Abstract

We have constructed a novel refractive index (RI) sensor based on a fiber optic Fabry–Perot interferometer (FPI) by splicing a section of hollow core fiber between a single-mode fiber and a photonic crystal fiber (PCF). Owing to the air holes in the cladding of the PCF, various substances, such as liquids and gases with different RI, can enter or leave the in-fiber air cavity, which makes the device usable as a refractometer. In this paper, the fiber optic FPI sensor has been used to monitor the RI changes of air with different pressures, and the experimental results show that such a sensor has an RI sensitivity of 805.1μm/RIU, and hysteresis is not observed. Moreover, the easy fabrication method gives the in-fiber refractometer many potential applications in the sensing field.

© 2010 Optical Society of America

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    [CrossRef]
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    [CrossRef]
  6. P. A. Fomitchov, A. K. Kromine, S. Krishnaswamy, and J. D. Achenbach, “Sagnac-type fiber-optic array sensor for detection of bulk ultrasonic waves,” IEEE Trans. Ultrason. Ferroelect. Freq. Contr. 47, 584-590 (2000).
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  23. J. Y. Lee, H. C. Shih, C. T. Hong, and T. K. Chou, “Measurement of refractive index change by surface plasmon resonance and phase quadrature interferometry,” Opt. Commun. 276, 283-287 (2007).
    [CrossRef]

2008

2007

J. Y. Lee, H. C. Shih, C. T. Hong, and T. K. Chou, “Measurement of refractive index change by surface plasmon resonance and phase quadrature interferometry,” Opt. Commun. 276, 283-287 (2007).
[CrossRef]

N. Skivesen, A. Tetu, and M. Kristensen, “Photonic-crystal waveguide biosensor,” Opt. Express 15, 3169-3176 (2007).
[CrossRef] [PubMed]

L. Y. Shao, A. P. Zhang, W. S. Liu, H. Y. Fu, and S. He, “Optical refractive-index sensor based on dual fiber-Bragg gratings interposed with a multimode-fiber taper,” IEEE Photon. Technol. Lett. 19, 30-32 (2007).
[CrossRef]

2006

K. Q. Kieu and M. Mansuripur, “Biconical fiber taper sensors,” IEEE Photon. Technol. Lett. 18, 2239-2241 (2006).
[CrossRef]

K. Q. Kieu and M. Mansuripur, “Biconical fiber taper sensors,” IEEE Photon. Technol. Lett. 18, 2239-2241 (2006).
[CrossRef]

Y. J. Rao, “Recent progress in fiber-optic extrinsic Fabry-Perot interferometric sensors,” Opt. Fiber Technol. 12, 227-237(2006).
[CrossRef]

D. Donlagic and M. Lesic, “All-fiber quasi-distributed polarimetric temperature sensor,” Opt. Express 14, 10245-10254(2006).
[CrossRef] [PubMed]

2005

J. Xu, G. Pickrell, X. Wang, W. Peng, K. Cooper, and A. Wang, “A novel temperature-insensitive optical fiber pressure sensor for harsh environments,” IEEE Photon. Technol. Lett. 17, 870-872 (2005).
[CrossRef]

G. Z. Xiao, A. Adnet, Z. Y. Zhang, F. G. Sun, and C. P. Grover, “Monitoring changes in the refractive index of gases by means of a fiber optic Fabry-Perot interferometer,” Sens. Actuators A, Phys. 118, 177-182 (2005).
[CrossRef]

T. Zhu, Y. J. Rao, and Q. J. Mo, “Simultaneous measurement of refractive index and temperature using a single ultralong-period fiber grating,” IEEE Photon. Technol. Lett. 17, 744(2005).
[CrossRef]

2004

J. Villatoro, D. Monzon-Hernandez, and D. Talavera, “High resolution refractive index sensing with cladding multimode tapered fiber,” Electron. Lett. 40, 106-107 (2004).
[CrossRef]

