Abstract

We study photothermal phase modulation in gas-filled hollow-core optical fibers with differential structural dimensions and attempt to develop highly sensitive practical gas sensors with an in-line Fabry-Perot interferometer for detection of the phase modulation. Analytical formulations based on a hollow-capillary model are developed to estimate the amplitude of photothermal phase modulation at low modulation frequencies as well as the -3 dB roll-off frequency, which provide a guide for the selection of hollow-core fibers and the pump modulation frequencies to maximize photothermal phase modulation. Numerical simulation with the capillary model and experiments with two types of hollow-core fibers support the analytical formulations. Further experiments with an Fabry-Perot interferometer made of 5.5-cm-long anti-resonant hollow-core fiber demonstrated ultra-sensitive gas detection with a noise-equivalent-absorption coefficient of 2.3×10−9 cm-1, unprecedented dynamic range of 4.3×106 and <2.5% instability over a period of 24 hours.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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  1. S. E. Bialkowski, Photothermal Spectroscopy Methods for Chemical Analysis, vol. 177. John Wiley & Sons, 1996.
  2. W. Jin, Y. Cao, F. Yang, and H. L. Ho, “Ultra-sensitive all-fibre photothermal spectroscopy with large dynamic range,” Nat. Commun. 6(1), 6767 (2015).
    [Crossref]
  3. B. Culshaw, G. Stewart, F. Dong, C. Tandy, and D. Moodie, “Fibre optic techniques for remote spectroscopic methane detection—from concept to system realisation,” Sens. Actuators, B 51(1-3), 25–37 (1998).
    [Crossref]
  4. C. Yao, Q. Wang, Y. Lin, W. Jin, L. Xiao, S. Gao, Y. Wang, P. Wang, and W. Ren, “Photothermal CO detection in a hollow-core negative curvature fiber,” Opt. Lett. 44(16), 4048–4051 (2019).
    [Crossref]
  5. Y. Lin, W. Jin, F. Yang, Y. Tan, and H. L. Ho, “Performance optimization of hollow-core fiber photothermal gas sensors,” Opt. Lett. 42(22), 4712–4715 (2017).
    [Crossref]
  6. Y. Lin, Wei Jin, Fan Yang, Jun Ma, Chao Wang, Hoi Lut Ho, and Yang Liu, “Pulsed photothermal interferometry for spectroscopic gas detection with hollow-core optical fibre,” Sci. Rep. 6(1), 1–12 (2016).
    [Crossref]
  7. F. Yang, Y. Tan, W. Jin, Y. Lin, Y. Qi, and H. L. Ho, “Hollow-core fiber Fabry–Perot photothermal gas sensor,” Opt. Lett. 41(13), 3025–3028 (2016).
    [Crossref]
  8. Y. Lin, F. Liu, X. He, W. Jin, M. Zhang, F. Yang, H. L. Ho, Y. Tan, and L. Gu, “Distributed gas sensing with optical fibre photothermal interferometry,” Opt. Express 25(25), 31568–31585 (2017).
    [Crossref]
  9. Z. Li, Z. Wang, F. Yang, W. Jin, and W. Ren, “Mid-infrared fiber-optic photothermal interferometry,” Opt. Lett. 42(18), 3718–3721 (2017).
    [Crossref]
  10. C. C. Davis and S. J. Petuchowski, “Phase fluctuation optical heterodyne spectroscopy of gases,” Appl. Opt. 20(14), 2539–2554 (1981).
    [Crossref]
  11. E. A. Mason and S. C. Saxena, “Approximate formula for the thermal conductivity of gas mixtures,” Phys. Fluids 1(5), 361–369 (1958).
    [Crossref]
  12. M. Zhu, T. Liu, S. Wang, and K. Zhang, “Capturing molecular multimode relaxation processes in excitable gases based on decomposition of acoustic relaxation spectra,” Meas. Sci. Technol. 28(8), 085008 (2017).
    [Crossref]
  13. T. Liu, S. Wang, and M. Zhu, “Predicting acoustic relaxation absorption in gas mixtures for extraction of composition relaxation contributions,” Proc. R. Soc. London, Ser. A 473(2208), 20170496 (2017).
    [Crossref]
  14. F. Yang, W. Jin, Y. Lin, C. Wang, H. Lut, and Y. Tan, “Hollow-core microstructured optical fiber gas sensors,” J. Lightwave Technol. 35(16), 3413–3424 (2017).
    [Crossref]
  15. S.-F. Gao, Y.-Y. Wang, W. Ding, and P. Wang, “Hollow-core negative-curvature fiber for UV guidance,” Opt. Lett. 43(6), 1347–1350 (2018).
    [Crossref]
  16. Y. Tan, W. Jin, F. Yang, Y. Jiang, and H. L. Ho, “Cavity-enhanced photothermal gas detection with a hollow fiber Fabry-Perot absorption cell,” J. Lightwave Technol. 37(17), 4222–4228 (2019).
    [Crossref]
  17. Y. Tan, W. Jin, F. Yang, H. L. Ho, and H. Kong, “High finesse hollow-core fiber resonating cavity for high sensitivity gas sensing application,” J. Lightwave Technol. 35(14), 2887–2893 (2017).
    [Crossref]
  18. J. P. Carvalho, H. Lehmann, H. Bartelt, F. Magalhães, R. Amezcua-Correa, J. L. Santos, J. Van Roosbroeck, F. M. Araújo, L. A. Ferreira, and J. C. Knight, “Remote system for detection of low-levels of methane based on photonic crystal fibres and wavelength modulation spectroscopy,” J. Sens. 2009, 1–10 (2009).
    [Crossref]

