Abstract

A novel parallel structured fiber-optic Fabry-Perot interferometer (FPI) based on Vernier-effect is theoretically proposed and experimentally demonstrated for ultrasensitive strain measurement. This proposed sensor consists of open-cavity and closed-cavity fiber-optic FPI, both of which are connected in parallel via a 3 dB coupler. The open-cavity is implemented for sensing, while the closed-cavity for reference. Experimental results show that the proposed parallel structured fiber-optic FPI can provide an ultra-high strain sensitivity of −43.2 pm/με, which is 4.6 times higher than that of a single open-cavity FPI. Furthermore, the sensor is simple in fabrication, robust in structure, and stable in measurement. Finally, the parallel structured fiber-optic FPI scheme proposed in this paper can also be applied to other sensing field, and provide a new perspective idea for high sensitivity sensing.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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2018 (2)

J. Xu, J. He, W. Huang, X. Xu, K. Guo, Z. Zhang, and Y. Wang, “Suppression of parasitic interference in a fiber-tip Fabry-Perot interferometer for high-pressure measurements,” Opt. Express 26(22), 28178–28186 (2018).
[Crossref] [PubMed]

Y. Liu and D. Wang, “Fiber in-line Fabry-Perot interferometer with offset splicing for strain measurement with enhanced sensitivity,” IEEE Photonics J. 10(1), 1–8 (2018).
[Crossref]

2017 (4)

2016 (1)

2015 (4)

W. Ding, Y. Jiang, R. Gao, and Y. Liu, “High-temperature fiber-optic Fabry-Perot interferometric sensors,” Rev. Sci. Instrum. 86(5), 055001 (2015).
[Crossref] [PubMed]

S. Liu, K. Yang, Y. Wang, J. Qu, C. Liao, J. He, Z. Li, G. Yin, B. Sun, J. Zhou, G. Wang, J. Tang, and J. Zhao, “High-sensitivity strain sensor based on in-fiber rectangular air bubble,” Sci. Rep. 5(1), 7624 (2015).
[Crossref] [PubMed]

P. Zhang, M. Tang, F. Gao, B. Zhu, Z. Zhao, L. Duan, S. Fu, J. Ouyang, H. Wei, P. Shum, and D. Liu, “Simplified hollow-core fiber-based Fabry-Perot interferometer with modified Vernier Effect for highly sensitive high-temperature measurement,” IEEE Photonics J. 7(1), 1 (2015).
[Crossref]

M. Quan, J. Tian, and Y. Yao, “Ultra-high sensitivity Fabry-Perot interferometer gas refractive index fiber sensor based on photonic crystal fiber and Vernier effect,” Opt. Lett. 40(21), 4891–4894 (2015).
[Crossref] [PubMed]

2014 (6)

2013 (1)

M. La Notte and V. M. N. Passaro, “Ultrahigh sensitivity chemical photonic sensing by Mach-Zehnder interferometer enhanced Vernier-effect,” Sens. Actuators B Chem. 176, 994–1007 (2013).
[Crossref]

2012 (3)

2010 (1)

2007 (1)

Araujo, L.

Avino, S.

Bienstman, P.

Bogaerts, W.

Bouwmans, G.

Braga, A. M.

Bruno, A. C.

Campanella, C. E.

Carvalho, I. C.

Chen, H. F.

W. P. Chen, D. N. Wang, B. Xu, C. L. Zhao, and H. F. Chen, “Multimode fiber tip Fabry-Perot cavity for highly sensitive pressure measurement,” Sci. Rep. 7(1), 368 (2017).
[Crossref] [PubMed]

Chen, W. P.

W. P. Chen, D. N. Wang, B. Xu, C. L. Zhao, and H. F. Chen, “Multimode fiber tip Fabry-Perot cavity for highly sensitive pressure measurement,” Sci. Rep. 7(1), 368 (2017).
[Crossref] [PubMed]

Cheng, G. H.

Claes, T.

Costa, G. K.

Deng, M.

Ding, W.

W. Ding, Y. Jiang, R. Gao, and Y. Liu, “High-temperature fiber-optic Fabry-Perot interferometric sensors,” Rev. Sci. Instrum. 86(5), 055001 (2015).
[Crossref] [PubMed]

Donlagic, D.

Duan, D. W.

Duan, L.