J. B. Jensen, L. H. Pedersen, P. E. Hoiby, L. B. Nielsen, J. R. Folkenberg, J. Riishede, D. Noordegraaf, K. Nielsen, A. Carlsen, and A. Bjarklev, “Photonic crystal fiber based evanescent-wave sensor for detection of biomolecules in aqueous solutions,” Opt. Lett. 29, 1974-1976 (2004).
[CrossRef] [PubMed]

J. Villatoro, D. Monzon-Hernandez, and D. Talavera, “High resolution refractive index sensing with cladded multimode tapered optical fibre,” Electron. Lett. 40, 106-107 (2004).
[CrossRef]

2003

2001

G. Laffout and P. Ferdinand, “Tilted short-period fibre-Bragg-grating-induced coupling to cladding modes for accurate refractometry,” Meas. Sci. Technol. 12, 765-770 (2001).
[CrossRef]

2000

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

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

P. A. Fomitchov, A. K. Kromine, S. Krishnaswamy, and J. D. Achenbach, “Sagnac-type fiber-optic array sensor for detection of bulk ultrasonic waves,” IEEE Trans. Ultrason. Ferroelect. Freq. Contr. 47, 584-590 (2000).
[CrossRef]

1993

K. P. Buch and M. J. Downs, “An updated Edlen equation for the refractive index of air,” Metrologia 30, 155-162 (1993).
[CrossRef]

1967

Achenbach, J. D.

P. A. Fomitchov, A. K. Kromine, S. Krishnaswamy, and J. D. Achenbach, “Sagnac-type fiber-optic array sensor for detection of bulk ultrasonic waves,” IEEE Trans. Ultrason. Ferroelect. Freq. Contr. 47, 584-590 (2000).
[CrossRef]

Adnet, A.

G. Z. Xiao, A. Adnet, Z. Y. Zhang, F. G. Sun, and C. P. Grover, “Monitoring changes in the refractive index of gases by means of a fiber optic Fabry-Perot interferometer,” Sens. Actuators A, Phys. 118, 177-182 (2005).
[CrossRef]

Bjarklev, A.

Buch, K. P.

K. P. Buch and M. J. Downs, “An updated Edlen equation for the refractive index of air,” Metrologia 30, 155-162 (1993).
[CrossRef]

Carlsen, A.

Chiang, K. S.

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

Chong, J. H.

Chou, T. K.

J. Y. Lee, H. C. Shih, C. T. Hong, and T. K. Chou, “Measurement of refractive index change by surface plasmon resonance and phase quadrature interferometry,” Opt. Commun. 276, 283-287 (2007).
[CrossRef]

Cooper, K.

J. Xu, G. Pickrell, X. Wang, W. Peng, K. Cooper, and A. Wang, “A novel temperature-insensitive optical fiber pressure sensor for harsh environments,” IEEE Photon. Technol. Lett. 17, 870-872 (2005).
[CrossRef]

Demokan, M. S.

Deng, M.

Y. J. Rao, M. Deng, D. W. Duan, and T. Zhu, “In-line fiber Fabry-Perot refractive-index tip sensor based on endlessly photonic crystal fiber,” Sens. Actuators A, Phys. 148, 33-38(2008).
[CrossRef]

Dong, X.

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

Donlagic, D.

Downs, M. J.

K. P. Buch and M. J. Downs, “An updated Edlen equation for the refractive index of air,” Metrologia 30, 155-162 (1993).
[CrossRef]

Duan, D. W.

Y. J. Rao, M. Deng, D. W. Duan, and T. Zhu, “In-line fiber Fabry-Perot refractive-index tip sensor based on endlessly photonic crystal fiber,” Sens. Actuators A, Phys. 148, 33-38(2008).
[CrossRef]

Ferdinand, P.

G. Laffout and P. Ferdinand, “Tilted short-period fibre-Bragg-grating-induced coupling to cladding modes for accurate refractometry,” Meas. Sci. Technol. 12, 765-770 (2001).
[CrossRef]

Folkenberg, J. R.

Fomitchov, P. A.

P. A. Fomitchov, A. K. Kromine, S. Krishnaswamy, and J. D. Achenbach, “Sagnac-type fiber-optic array sensor for detection of bulk ultrasonic waves,” IEEE Trans. Ultrason. Ferroelect. Freq. Contr. 47, 584-590 (2000).
[CrossRef]

Fu, H. Y.