2019 (2)

2018 (1)

2017 (7)

2016 (2)

Y. Lin, Wei Jin, Fan Yang, Jun Ma, Chao Wang, Hoi Lut Ho, and Yang Liu, “Pulsed photothermal interferometry for spectroscopic gas detection with hollow-core optical fibre,” Sci. Rep. 6(1), 1–12 (2016).
[Crossref]

F. Yang, Y. Tan, W. Jin, Y. Lin, Y. Qi, and H. L. Ho, “Hollow-core fiber Fabry–Perot photothermal gas sensor,” Opt. Lett. 41(13), 3025–3028 (2016).
[Crossref]

2015 (1)

W. Jin, Y. Cao, F. Yang, and H. L. Ho, “Ultra-sensitive all-fibre photothermal spectroscopy with large dynamic range,” Nat. Commun. 6(1), 6767 (2015).
[Crossref]

2009 (1)

J. P. Carvalho, H. Lehmann, H. Bartelt, F. Magalhães, R. Amezcua-Correa, J. L. Santos, J. Van Roosbroeck, F. M. Araújo, L. A. Ferreira, and J. C. Knight, “Remote system for detection of low-levels of methane based on photonic crystal fibres and wavelength modulation spectroscopy,” J. Sens. 2009, 1–10 (2009).
[Crossref]

1998 (1)

B. Culshaw, G. Stewart, F. Dong, C. Tandy, and D. Moodie, “Fibre optic techniques for remote spectroscopic methane detection—from concept to system realisation,” Sens. Actuators, B 51(1-3), 25–37 (1998).
[Crossref]

1981 (1)

1958 (1)

E. A. Mason and S. C. Saxena, “Approximate formula for the thermal conductivity of gas mixtures,” Phys. Fluids 1(5), 361–369 (1958).
[Crossref]

Amezcua-Correa, R.

J. P. Carvalho, H. Lehmann, H. Bartelt, F. Magalhães, R. Amezcua-Correa, J. L. Santos, J. Van Roosbroeck, F. M. Araújo, L. A. Ferreira, and J. C. Knight, “Remote system for detection of low-levels of methane based on photonic crystal fibres and wavelength modulation spectroscopy,” J. Sens. 2009, 1–10 (2009).
[Crossref]

Araújo, F. M.

J. P. Carvalho, H. Lehmann, H. Bartelt, F. Magalhães, R. Amezcua-Correa, J. L. Santos, J. Van Roosbroeck, F. M. Araújo, L. A. Ferreira, and J. C. Knight, “Remote system for detection of low-levels of methane based on photonic crystal fibres and wavelength modulation spectroscopy,” J. Sens. 2009, 1–10 (2009).
[Crossref]

Bartelt, H.

J. P. Carvalho, H. Lehmann, H. Bartelt, F. Magalhães, R. Amezcua-Correa, J. L. Santos, J. Van Roosbroeck, F. M. Araújo, L. A. Ferreira, and J. C. Knight, “Remote system for detection of low-levels of methane based on photonic crystal fibres and wavelength modulation spectroscopy,” J. Sens. 2009, 1–10 (2009).
[Crossref]

Bialkowski, S. E.

S. E. Bialkowski, Photothermal Spectroscopy Methods for Chemical Analysis, vol. 177. John Wiley & Sons, 1996.

Cao, Y.

W. Jin, Y. Cao, F. Yang, and H. L. Ho, “Ultra-sensitive all-fibre photothermal spectroscopy with large dynamic range,” Nat. Commun. 6(1), 6767 (2015).
[Crossref]

Carvalho, J. P.

J. P. Carvalho, H. Lehmann, H. Bartelt, F. Magalhães, R. Amezcua-Correa, J. L. Santos, J. Van Roosbroeck, F. M. Araújo, L. A. Ferreira, and J. C. Knight, “Remote system for detection of low-levels of methane based on photonic crystal fibres and wavelength modulation spectroscopy,” J. Sens. 2009, 1–10 (2009).
[Crossref]

Culshaw, B.