P. Zhang, M. Tang, F. Gao, B. Zhu, Z. Zhao, L. Duan, S. Fu, J. Ouyang, H. Wei, P. Shum, and D. Liu, “Simplified hollow-core fiber-based Fabry-Perot interferometer with modified Vernier Effect for highly sensitive high-temperature measurement,” IEEE Photonics J. 7(1), 1 (2015).
[Crossref]

Favero, F.

Favero, F. C.

Finazzi, V.

Fu, S.

P. Zhang, M. Tang, F. Gao, B. Zhu, Z. Zhao, L. Duan, S. Fu, J. Ouyang, H. Wei, P. Shum, and D. Liu, “Simplified hollow-core fiber-based Fabry-Perot interferometer with modified Vernier Effect for highly sensitive high-temperature measurement,” IEEE Photonics J. 7(1), 1 (2015).
[Crossref]

Fu, X.

Gagliardi, G.

Gao, F.

P. Zhang, M. Tang, F. Gao, B. Zhu, Z. Zhao, L. Duan, S. Fu, J. Ouyang, H. Wei, P. Shum, and D. Liu, “Simplified hollow-core fiber-based Fabry-Perot interferometer with modified Vernier Effect for highly sensitive high-temperature measurement,” IEEE Photonics J. 7(1), 1 (2015).
[Crossref]

Gao, R.

W. Ding, Y. Jiang, R. Gao, and Y. Liu, “High-temperature fiber-optic Fabry-Perot interferometric sensors,” Rev. Sci. Instrum. 86(5), 055001 (2015).
[Crossref] [PubMed]

Gao, W.

Giorgini, A.

Gouvêa, P. M.

Guan, B. O.

Guo, K.

He, J.

J. Xu, J. He, W. Huang, X. Xu, K. Guo, Z. Zhang, and Y. Wang, “Suppression of parasitic interference in a fiber-tip Fabry-Perot interferometer for high-pressure measurements,” Opt. Express 26(22), 28178–28186 (2018).
[Crossref] [PubMed]

S. Liu, K. Yang, Y. Wang, J. Qu, C. Liao, J. He, Z. Li, G. Yin, B. Sun, J. Zhou, G. Wang, J. Tang, and J. Zhao, “High-sensitivity strain sensor based on in-fiber rectangular air bubble,” Sci. Rep. 5(1), 7624 (2015).
[Crossref] [PubMed]

He, X.

Hou, Y. S.

Hu, T. Y.

Huang, W.

Jiang, J.

Jiang, X.

Jiang, Y.

W. Ding, Y. Jiang, R. Gao, and Y. Liu, “High-temperature fiber-optic Fabry-Perot interferometric sensors,” Rev. Sci. Instrum. 86(5), 055001 (2015).
[Crossref] [PubMed]

La Notte, M.

M. La Notte and V. M. N. Passaro, “Ultrahigh sensitivity chemical photonic sensing by Mach-Zehnder interferometer enhanced Vernier-effect,” Sens. Actuators B Chem. 176, 994–1007 (2013).
[Crossref]

Li, L.

Li, Z.

Liao, C.

Liao, C. R.

Liao, H.

Liu, D.

H. Liao, P. Lu, X. Fu, X. Jiang, W. Ni, D. Liu, and J. Zhang, “Sensitivity amplification of fiber-optic in-line Mach-Zehnder Interferometer sensors with modified Vernier-effect,” Opt. Express 25(22), 26898–26909 (2017).
[Crossref] [PubMed]

P. Zhang, M. Tang, F. Gao, B. Zhu, Z. Zhao, L. Duan, S. Fu, J. Ouyang, H. Wei, P. Shum, and D. Liu, “Simplified hollow-core fiber-based Fabry-Perot interferometer with modified Vernier Effect for highly sensitive high-temperature measurement,” IEEE Photonics J. 7(1), 1 (2015).
[Crossref]

Liu, S.

Liu, Y.

Y. Liu and D. Wang, “Fiber in-line Fabry-Perot interferometer with offset splicing for strain measurement with enhanced sensitivity,” IEEE Photonics J. 10(1), 1–8 (2018).
[Crossref]

W. Ding, Y. Jiang, R. Gao, and Y. Liu, “High-temperature fiber-optic Fabry-Perot interferometric sensors,” Rev. Sci. Instrum. 86(5), 055001 (2015).
[Crossref] [PubMed]

Liu, Z.

Lu, P.

Malara, P.

Mastronardi, L.

Ni, W.

Ouyang, J.