L. Y. Shao, A. P. Zhang, W. S. Liu, H. Y. Fu, and S. He, “Optical refractive-index sensor based on dual fiber-Bragg gratings interposed with a multimode-fiber taper,” IEEE Photon. Technol. Lett. 19, 30-32 (2007).
[CrossRef]

Grattan, K. T. V.

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

Grover, C. P.

G. Z. Xiao, A. Adnet, Z. Y. Zhang, F. G. Sun, and C. P. Grover, “Monitoring changes in the refractive index of gases by means of a fiber optic Fabry-Perot interferometer,” Sens. Actuators A, Phys. 118, 177-182 (2005).
[CrossRef]

Han, Y.

He, S.

L. Y. Shao, A. P. Zhang, W. S. Liu, H. Y. Fu, and S. He, “Optical refractive-index sensor based on dual fiber-Bragg gratings interposed with a multimode-fiber taper,” IEEE Photon. Technol. Lett. 19, 30-32 (2007).
[CrossRef]

Hoiby, P. E.

Hong, C. T.

J. Y. Lee, H. C. Shih, C. T. Hong, and T. K. Chou, “Measurement of refractive index change by surface plasmon resonance and phase quadrature interferometry,” Opt. Commun. 276, 283-287 (2007).
[CrossRef]

Jensen, J. B.

Jin, W.

Kieu, K. Q.

K. Q. Kieu and M. Mansuripur, “Biconical fiber taper sensors,” IEEE Photon. Technol. Lett. 18, 2239-2241 (2006).
[CrossRef]

K. Q. Kieu and M. Mansuripur, “Biconical fiber taper sensors,” IEEE Photon. Technol. Lett. 18, 2239-2241 (2006).
[CrossRef]

Krishnaswamy, S.

P. A. Fomitchov, A. K. Kromine, S. Krishnaswamy, and J. D. Achenbach, “Sagnac-type fiber-optic array sensor for detection of bulk ultrasonic waves,” IEEE Trans. Ultrason. Ferroelect. Freq. Contr. 47, 584-590 (2000).
[CrossRef]

Kristensen, M.

Kromine, A. K.

P. A. Fomitchov, A. K. Kromine, S. Krishnaswamy, and J. D. Achenbach, “Sagnac-type fiber-optic array sensor for detection of bulk ultrasonic waves,” IEEE Trans. Ultrason. Ferroelect. Freq. Contr. 47, 584-590 (2000).
[CrossRef]

Laffout, G.

G. Laffout and P. Ferdinand, “Tilted short-period fibre-Bragg-grating-induced coupling to cladding modes for accurate refractometry,” Meas. Sci. Technol. 12, 765-770 (2001).
[CrossRef]

Lee, J. Y.

J. Y. Lee, H. C. Shih, C. T. Hong, and T. K. Chou, “Measurement of refractive index change by surface plasmon resonance and phase quadrature interferometry,” Opt. Commun. 276, 283-287 (2007).
[CrossRef]

Lesic, M.

Li, Y.

Liu, W. S.

L. Y. Shao, A. P. Zhang, W. S. Liu, H. Y. Fu, and S. He, “Optical refractive-index sensor based on dual fiber-Bragg gratings interposed with a multimode-fiber taper,” IEEE Photon. Technol. Lett. 19, 30-32 (2007).
[CrossRef]

Liu, Y.

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

Mansuripur, M.

K. Q. Kieu and M. Mansuripur, “Biconical fiber taper sensors,” IEEE Photon. Technol. Lett. 18, 2239-2241 (2006).
[CrossRef]

K. Q. Kieu and M. Mansuripur, “Biconical fiber taper sensors,” IEEE Photon. Technol. Lett. 18, 2239-2241 (2006).
[CrossRef]

Mo, Q. J.

T. Zhu, Y. J. Rao, and Q. J. Mo, “Simultaneous measurement of refractive index and temperature using a single ultralong-period fiber grating,” IEEE Photon. Technol. Lett. 17, 744(2005).
[CrossRef]

Monzon-Hernandez, D.

