= I 0 2 T R R S ( 1 + R S R R + R S 2 R 1 2 + R S 3 R R 3 + ) + I 0 2 T R ( 1 + R S R R + R S 2 R S 2 + R R 3 R S 3 + )
= I 0 2 T R ( R S + 1 ) [ 1 ( R R R S ) m 1 R R R S ]
= I 0 2 ( 1 R R ) ( 1 + R S ) 1 R R R S when m
I R I 0 = 0.5 × ( 1 + R R ) ( 1 + R S ) ( 1 R R R S ) × 100 %
I R I 0 = 0.5 × ( 1 + R S ) × 100 %
I R = I 0
I R 0.5 I 0 | R S = R R

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