Abstract

We demonstrate simultaneous monitoring of the real and imaginary parts of the liquid analyte refractive index by using a hollow-core Bragg fiber. We apply this two-channel fiber sensor to monitor concentrations of various commercial cooling oils. The sensor operates using spectral monitoring of the fiber bandgap center wavelength, as well as monitoring of the fiber transmission amplitude at mid-bandgap position. The sensitivity of the fiber sensor to changes in the real part of the core refractive index is found to be 1460nm/Refractive index unit (RIU). By using spectral modality and effective medium theory, we determine the concentrations of the two commercial fluids from the measured refractive indices with an accuracy of ~0.57% for both low- and high-loss oils. Moreover, using an amplitude-based detection modality allows determination of the oil concentration with accuracy of ~1.64% for low-loss oils and ~2.81% for the high-loss oils.

© 2015 Optical Society of America

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References

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2014 (5)

2012 (3)

H. Qu and M. Skorobogatiy, “Resonant bio- and chemical sensors using low-refractive-index-contrast liquid-core Bragg fibers,” Sens. Actuators B Chem. 161(1), 261–268 (2012).
[Crossref]

H. Qu, B. Ung, M. Roze, and M. Skorobogatiy, “All photonic bandgap fiber spectroscopic system for detection of refractive index changes in aqueous analytes,” Sens. Actuators B Chem. 161(1), 235–243 (2012).
[Crossref]

S. Kedenburg, M. Vieweg, T. Gissibl, and H. Giessen, “Linear refractive index and absorption measurements of nonlinear optical liquids in the visible and near-infrared spectral region,” Opt. Mater. Express 2(11), 1588–1611 (2012).
[Crossref]

2011 (1)

H. Qu and M. Skorobogatiy, “liquid-core low-refractive-index-contrast Bragg fiber sensor,” Appl. Phys. Lett. 98(20), 201114 (2011).
[Crossref]

2010 (1)

N. J. Hutchinson, T. Coquil, A. Navid, and L. Pilon, “Effective optical properties of highly ordered mesoporous thin films,” Thin Solid Films 518(8), 2141–2146 (2010).
[Crossref]

2008 (4)

V. Janicki, J. Sancho-Parramon, and H. Zorc, “Refractive index profile modeling of dielectric inhomogeneous coatings using effective medium theories,” Thin Solid Films 516(10), 3368–3373 (2008).
[Crossref]

Y. Han, M. K. Khaing, Y. Zhu, L. Xiao, M. S. Demohan, W. Jin, and H. Du, “Index-guiding liquid-core photonic crystal fiber for solution measurement using normal and surface-enhanced Raman scattering,” Opt. Eng. 47(4), 040502 (2008).
[Crossref]

L. Rindorf and O. Bang, “Highly sensitive refractometer with a photonic-crystal-fiber long-period grating,” Opt. Lett. 33(6), 563–565 (2008).
[Crossref] [PubMed]

X. Fan, I. M. White, S. I. Shopova, H. Zhu, J. D. Suter, and Y. Sun, “Sensitive optical biosensors for unlabeled targets: A review,” Anal. Chim. Acta 620(1-2), 8–26 (2008).
[Crossref] [PubMed]

2007 (3)

Y. Zhang, C. Shi, C. Gu, L. Seballos, and J. Zhang, “Liquid core photonic crystal fiber sensor based on surface enhanced Raman scattering,” Appl. Phys. Lett. 90(19), 193504 (2007).
[Crossref]

H. F. Xuan, W. Jin, J. Ju, H. L. Ho, M. Zhang, and Y. B. Liao, “Low-contrast photonic bandgap fibers and their potential applications in liquid-base sensors,” Proc. SPIE 6619, 661936 (2007).
[Crossref]

J. Sun and C. C. Chan, “Photonic bandgap fiber for refractive index measurement,” Sens. Actuators B Chem. 128(1), 46–50 (2007).
[Crossref]

2006 (1)

2005 (1)

2003 (1)

R. Manor, A. Datta, I. Ahmad, M. Holta, S. Gangopadhyay, and T. Dallsa, “Microfabrication and characterization of liquid core waveguide glass channels coated with Teflon AF,” IEEE Sens. J. 3(6), 687–692 (2003).
[Crossref]