J. Villatoro, D. Monzon-Hernandez, and D. Talavera, “High resolution refractive index sensing with cladding multimode tapered fiber,” Electron. Lett. 40, 106-107 (2004).
[CrossRef]

J. Villatoro, D. Monzon-Hernandez, and D. Talavera, “High resolution refractive index sensing with cladded multimode tapered optical fibre,” Electron. Lett. 40, 106-107 (2004).
[CrossRef]

Ng, M. N.

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

Nielsen, K.

Nielsen, L. B.

Noordegraaf, D.

Owens, J. C.

Pedersen, L. H.

Peng, W.

J. Xu, G. Pickrell, X. Wang, W. Peng, K. Cooper, and A. Wang, “A novel temperature-insensitive optical fiber pressure sensor for harsh environments,” IEEE Photon. Technol. Lett. 17, 870-872 (2005).
[CrossRef]

Pickrell, G.

J. Xu, G. Pickrell, X. Wang, W. Peng, K. Cooper, and A. Wang, “A novel temperature-insensitive optical fiber pressure sensor for harsh environments,” IEEE Photon. Technol. Lett. 17, 870-872 (2005).
[CrossRef]

Rao, M. K.

Rao, Y. J.

Y. J. Rao, M. Deng, D. W. Duan, and T. Zhu, “In-line fiber Fabry-Perot refractive-index tip sensor based on endlessly photonic crystal fiber,” Sens. Actuators A, Phys. 148, 33-38(2008).
[CrossRef]

Y. J. Rao, “Recent progress in fiber-optic extrinsic Fabry-Perot interferometric sensors,” Opt. Fiber Technol. 12, 227-237(2006).
[CrossRef]

T. Zhu, Y. J. Rao, and Q. J. Mo, “Simultaneous measurement of refractive index and temperature using a single ultralong-period fiber grating,” IEEE Photon. Technol. Lett. 17, 744(2005).
[CrossRef]

Riishede, J.

Shao, L. Y.

L. Y. Shao, A. P. Zhang, W. S. Liu, H. Y. Fu, and S. He, “Optical refractive-index sensor based on dual fiber-Bragg gratings interposed with a multimode-fiber taper,” IEEE Photon. Technol. Lett. 19, 30-32 (2007).
[CrossRef]

Shih, H. C.

J. Y. Lee, H. C. Shih, C. T. Hong, and T. K. Chou, “Measurement of refractive index change by surface plasmon resonance and phase quadrature interferometry,” Opt. Commun. 276, 283-287 (2007).
[CrossRef]

Skivesen, N.

Sun, F. G.

G. Z. Xiao, A. Adnet, Z. Y. Zhang, F. G. Sun, and C. P. Grover, “Monitoring changes in the refractive index of gases by means of a fiber optic Fabry-Perot interferometer,” Sens. Actuators A, Phys. 118, 177-182 (2005).
[CrossRef]

Sun, T.

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

Talavera, D.

J. Villatoro, D. Monzon-Hernandez, and D. Talavera, “High resolution refractive index sensing with cladding multimode tapered fiber,” Electron. Lett. 40, 106-107 (2004).
[CrossRef]

J. Villatoro, D. Monzon-Hernandez, and D. Talavera, “High resolution refractive index sensing with cladded multimode tapered optical fibre,” Electron. Lett. 40, 106-107 (2004).
[CrossRef]

Tetu, A.

Tsai, H. L.

Villatoro, J.

J. Villatoro, D. Monzon-Hernandez, and D. Talavera, “High resolution refractive index sensing with cladding multimode tapered fiber,” Electron. Lett. 40, 106-107 (2004).
[CrossRef]

J. Villatoro, D. Monzon-Hernandez, and D. Talavera, “High resolution refractive index sensing with cladded multimode tapered optical fibre,” Electron. Lett. 40, 106-107 (2004).
[CrossRef]

Wang, A.