P. Zhang, M. Tang, F. Gao, B. Zhu, Z. Zhao, L. Duan, S. Fu, J. Ouyang, H. Wei, P. Shum, and D. Liu, “Simplified hollow-core fiber-based Fabry-Perot interferometer with modified Vernier Effect for highly sensitive high-temperature measurement,” IEEE Photonics J. 7(1), 1 (2015).
[Crossref]

Palffy-Muhoray, P.

Passaro, V. M. N.

P. Malara, L. Mastronardi, C. E. Campanella, A. Giorgini, S. Avino, V. M. N. Passaro, and G. Gagliardi, “Split-mode fiber Bragg grating sensor for high-resolution static strain measurements,” Opt. Lett. 39(24), 6899–6902 (2014).
[Crossref] [PubMed]

M. La Notte and V. M. N. Passaro, “Ultrahigh sensitivity chemical photonic sensing by Mach-Zehnder interferometer enhanced Vernier-effect,” Sens. Actuators B Chem. 176, 994–1007 (2013).
[Crossref]

Pereira, J. M.

Pevec, S.

Pruneri, V.

Qin, B.

Qu, J.

S. Liu, K. Yang, Y. Wang, J. Qu, C. Liao, J. He, Z. Li, G. Yin, B. Sun, J. Zhou, G. Wang, J. Tang, and J. Zhao, “High-sensitivity strain sensor based on in-fiber rectangular air bubble,” Sci. Rep. 5(1), 7624 (2015).
[Crossref] [PubMed]

Quan, M.

Rao, Y. J.

Shum, P.

P. Zhang, M. Tang, F. Gao, B. Zhu, Z. Zhao, L. Duan, S. Fu, J. Ouyang, H. Wei, P. Shum, and D. Liu, “Simplified hollow-core fiber-based Fabry-Perot interferometer with modified Vernier Effect for highly sensitive high-temperature measurement,” IEEE Photonics J. 7(1), 1 (2015).
[Crossref]

Soares, L. M.

Sun, B.

S. Liu, K. Yang, Y. Wang, J. Qu, C. Liao, J. He, Z. Li, G. Yin, B. Sun, J. Zhou, G. Wang, J. Tang, and J. Zhao, “High-sensitivity strain sensor based on in-fiber rectangular air bubble,” Sci. Rep. 5(1), 7624 (2015).
[Crossref] [PubMed]

Tam, H. Y.

Tang, J.

S. Liu, K. Yang, Y. Wang, J. Qu, C. Liao, J. He, Z. Li, G. Yin, B. Sun, J. Zhou, G. Wang, J. Tang, and J. Zhao, “High-sensitivity strain sensor based on in-fiber rectangular air bubble,” Sci. Rep. 5(1), 7624 (2015).
[Crossref] [PubMed]

S. Liu, Y. Wang, C. Liao, G. Wang, Z. Li, Q. Wang, J. Zhou, K. Yang, X. Zhong, J. Zhao, and J. Tang, “High-sensitivity strain sensor based on in-fiber improved Fabry-Perot interferometer,” Opt. Lett. 39(7), 2121–2124 (2014).
[Crossref] [PubMed]

Tang, M.

P. Zhang, M. Tang, F. Gao, B. Zhu, Z. Zhao, L. Duan, S. Fu, J. Ouyang, H. Wei, P. Shum, and D. Liu, “Simplified hollow-core fiber-based Fabry-Perot interferometer with modified Vernier Effect for highly sensitive high-temperature measurement,” IEEE Photonics J. 7(1), 1 (2015).
[Crossref]

Tian, J.

Villatoro, J.

Wang, C.

Wang, D.

Y. Liu and D. Wang, “Fiber in-line Fabry-Perot interferometer with offset splicing for strain measurement with enhanced sensitivity,” IEEE Photonics J. 10(1), 1–8 (2018).
[Crossref]

Wang, D. N.

Wang, G.

S. Liu, K. Yang, Y. Wang, J. Qu, C. Liao, J. He, Z. Li, G. Yin, B. Sun, J. Zhou, G. Wang, J. Tang, and J. Zhao, “High-sensitivity strain sensor based on in-fiber rectangular air bubble,” Sci. Rep. 5(1), 7624 (2015).
[Crossref] [PubMed]

S. Liu, Y. Wang, C. Liao, G. Wang, Z. Li, Q. Wang, J. Zhou, K. Yang, X. Zhong, J. Zhao, and J. Tang, “High-sensitivity strain sensor based on in-fiber improved Fabry-Perot interferometer,” Opt. Lett. 39(7), 2121–2124 (2014).
[Crossref] [PubMed]

Wang, Q.