2002 (1)

S. Singh, “Refractive index measurement and its applications,” Phys. Scr. 65(2), 167–180 (2002).
[Crossref]

1997 (1)

1996 (2)

J. Beuthan, O. Minet, J. Helfmann, M. Herrig, and G. Müller, “The spatial variation of the refractive index in biological cells,” Phys. Med. Biol. 41(3), 369–382 (1996).
[Crossref] [PubMed]

V. Benoit and M. C. Yappert, “Effect of capillary properties on the sensitivity enhancement in capillary/fiber optical sensors,” Anal. Chem. 68(1), 183–188 (1996).
[Crossref] [PubMed]

1981 (2)

Abu Bakar, M. H.

Ahmad, I.

R. Manor, A. Datta, I. Ahmad, M. Holta, S. Gangopadhyay, and T. Dallsa, “Microfabrication and characterization of liquid core waveguide glass channels coated with Teflon AF,” IEEE Sens. J. 3(6), 687–692 (2003).
[Crossref]

Argyros, A.

Bang, O.

Barnard, A. H.

Bartelt, H.

Benoit, V.

V. Benoit and M. C. Yappert, “Effect of capillary properties on the sensitivity enhancement in capillary/fiber optical sensors,” Anal. Chem. 68(1), 183–188 (1996).
[Crossref] [PubMed]

Beuthan, J.

J. Beuthan, O. Minet, J. Helfmann, M. Herrig, and G. Müller, “The spatial variation of the refractive index in biological cells,” Phys. Med. Biol. 41(3), 369–382 (1996).
[Crossref] [PubMed]

Chan, C. C.

J. Sun and C. C. Chan, “Photonic bandgap fiber for refractive index measurement,” Sens. Actuators B Chem. 128(1), 46–50 (2007).
[Crossref]

Chen, Z.

H. Yu, L. Xiong, Z. Chen, Q. Li, X. Yi, Y. Ding, F. Wang, H. Lv, and Y. Ding, “Solution concentration and refractive index sensing based on polymer microfiber knot resonator,” Appl. Phys. Express 7(2), 022501 (2014).
[Crossref]

Coquil, T.

N. J. Hutchinson, T. Coquil, A. Navid, and L. Pilon, “Effective optical properties of highly ordered mesoporous thin films,” Thin Solid Films 518(8), 2141–2146 (2010).
[Crossref]

Dallsa, T.

R. Manor, A. Datta, I. Ahmad, M. Holta, S. Gangopadhyay, and T. Dallsa, “Microfabrication and characterization of liquid core waveguide glass channels coated with Teflon AF,” IEEE Sens. J. 3(6), 687–692 (2003).
[Crossref]

Datta, A.

R. Manor, A. Datta, I. Ahmad, M. Holta, S. Gangopadhyay, and T. Dallsa, “Microfabrication and characterization of liquid core waveguide glass channels coated with Teflon AF,” IEEE Sens. J. 3(6), 687–692 (2003).
[Crossref]

Dellith, J.

Demohan, M. S.

Y. Han, M. K. Khaing, Y. Zhu, L. Xiao, M. S. Demohan, W. Jin, and H. Du, “Index-guiding liquid-core photonic crystal fiber for solution measurement using normal and surface-enhanced Raman scattering,” Opt. Eng. 47(4), 040502 (2008).
[Crossref]

Ding, Y.

H. Yu, L. Xiong, Z. Chen, Q. Li, X. Yi, Y. Ding, F. Wang, H. Lv, and Y. Ding, “Solution concentration and refractive index sensing based on polymer microfiber knot resonator,” Appl. Phys. Express 7(2), 022501 (2014).
[Crossref]

H. Yu, L. Xiong, Z. Chen, Q. Li, X. Yi, Y. Ding, F. Wang, H. Lv, and Y. Ding, “Solution concentration and refractive index sensing based on polymer microfiber knot resonator,” Appl. Phys. Express 7(2), 022501 (2014).
[Crossref]

Donaghay, P. L.

Du, H.