J. Xu, G. Pickrell, X. Wang, W. Peng, K. Cooper, and A. Wang, “A novel temperature-insensitive optical fiber pressure sensor for harsh environments,” IEEE Photon. Technol. Lett. 17, 870-872 (2005).
[CrossRef]

Wang, X.

J. Xu, G. Pickrell, X. Wang, W. Peng, K. Cooper, and A. Wang, “A novel temperature-insensitive optical fiber pressure sensor for harsh environments,” IEEE Photon. Technol. Lett. 17, 870-872 (2005).
[CrossRef]

Wei, T.

Xiao, G. Z.

G. Z. Xiao, A. Adnet, Z. Y. Zhang, F. G. Sun, and C. P. Grover, “Monitoring changes in the refractive index of gases by means of a fiber optic Fabry-Perot interferometer,” Sens. Actuators A, Phys. 118, 177-182 (2005).
[CrossRef]

Xiao, H.

Xiao, L.

Xu, J.

J. Xu, G. Pickrell, X. Wang, W. Peng, K. Cooper, and A. Wang, “A novel temperature-insensitive optical fiber pressure sensor for harsh environments,” IEEE Photon. Technol. Lett. 17, 870-872 (2005).
[CrossRef]

Zhang, A. P.

L. Y. Shao, A. P. Zhang, W. S. Liu, H. Y. Fu, and S. He, “Optical refractive-index sensor based on dual fiber-Bragg gratings interposed with a multimode-fiber taper,” IEEE Photon. Technol. Lett. 19, 30-32 (2007).
[CrossRef]

Zhang, Z. Y.

G. Z. Xiao, A. Adnet, Z. Y. Zhang, F. G. Sun, and C. P. Grover, “Monitoring changes in the refractive index of gases by means of a fiber optic Fabry-Perot interferometer,” Sens. Actuators A, Phys. 118, 177-182 (2005).
[CrossRef]

Zhao, C. L.

Zhu, T.

Y. J. Rao, M. Deng, D. W. Duan, and T. Zhu, “In-line fiber Fabry-Perot refractive-index tip sensor based on endlessly photonic crystal fiber,” Sens. Actuators A, Phys. 148, 33-38(2008).
[CrossRef]

T. Zhu, Y. J. Rao, and Q. J. Mo, “Simultaneous measurement of refractive index and temperature using a single ultralong-period fiber grating,” IEEE Photon. Technol. Lett. 17, 744(2005).
[CrossRef]

Appl. Opt.

Electron. Lett.

J. Villatoro, D. Monzon-Hernandez, and D. Talavera, “High resolution refractive index sensing with cladded multimode tapered optical fibre,” Electron. Lett. 40, 106-107 (2004).
[CrossRef]

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

J. Villatoro, D. Monzon-Hernandez, and D. Talavera, “High resolution refractive index sensing with cladding multimode tapered fiber,” Electron. Lett. 40, 106-107 (2004).
[CrossRef]

IEEE Photon. Technol. Lett.

K. Q. Kieu and M. Mansuripur, “Biconical fiber taper sensors,” IEEE Photon. Technol. Lett. 18, 2239-2241 (2006).
[CrossRef]

T. Zhu, Y. J. Rao, and Q. J. Mo, “Simultaneous measurement of refractive index and temperature using a single ultralong-period fiber grating,” IEEE Photon. Technol. Lett. 17, 744(2005).
[CrossRef]

K. Q. Kieu and M. Mansuripur, “Biconical fiber taper sensors,” IEEE Photon. Technol. Lett. 18, 2239-2241 (2006).
[CrossRef]

J. Xu, G. Pickrell, X. Wang, W. Peng, K. Cooper, and A. Wang, “A novel temperature-insensitive optical fiber pressure sensor for harsh environments,” IEEE Photon. Technol. Lett. 17, 870-872 (2005).
[CrossRef]

L. Y. Shao, A. P. Zhang, W. S. Liu, H. Y. Fu, and S. He, “Optical refractive-index sensor based on dual fiber-Bragg gratings interposed with a multimode-fiber taper,” IEEE Photon. Technol. Lett. 19, 30-32 (2007).
[CrossRef]

IEEE Trans. Ultrason. Ferroelect. Freq. Contr.