Wang, Y.

Wei, H.

P. Zhang, M. Tang, F. Gao, B. Zhu, Z. Zhao, L. Duan, S. Fu, J. Ouyang, H. Wei, P. Shum, and D. Liu, “Simplified hollow-core fiber-based Fabry-Perot interferometer with modified Vernier Effect for highly sensitive high-temperature measurement,” IEEE Photonics J. 7(1), 1 (2015).
[Crossref]

Wu, C.

Wu, J.

Wu, Y.

Xu, B.

W. P. Chen, D. N. Wang, B. Xu, C. L. Zhao, and H. F. Chen, “Multimode fiber tip Fabry-Perot cavity for highly sensitive pressure measurement,” Sci. Rep. 7(1), 368 (2017).
[Crossref] [PubMed]

Xu, J.

Xu, L.

Xu, X.

Yang, J.

Yang, K.

S. Liu, K. Yang, Y. Wang, J. Qu, C. Liao, J. He, Z. Li, G. Yin, B. Sun, J. Zhou, G. Wang, J. Tang, and J. Zhao, “High-sensitivity strain sensor based on in-fiber rectangular air bubble,” Sci. Rep. 5(1), 7624 (2015).
[Crossref] [PubMed]

S. Liu, Y. Wang, C. Liao, G. Wang, Z. Li, Q. Wang, J. Zhou, K. Yang, X. Zhong, J. Zhao, and J. Tang, “High-sensitivity strain sensor based on in-fiber improved Fabry-Perot interferometer,” Opt. Lett. 39(7), 2121–2124 (2014).
[Crossref] [PubMed]

Yang, W.

Yang, X. C.

Yang, Y.

Yao, Y.

Yin, G.

S. Liu, K. Yang, Y. Wang, J. Qu, C. Liao, J. He, Z. Li, G. Yin, B. Sun, J. Zhou, G. Wang, J. Tang, and J. Zhao, “High-sensitivity strain sensor based on in-fiber rectangular air bubble,” Sci. Rep. 5(1), 7624 (2015).
[Crossref] [PubMed]

Yuan, L.

Yuan, P.

Zhang, A. P.

Zhang, J.

Zhang, P.

P. Zhang, M. Tang, F. Gao, B. Zhu, Z. Zhao, L. Duan, S. Fu, J. Ouyang, H. Wei, P. Shum, and D. Liu, “Simplified hollow-core fiber-based Fabry-Perot interferometer with modified Vernier Effect for highly sensitive high-temperature measurement,” IEEE Photonics J. 7(1), 1 (2015).
[Crossref]

Zhang, Y.

Zhang, Z.

Zhao, C. L.

W. P. Chen, D. N. Wang, B. Xu, C. L. Zhao, and H. F. Chen, “Multimode fiber tip Fabry-Perot cavity for highly sensitive pressure measurement,” Sci. Rep. 7(1), 368 (2017).
[Crossref] [PubMed]

Zhao, J.

S. Liu, K. Yang, Y. Wang, J. Qu, C. Liao, J. He, Z. Li, G. Yin, B. Sun, J. Zhou, G. Wang, J. Tang, and J. Zhao, “High-sensitivity strain sensor based on in-fiber rectangular air bubble,” Sci. Rep. 5(1), 7624 (2015).
[Crossref] [PubMed]

S. Liu, Y. Wang, C. Liao, G. Wang, Z. Li, Q. Wang, J. Zhou, K. Yang, X. Zhong, J. Zhao, and J. Tang, “High-sensitivity strain sensor based on in-fiber improved Fabry-Perot interferometer,” Opt. Lett. 39(7), 2121–2124 (2014).
[Crossref] [PubMed]

Zhao, Y.

Zhao, Z.

P. Zhang, M. Tang, F. Gao, B. Zhu, Z. Zhao, L. Duan, S. Fu, J. Ouyang, H. Wei, P. Shum, and D. Liu, “Simplified hollow-core fiber-based Fabry-Perot interferometer with modified Vernier Effect for highly sensitive high-temperature measurement,” IEEE Photonics J. 7(1), 1 (2015).
[Crossref]

Zhong, X.

Zhou, A.

Zhou, J.