Y. Han, M. K. Khaing, Y. Zhu, L. Xiao, M. S. Demohan, W. Jin, and H. Du, “Index-guiding liquid-core photonic crystal fiber for solution measurement using normal and surface-enhanced Raman scattering,” Opt. Eng. 47(4), 040502 (2008).
[Crossref]

Fan, X.

X. Fan, I. M. White, S. I. Shopova, H. Zhu, J. D. Suter, and Y. Sun, “Sensitive optical biosensors for unlabeled targets: A review,” Anal. Chim. Acta 620(1-2), 8–26 (2008).
[Crossref] [PubMed]

Gangopadhyay, S.

R. Manor, A. Datta, I. Ahmad, M. Holta, S. Gangopadhyay, and T. Dallsa, “Microfabrication and characterization of liquid core waveguide glass channels coated with Teflon AF,” IEEE Sens. J. 3(6), 687–692 (2003).
[Crossref]

Giessen, H.

Gissibl, T.

Granqvist, C. G.

Gray, D.

Gu, C.

Y. Zhang, C. Shi, C. Gu, L. Seballos, and J. Zhang, “Liquid core photonic crystal fiber sensor based on surface enhanced Raman scattering,” Appl. Phys. Lett. 90(19), 193504 (2007).
[Crossref]

Han, Y.

Y. Han, M. K. Khaing, Y. Zhu, L. Xiao, M. S. Demohan, W. Jin, and H. Du, “Index-guiding liquid-core photonic crystal fiber for solution measurement using normal and surface-enhanced Raman scattering,” Opt. Eng. 47(4), 040502 (2008).
[Crossref]

Helfmann, J.

J. Beuthan, O. Minet, J. Helfmann, M. Herrig, and G. Müller, “The spatial variation of the refractive index in biological cells,” Phys. Med. Biol. 41(3), 369–382 (1996).
[Crossref] [PubMed]

Herrig, M.

J. Beuthan, O. Minet, J. Helfmann, M. Herrig, and G. Müller, “The spatial variation of the refractive index in biological cells,” Phys. Med. Biol. 41(3), 369–382 (1996).
[Crossref] [PubMed]

Ho, H. L.

H. F. Xuan, W. Jin, J. Ju, H. L. Ho, M. Zhang, and Y. B. Liao, “Low-contrast photonic bandgap fibers and their potential applications in liquid-base sensors,” Proc. SPIE 6619, 661936 (2007).
[Crossref]

Holta, M.

R. Manor, A. Datta, I. Ahmad, M. Holta, S. Gangopadhyay, and T. Dallsa, “Microfabrication and characterization of liquid core waveguide glass channels coated with Teflon AF,” IEEE Sens. J. 3(6), 687–692 (2003).
[Crossref]

Hunderi, O.

Hutchinson, N. J.

N. J. Hutchinson, T. Coquil, A. Navid, and L. Pilon, “Effective optical properties of highly ordered mesoporous thin films,” Thin Solid Films 518(8), 2141–2146 (2010).
[Crossref]

Janicki, V.

V. Janicki, J. Sancho-Parramon, and H. Zorc, “Refractive index profile modeling of dielectric inhomogeneous coatings using effective medium theories,” Thin Solid Films 516(10), 3368–3373 (2008).
[Crossref]

Jin, W.

Y. Han, M. K. Khaing, Y. Zhu, L. Xiao, M. S. Demohan, W. Jin, and H. Du, “Index-guiding liquid-core photonic crystal fiber for solution measurement using normal and surface-enhanced Raman scattering,” Opt. Eng. 47(4), 040502 (2008).
[Crossref]

H. F. Xuan, W. Jin, J. Ju, H. L. Ho, M. Zhang, and Y. B. Liao, “Low-contrast photonic bandgap fibers and their potential applications in liquid-base sensors,” Proc. SPIE 6619, 661936 (2007).
[Crossref]

Ju, J.

H. F. Xuan, W. Jin, J. Ju, H. L. Ho, M. Zhang, and Y. B. Liao, “Low-contrast photonic bandgap fibers and their potential applications in liquid-base sensors,” Proc. SPIE 6619, 661936 (2007).
[Crossref]

Kamil, Y. M.

Kedenburg, S.

Khaing, M. K.