P. A. Fomitchov, A. K. Kromine, S. Krishnaswamy, and J. D. Achenbach, “Sagnac-type fiber-optic array sensor for detection of bulk ultrasonic waves,” IEEE Trans. Ultrason. Ferroelect. Freq. Contr. 47, 584-590 (2000).
[CrossRef]

J. Lightwave Technol.

Meas. Sci. Technol.

G. Laffout and P. Ferdinand, “Tilted short-period fibre-Bragg-grating-induced coupling to cladding modes for accurate refractometry,” Meas. Sci. Technol. 12, 765-770 (2001).
[CrossRef]

Metrologia

K. P. Buch and M. J. Downs, “An updated Edlen equation for the refractive index of air,” Metrologia 30, 155-162 (1993).
[CrossRef]

Opt. Commun.

J. Y. Lee, H. C. Shih, C. T. Hong, and T. K. Chou, “Measurement of refractive index change by surface plasmon resonance and phase quadrature interferometry,” Opt. Commun. 276, 283-287 (2007).
[CrossRef]

Opt. Express

Opt. Fiber Technol.

Y. J. Rao, “Recent progress in fiber-optic extrinsic Fabry-Perot interferometric sensors,” Opt. Fiber Technol. 12, 227-237(2006).
[CrossRef]

Opt. Lett.

Sens. Actuators A, Phys.

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

Y. J. Rao, M. Deng, D. W. Duan, and T. Zhu, “In-line fiber Fabry-Perot refractive-index tip sensor based on endlessly photonic crystal fiber,” Sens. Actuators A, Phys. 148, 33-38(2008).
[CrossRef]

G. Z. Xiao, A. Adnet, Z. Y. Zhang, F. G. Sun, and C. P. Grover, “Monitoring changes in the refractive index of gases by means of a fiber optic Fabry-Perot interferometer,” Sens. Actuators A, Phys. 118, 177-182 (2005).
[CrossRef]

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Figures (8)

Fig. 1
Fig. 1

Schematic diagram of the novel FP refractometer.

Fig. 2
Fig. 2

Structure of the PCF.

Fig. 3
Fig. 3

Microscopic optical image of the fabricated FPI sensor: (a) with collapsed air holes and (b) without collapsed air holes.

Fig. 4
Fig. 4

(a) Interference spectrum of the FPI sensor in air. (b) Close-up display of the interference fringe within 10 nm .

Fig. 5
Fig. 5

Experimental setup for RI measurement.

Fig. 6
Fig. 6

Drift of the interference spectra of an FPI sensor as a function of RI changes.

Fig. 7
Fig. 7

RI versus optical path distance for the FP refractometer.

Fig. 8
Fig. 8

Drift of the interference spectra of an FPI sensor with the increment of CO 2 gas concentration.

Equations (5)

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I Rtotal ( λ ) = | E r E 0 | 2 = R 1 + ( 1 α 1 ) 2 ( 1 R 1 ) 2 R 2 + ( 1 α 1 ) 2 ( 1 α 2 ) 2 ( 1 R 1 ) 2 ( 1 R 2 ) 2 R 3 + 2 R 1 R 3 ( 1 α 1 ) ( 1 α 2 ) ( 1 R 1 ) ( 1 R 2 ) cos [ 2 ( Φ 1 + Φ 2 ) ] + 2 R 2 R 3 ( 1 α 1 ) 2 ( 1 α 2 ) ( 1 R 1 ) 2 ( 1 R 2 ) cos ( 2 Φ 2 ) + 2 R 1 R 2 ( 1 α 1 ) ( 1 R 1 ) cos ( 2 Φ 1 ) ,
Φ 1 = 4 π n HF L 1 λ , Φ 2 = 4 π n PCF L 2 λ ,
L · n = k 2 N δ ν k = 0 , 1 , 2 , N 1 ,
Δ n = Δ λ m λ m 0 n 0 ,
n = 1 + 2.8793 × 10 9 × P / ( 1 + 0.003671 × t ) ,

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