S. Liu, K. Yang, Y. Wang, J. Qu, C. Liao, J. He, Z. Li, G. Yin, B. Sun, J. Zhou, G. Wang, J. Tang, and J. Zhao, “High-sensitivity strain sensor based on in-fiber rectangular air bubble,” Sci. Rep. 5(1), 7624 (2015).
[Crossref] [PubMed]

S. Liu, Y. Wang, C. Liao, G. Wang, Z. Li, Q. Wang, J. Zhou, K. Yang, X. Zhong, J. Zhao, and J. Tang, “High-sensitivity strain sensor based on in-fiber improved Fabry-Perot interferometer,” Opt. Lett. 39(7), 2121–2124 (2014).
[Crossref] [PubMed]

Zhu, B.

P. Zhang, M. Tang, F. Gao, B. Zhu, Z. Zhao, L. Duan, S. Fu, J. Ouyang, H. Wei, P. Shum, and D. Liu, “Simplified hollow-core fiber-based Fabry-Perot interferometer with modified Vernier Effect for highly sensitive high-temperature measurement,” IEEE Photonics J. 7(1), 1 (2015).
[Crossref]

Zhu, T.

Zhu, Z.

Appl. Opt. (1)

IEEE Photonics J. (2)

P. Zhang, M. Tang, F. Gao, B. Zhu, Z. Zhao, L. Duan, S. Fu, J. Ouyang, H. Wei, P. Shum, and D. Liu, “Simplified hollow-core fiber-based Fabry-Perot interferometer with modified Vernier Effect for highly sensitive high-temperature measurement,” IEEE Photonics J. 7(1), 1 (2015).
[Crossref]

Y. Liu and D. Wang, “Fiber in-line Fabry-Perot interferometer with offset splicing for strain measurement with enhanced sensitivity,” IEEE Photonics J. 10(1), 1–8 (2018).
[Crossref]

J. Lightwave Technol. (1)

Opt. Express (9)

Y. J. Rao, M. Deng, D. W. Duan, X. C. Yang, T. Zhu, and G. H. Cheng, “Micro Fabry-Perot interferometers in silica fibers machined by femtosecond laser,” Opt. Express 15(21), 14123–14128 (2007).
[Crossref] [PubMed]

F. C. Favero, L. Araujo, G. Bouwmans, V. Finazzi, J. Villatoro, and V. Pruneri, “Spheroidal Fabry-Perot microcavities in optical fibers for high-sensitivity sensing,” Opt. Express 20(7), 7112–7118 (2012).
[Crossref] [PubMed]

J. Xu, J. He, W. Huang, X. Xu, K. Guo, Z. Zhang, and Y. Wang, “Suppression of parasitic interference in a fiber-tip Fabry-Perot interferometer for high-pressure measurements,” Opt. Express 26(22), 28178–28186 (2018).
[Crossref] [PubMed]

C. R. Liao, T. Y. Hu, and D. N. Wang, “Optical fiber Fabry-Perot interferometer cavity fabricated by femtosecond laser micromachining and fusion splicing for refractive index sensing,” Opt. Express 20(20), 22813–22818 (2012).
[Crossref] [PubMed]

C. Wu, Z. Liu, A. P. Zhang, B. O. Guan, and H. Y. Tam, “In-line open-cavity Fabry-Pérot interferometer formed by C-shaped fiber fortemperature-insensitive refractive index sensing,” Opt. Express 22(18), 21757–21766 (2014).
[Crossref] [PubMed]

G. K. Costa, P. M. Gouvêa, L. M. Soares, J. M. Pereira, F. Favero, A. M. Braga, P. Palffy-Muhoray, A. C. Bruno, and I. C. Carvalho, “In-fiber Fabry-Perot interferometer for strain and magnetic field sensing,” Opt. Express 24(13), 14690–14696 (2016).
[Crossref] [PubMed]

H. Liao, P. Lu, X. Fu, X. Jiang, W. Ni, D. Liu, and J. Zhang, “Sensitivity amplification of fiber-optic in-line Mach-Zehnder Interferometer sensors with modified Vernier-effect,” Opt. Express 25(22), 26898–26909 (2017).
[Crossref] [PubMed]

T. Claes, W. Bogaerts, and P. Bienstman, “Experimental characterization of a silicon photonic biosensor consisting of two cascaded ring resonators based on the Vernier-effect and introduction of a curve fitting method for an improved detection limit,” Opt. Express 18(22), 22747–22761 (2010).
[Crossref] [PubMed]

Y. Yang, Y. Wang, Y. Zhao, J. Jiang, X. He, W. Yang, Z. Zhu, W. Gao, and L. Li, “Sensitivity-enhanced temperature sensor by hybrid cascaded configuration of a Sagnac loop and a F-P cavity,” Opt. Express 25(26), 33290–33296 (2017).
[Crossref]