Y. Han, M. K. Khaing, Y. Zhu, L. Xiao, M. S. Demohan, W. Jin, and H. Du, “Index-guiding liquid-core photonic crystal fiber for solution measurement using normal and surface-enhanced Raman scattering,” Opt. Eng. 47(4), 040502 (2008).
[Crossref]

Kuhlmey, B. T.

Lee, K. J.

Leon-Saval, S. G.

Li, Q.

H. Yu, L. Xiong, Z. Chen, Q. Li, X. Yi, Y. Ding, F. Wang, H. Lv, and Y. Ding, “Solution concentration and refractive index sensing based on polymer microfiber knot resonator,” Appl. Phys. Express 7(2), 022501 (2014).
[Crossref]

Liao, Y. B.

H. F. Xuan, W. Jin, J. Ju, H. L. Ho, M. Zhang, and Y. B. Liao, “Low-contrast photonic bandgap fibers and their potential applications in liquid-base sensors,” Proc. SPIE 6619, 661936 (2007).
[Crossref]

Liu, X.

Lv, H.

H. Yu, L. Xiong, Z. Chen, Q. Li, X. Yi, Y. Ding, F. Wang, H. Lv, and Y. Ding, “Solution concentration and refractive index sensing based on polymer microfiber knot resonator,” Appl. Phys. Express 7(2), 022501 (2014).
[Crossref]

Lwin, R.

Mahdi, M. A.

Manor, R.

R. Manor, A. Datta, I. Ahmad, M. Holta, S. Gangopadhyay, and T. Dallsa, “Microfabrication and characterization of liquid core waveguide glass channels coated with Teflon AF,” IEEE Sens. J. 3(6), 687–692 (2003).
[Crossref]

McKee, D.

Minet, O.

J. Beuthan, O. Minet, J. Helfmann, M. Herrig, and G. Müller, “The spatial variation of the refractive index in biological cells,” Phys. Med. Biol. 41(3), 369–382 (1996).
[Crossref] [PubMed]

Moore, C. M.

Müller, G.

J. Beuthan, O. Minet, J. Helfmann, M. Herrig, and G. Müller, “The spatial variation of the refractive index in biological cells,” Phys. Med. Biol. 41(3), 369–382 (1996).
[Crossref] [PubMed]

Narayanaswamy, R.

Navid, A.

N. J. Hutchinson, T. Coquil, A. Navid, and L. Pilon, “Effective optical properties of highly ordered mesoporous thin films,” Thin Solid Films 518(8), 2141–2146 (2010).
[Crossref]

Niklasson, G. A.

Pegau, W. S.

Pilon, L.

N. J. Hutchinson, T. Coquil, A. Navid, and L. Pilon, “Effective optical properties of highly ordered mesoporous thin films,” Thin Solid Films 518(8), 2141–2146 (2010).
[Crossref]

Qu, H.

H. Qu and M. Skorobogatiy, “Resonant bio- and chemical sensors using low-refractive-index-contrast liquid-core Bragg fibers,” Sens. Actuators B Chem. 161(1), 261–268 (2012).
[Crossref]

H. Qu, B. Ung, M. Roze, and M. Skorobogatiy, “All photonic bandgap fiber spectroscopic system for detection of refractive index changes in aqueous analytes,” Sens. Actuators B Chem. 161(1), 235–243 (2012).
[Crossref]

H. Qu and M. Skorobogatiy, “liquid-core low-refractive-index-contrast Bragg fiber sensor,” Appl. Phys. Lett. 98(20), 201114 (2011).
[Crossref]

Rhoades, B.

Rindorf, L.

Röttgers, R.

Roze, M.

H. Qu, B. Ung, M. Roze, and M. Skorobogatiy, “All photonic bandgap fiber spectroscopic system for detection of refractive index changes in aqueous analytes,” Sens. Actuators B Chem. 161(1), 235–243 (2012).
[Crossref]

Sancho-Parramon, J.

V. Janicki, J. Sancho-Parramon, and H. Zorc, “Refractive index profile modeling of dielectric inhomogeneous coatings using effective medium theories,” Thin Solid Films 516(10), 3368–3373 (2008).
[Crossref]

Schmidt, M. A.

Seballos, L.

Y. Zhang, C. Shi, C. Gu, L. Seballos, and J. Zhang, “Liquid core photonic crystal fiber sensor based on surface enhanced Raman scattering,” Appl. Phys. Lett. 90(19), 193504 (2007).
[Crossref]

Shi, C.

Y. Zhang, C. Shi, C. Gu, L. Seballos, and J. Zhang, “Liquid core photonic crystal fiber sensor based on surface enhanced Raman scattering,” Appl. Phys. Lett. 90(19), 193504 (2007).
[Crossref]

Shopova, S. I.

X. Fan, I. M. White, S. I. Shopova, H. Zhu, J. D. Suter, and Y. Sun, “Sensitive optical biosensors for unlabeled targets: A review,” Anal. Chim. Acta 620(1-2), 8–26 (2008).
[Crossref] [PubMed]

Singh, S.

S. Singh, “Refractive index measurement and its applications,” Phys. Scr. 65(2), 167–180 (2002).
[Crossref]

Skorobogatiy, M.

H. Qu and M. Skorobogatiy, “Resonant bio- and chemical sensors using low-refractive-index-contrast liquid-core Bragg fibers,” Sens. Actuators B Chem. 161(1), 261–268 (2012).
[Crossref]

H. Qu, B. Ung, M. Roze, and M. Skorobogatiy, “All photonic bandgap fiber spectroscopic system for detection of refractive index changes in aqueous analytes,” Sens. Actuators B Chem. 161(1), 235–243 (2012).
[Crossref]

H. Qu and M. Skorobogatiy, “liquid-core low-refractive-index-contrast Bragg fiber sensor,” Appl. Phys. Lett. 98(20), 201114 (2011).
[Crossref]

M. Skorobogatiy, “Efficient antiguiding of TE and TM polarizations in low-index core waveguides without the need for an omnidirectional reflector,” Opt. Lett. 30(22), 2991–2993 (2005).
[Crossref] [PubMed]

Sullivan, J. M.

Sun, J.

J. Sun and C. C. Chan, “Photonic bandgap fiber for refractive index measurement,” Sens. Actuators B Chem. 128(1), 46–50 (2007).
[Crossref]

Sun, Y.

X. Fan, I. M. White, S. I. Shopova, H. Zhu, J. D. Suter, and Y. Sun, “Sensitive optical biosensors for unlabeled targets: A review,” Anal. Chim. Acta 620(1-2), 8–26 (2008).
[Crossref] [PubMed]

Suter, J. D.

X. Fan, I. M. White, S. I. Shopova, H. Zhu, J. D. Suter, and Y. Sun, “Sensitive optical biosensors for unlabeled targets: A review,” Anal. Chim. Acta 620(1-2), 8–26 (2008).
[Crossref] [PubMed]

Talkenberg, F.

Twardowski, M. S.

Ung, B.

H. Qu, B. Ung, M. Roze, and M. Skorobogatiy, “All photonic bandgap fiber spectroscopic system for detection of refractive index changes in aqueous analytes,” Sens. Actuators B Chem. 161(1), 235–243 (2012).
[Crossref]

Utschig, C.

Vieweg, M.

Vuillemin, N.

Wang, F.

H. Yu, L. Xiong, Z. Chen, Q. Li, X. Yi, Y. Ding, F. Wang, H. Lv, and Y. Ding, “Solution concentration and refractive index sensing based on polymer microfiber knot resonator,” Appl. Phys. Express 7(2), 022501 (2014).
[Crossref]

White, I. M.

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Y. Han, M. K. Khaing, Y. Zhu, L. Xiao, M. S. Demohan, W. Jin, and H. Du, “Index-guiding liquid-core photonic crystal fiber for solution measurement using normal and surface-enhanced Raman scattering,” Opt. Eng. 47(4), 040502 (2008).
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H. Yu, L. Xiong, Z. Chen, Q. Li, X. Yi, Y. Ding, F. Wang, H. Lv, and Y. Ding, “Solution concentration and refractive index sensing based on polymer microfiber knot resonator,” Appl. Phys. Express 7(2), 022501 (2014).
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[Crossref]

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H. Yu, L. Xiong, Z. Chen, Q. Li, X. Yi, Y. Ding, F. Wang, H. Lv, and Y. Ding, “Solution concentration and refractive index sensing based on polymer microfiber knot resonator,” Appl. Phys. Express 7(2), 022501 (2014).
[Crossref]

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H. Yu, L. Xiong, Z. Chen, Q. Li, X. Yi, Y. Ding, F. Wang, H. Lv, and Y. Ding, “Solution concentration and refractive index sensing based on polymer microfiber knot resonator,” Appl. Phys. Express 7(2), 022501 (2014).
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Zaneveld, J. R. V.