Opt. Lett. (6)

Rev. Sci. Instrum. (1)

W. Ding, Y. Jiang, R. Gao, and Y. Liu, “High-temperature fiber-optic Fabry-Perot interferometric sensors,” Rev. Sci. Instrum. 86(5), 055001 (2015).
[Crossref] [PubMed]

Sci. Rep. (2)

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[Crossref] [PubMed]

S. Liu, K. Yang, Y. Wang, J. Qu, C. Liao, J. He, Z. Li, G. Yin, B. Sun, J. Zhou, G. Wang, J. Tang, and J. Zhao, “High-sensitivity strain sensor based on in-fiber rectangular air bubble,” Sci. Rep. 5(1), 7624 (2015).
[Crossref] [PubMed]

Sens. Actuators B Chem. (1)

M. La Notte and V. M. N. Passaro, “Ultrahigh sensitivity chemical photonic sensing by Mach-Zehnder interferometer enhanced Vernier-effect,” Sens. Actuators B Chem. 176, 994–1007 (2013).
[Crossref]

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Figures (13)

Fig. 1
Fig. 1 (a)-(c) The fabrication process of open-cavity FPI; (d)-(f) the fabrication process of closed-cavity FPI.
Fig. 2
Fig. 2 Schematic diagram of the sensor based on parallel configuration of two FPIs.
Fig. 3
Fig. 3 Simulation results of the spectrum of (a) single open-cavity FPI and (b) single closed-cavity FPI and (c) parallel open-cavity FPI and closed-cavity FPI.
Fig. 4
Fig. 4 Simulation results of the spectrum of (a) single open-cavity FPI and (b) single closed-cavity FPI and (c) parallel open-cavity FPI and closed-cavity FPI.
Fig. 5
Fig. 5 Spectra of (a) single open-cavity FPI and (b) single closed-cavity FPI and (c) parallel open-cavity FPI and closed-cavity FPI.
Fig. 6
Fig. 6 The microscope image of (a) the open-cavity FPI and (b) the closed-cavity FPI.
Fig. 7
Fig. 7 The schematic of the open-cavity FPI packaging to the inside of the SiO2 micro-tube
Fig. 8
Fig. 8 Experiment setup of the strain sensing system based on parallel FPIs.
Fig. 9
Fig. 9 (a) and (b) Reflection spectrum evolution of the open-cavity FPI while the strain increases from 0 to 1750 με; (c) Strain response of the open-cavity FPI.
Fig. 10
Fig. 10 (a) and (b) Reflection spectrum evolution of the parallel open-cavity FPI and closed-cavity FPI while the strain increases from 0 to 1750 με; (c) Strain response of the parallel open-cavity FPI and closed-cavity FPI.
Fig. 11
Fig. 11 Experiment setup of the temperature sensing system based on parallel FPIs.
Fig. 12
Fig. 12 (a) Reflection spectrum evolution of the open-cavity FPI while the temperature increases from 30 ° C to 100 ° C ; (b) Temperature response of the open-cavity FPI.
Fig. 13
Fig. 13 (a) Reflection spectrum evolution of the parallel open-cavity FPI and closed-cavity FPI while the temperature increases from 30 ° C to 100 ° C ; (b) Temperature response of the parallel open-cavity FPI and closed-cavity FPI.

Equations (11)

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I = I 1 + I 2 + 2 I 1 I 2 cos ( 4 π n L λ + ϕ 0 )
4 π n L λ m + ϕ 0 = ( 2 m + 1 ) π
λ d i p = 4 n L 2 m + 1
F S R S = λ d i p ( m 1 ) λ d i p ( m ) λ 2 2 n L 1
F S R R = λ d i p ( m 1 ) λ d i p ( m ) λ 2 2 n L 2
I S = I S 1 + I S 2 + 2 I S 1 I S 2 cos ϕ 1 I R = I R 1 + I R 2 + 2 I R 1 I R 2 cos ϕ 2
I = I R + I S A + B cos ϕ 2 + ϕ 1 2 cos ϕ 2 ϕ 1 2
a = 10 lg ( I S I 0 ) b = 10 lg ( I R I 0 ) c = 10 lg ( I S + I R I 0 ) = 10 lg ( I I 0 )
R = ( n 2 n 1 n 2 + n 1 ) 2
F S R e n v e l o p e = F S R S F S R R | F S R S F S R R |
M = F S R S | F S R S F S R R |

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