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Y. Zhang, C. Shi, C. Gu, L. Seballos, and J. Zhang, “Liquid core photonic crystal fiber sensor based on surface enhanced Raman scattering,” Appl. Phys. Lett. 90(19), 193504 (2007).
[Crossref]

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H. F. Xuan, W. Jin, J. Ju, H. L. Ho, M. Zhang, and Y. B. Liao, “Low-contrast photonic bandgap fibers and their potential applications in liquid-base sensors,” Proc. SPIE 6619, 661936 (2007).
[Crossref]

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Y. Zhang, C. Shi, C. Gu, L. Seballos, and J. Zhang, “Liquid core photonic crystal fiber sensor based on surface enhanced Raman scattering,” Appl. Phys. Lett. 90(19), 193504 (2007).
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X. Fan, I. M. White, S. I. Shopova, H. Zhu, J. D. Suter, and Y. Sun, “Sensitive optical biosensors for unlabeled targets: A review,” Anal. Chim. Acta 620(1-2), 8–26 (2008).
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Y. Han, M. K. Khaing, Y. Zhu, L. Xiao, M. S. Demohan, W. Jin, and H. Du, “Index-guiding liquid-core photonic crystal fiber for solution measurement using normal and surface-enhanced Raman scattering,” Opt. Eng. 47(4), 040502 (2008).
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V. Benoit and M. C. Yappert, “Effect of capillary properties on the sensitivity enhancement in capillary/fiber optical sensors,” Anal. Chem. 68(1), 183–188 (1996).
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X. Fan, I. M. White, S. I. Shopova, H. Zhu, J. D. Suter, and Y. Sun, “Sensitive optical biosensors for unlabeled targets: A review,” Anal. Chim. Acta 620(1-2), 8–26 (2008).
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Appl. Phys. Express (1)

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Figures (9)

Fig. 1
Fig. 1 (a) Cross section of the fiber sensor under microscope. (b) Cross section of the Bragg reflector taken by a scanning electron microscope (SEM), which features alternating polystyrene (PS) /poly-methacrylate (PMMA) layers, with thickness of approximately 310nm.
Fig. 2
Fig. 2 (a) Low-loss cooling oil (heat transfer fluid), (b) High-loss cooling oil (sawing fluid).
Fig. 3
Fig. 3 Schematic of the two possible behavior of the Bragg fiber spectra when increasing the concentration of the cooling oil in the liquid-filled fiber core. (a) Low-absorption-loss cooling oil, (b) High-absorption-loss cooling oil.
Fig. 4
Fig. 4 Experimental set-up of the fiber sensor. The 24cm long Bragg fiber is integrated into the set-up using two opto-fluidic blocks. A broadband supercontinuum beam is launched into one end of the liquid-core Bragg fiber using an objective, and the output spectrum of the fiber sensor is registered by a grating monochromator.
Fig. 5
Fig. 5 (a) Experimental transmission spectra of the ~24cm long Bragg fiber filled with NaCl solutions. The weight concentrations (wt.%) and the corresponding RIs of the NaCl solutions are listed as following. DI water: 1.333, 2%: 1.3366, 4%: 1.3400, 6%: 1.3435, 8%: 1.3470, 10%: 1.3505. (b) Spectral shifts of the fiber maxima transmission peaks obtained from the experimental measurements and their linear fit. (c) Transmission amplitudes at the maxima transmission peaks obtained from the experimental measurements and their linear fit.
Fig. 6
Fig. 6 (a) Experimental set-up for bulk absorption measurements using a cut-back technique, inset: containers of different length (5cm, 10cm, 15cm). (b) and (c) Optical beam output spot at the end-face of a container filled with the low-loss heat-transfer fluid. (d) and (e) Optical beam output spot at the end-face of a container filled with the high-loss sawing fluid. During measurements, the output spots at the end-face of the container are somewhat distorted and vary with time, the time intervals between (b) and (c), as well as (d) and (e) are both five minutes.
Fig. 7
Fig. 7 (a) Absorption coefficients of distilled water and NaCl solutions at concentrations of 3%, 6%, and 9% (by weight) measured using a cut-back technique. (b) Absorption coefficients of the low-loss-absorption oil (heat-transfer fluid) measured using a cut-back technique and (c) Absorption coefficients of the high-absorption-loss oil (sawing fluid) measured using a cut-back technique
Fig. 8
Fig. 8 (a) Experimental transmission spectra of the 24cm long Bragg fiber filled with heat-transfer fluid at different concentrations (by volume). (b) Comparison of the refractive indices measured in experiment and the reference data provided by the supplier. (c) Comparison of the experimental concentrations with the concentrations predicted using spectral measurement modality and the BG model, as well as concentrations calculated using amplitude-based detection modality.
Fig. 9
Fig. 9 (a) Experimental transmission spectra of the 24cm long Bragg fiber filled with sawing fluid at different concentrations (by volume). (b) Comparison of the refractive indices measured in experiment and the reference data provided by the supplier. (c) Comparison of the experimental concentrations with the concentrations predicted by spectral modality and the BG model, as well as concentrations calculated using amplitude-based detection modality.

Equations (12)

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λ g 2 = d l ε l r ε c r + d h ε h r ε c r
c ε o ε e f f ε o + 2 ε e f f + ( 1 c ) ε w ε e f f ε w + 2 ε e f f = 0
α r a d = ( n c r , n h r , n l r , d c , d h , d l )
α e f f = Φ o ( c ) α o + Φ w ( c ) α w
T ( λ ) = I I 0 = e ( α r a d + α e f f ) L = e [ + Γ ( Φ o ( c ) α o + Φ w ( c ) α w ) ] L
T r e f ( λ g ) = e ( + Γ α r e f ) L T o i l ( λ g ) = e [ + Γ ( Φ o ( c ) α o + Φ w ( c ) α w ) ] L Φ o ( c ) α o + Φ w ( c ) α w = α r e f + 1 Γ L I n ( T r e f ( λ g ) T o i l ( λ g ) )
I l i q u i d ( L 1 , λ ) I e m p t y ( L 1 , λ ) / I l i q u i d ( L 2 , λ ) I e m p t y ( L 2 , λ ) = e α a b s ( L 2 L 1 )
α a b s ( λ ) = I n ( I l i q u i d ( L 1 , λ ) I l i q u i d ( L 2 , λ ) I e m p t y ( L 2 , λ ) I e m p t y ( L 1 , λ ) ) L 2 L 1
c ε o r + i ε o i ( ε e f f r + i ε e f f i ) ε o r + i ε o i + ( ε e f f r + 2 i ε e f f i ) = ( c 1 ) ε w r + i ε w i ( ε e f f r + i ε e f f i ) ε w r + i ε w i + ( ε e f f r + 2 i ε e f f i )
ε e f f i = ε o i ε e f f r 3 c ε e f f r ε w r 3 c ε o r ε o r + 2 ε w r 3 c ε w r 4 ε e f f r + ε w i ε o r + 3 c ε e f f r 2 ε e f f r 3 c ε o r ε o r + 2 ε w r 3 c ε w r 4 ε e f f r
α e f f = α o n o r n e f f r ε e f f r 3 c ε e f f r ε w r 3 c ε o r ε o r + 2 ε w r 3 c ε w r 4 ε e f f r + α w n w r n e f f r ε o r + 3 c ε e f f r 2 ε e f f r 3 c ε o r ε o r + 2 ε w r 3 c ε w r 4 ε e f f r
α e f f = Φ o ( c ) α o + Φ w ( c ) α w Φ o ( c ) = n o r n e f f r ε e f f r 3 c ε e f f r ε w r 3 c ε o r ε o r + 2 ε w r 3 c ε w r 4 ε e f f r Φ w ( c ) = n w r n e f f r ε o r + 3 c ε e f f r 2 ε e f f r 3 c ε o r ε o r + 2 ε w r 3 c ε w r 4 ε e f f r

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