B. Culshaw, G. Stewart, F. Dong, C. Tandy, and D. Moodie, “Fibre optic techniques for remote spectroscopic methane detection—from concept to system realisation,” Sens. Actuators, B 51(1-3), 25–37 (1998).
[Crossref]

Davis, C. C.

Ding, W.

Dong, F.

B. Culshaw, G. Stewart, F. Dong, C. Tandy, and D. Moodie, “Fibre optic techniques for remote spectroscopic methane detection—from concept to system realisation,” Sens. Actuators, B 51(1-3), 25–37 (1998).
[Crossref]

Ferreira, L. A.

J. P. Carvalho, H. Lehmann, H. Bartelt, F. Magalhães, R. Amezcua-Correa, J. L. Santos, J. Van Roosbroeck, F. M. Araújo, L. A. Ferreira, and J. C. Knight, “Remote system for detection of low-levels of methane based on photonic crystal fibres and wavelength modulation spectroscopy,” J. Sens. 2009, 1–10 (2009).
[Crossref]

Gao, S.

Gao, S.-F.

Gu, L.

He, X.

Ho, H. L.

Ho, Hoi Lut

Y. Lin, Wei Jin, Fan Yang, Jun Ma, Chao Wang, Hoi Lut Ho, and Yang Liu, “Pulsed photothermal interferometry for spectroscopic gas detection with hollow-core optical fibre,” Sci. Rep. 6(1), 1–12 (2016).
[Crossref]

Jiang, Y.

Jin, W.

Y. Tan, W. Jin, F. Yang, Y. Jiang, and H. L. Ho, “Cavity-enhanced photothermal gas detection with a hollow fiber Fabry-Perot absorption cell,” J. Lightwave Technol. 37(17), 4222–4228 (2019).
[Crossref]

C. Yao, Q. Wang, Y. Lin, W. Jin, L. Xiao, S. Gao, Y. Wang, P. Wang, and W. Ren, “Photothermal CO detection in a hollow-core negative curvature fiber,” Opt. Lett. 44(16), 4048–4051 (2019).
[Crossref]

Z. Li, Z. Wang, F. Yang, W. Jin, and W. Ren, “Mid-infrared fiber-optic photothermal interferometry,” Opt. Lett. 42(18), 3718–3721 (2017).
[Crossref]

Y. Tan, W. Jin, F. Yang, H. L. Ho, and H. Kong, “High finesse hollow-core fiber resonating cavity for high sensitivity gas sensing application,” J. Lightwave Technol. 35(14), 2887–2893 (2017).
[Crossref]

Y. Lin, F. Liu, X. He, W. Jin, M. Zhang, F. Yang, H. L. Ho, Y. Tan, and L. Gu, “Distributed gas sensing with optical fibre photothermal interferometry,” Opt. Express 25(25), 31568–31585 (2017).
[Crossref]

F. Yang, W. Jin, Y. Lin, C. Wang, H. Lut, and Y. Tan, “Hollow-core microstructured optical fiber gas sensors,” J. Lightwave Technol. 35(16), 3413–3424 (2017).
[Crossref]

Y. Lin, W. Jin, F. Yang, Y. Tan, and H. L. Ho, “Performance optimization of hollow-core fiber photothermal gas sensors,” Opt. Lett. 42(22), 4712–4715 (2017).
[Crossref]

F. Yang, Y. Tan, W. Jin, Y. Lin, Y. Qi, and H. L. Ho, “Hollow-core fiber Fabry–Perot photothermal gas sensor,” Opt. Lett. 41(13), 3025–3028 (2016).
[Crossref]

W. Jin, Y. Cao, F. Yang, and H. L. Ho, “Ultra-sensitive all-fibre photothermal spectroscopy with large dynamic range,” Nat. Commun. 6(1), 6767 (2015).
[Crossref]

Jin, Wei

Y. Lin, Wei Jin, Fan Yang, Jun Ma, Chao Wang, Hoi Lut Ho, and Yang Liu, “Pulsed photothermal interferometry for spectroscopic gas detection with hollow-core optical fibre,” Sci. Rep. 6(1), 1–12 (2016).
[Crossref]

Knight, J. C.

J. P. Carvalho, H. Lehmann, H. Bartelt, F. Magalhães, R. Amezcua-Correa, J. L. Santos, J. Van Roosbroeck, F. M. Araújo, L. A. Ferreira, and J. C. Knight, “Remote system for detection of low-levels of methane based on photonic crystal fibres and wavelength modulation spectroscopy,” J. Sens. 2009, 1–10 (2009).
[Crossref]

Kong, H.

Lehmann, H.

J. P. Carvalho, H. Lehmann, H. Bartelt, F. Magalhães, R. Amezcua-Correa, J. L. Santos, J. Van Roosbroeck, F. M. Araújo, L. A. Ferreira, and J. C. Knight, “Remote system for detection of low-levels of methane based on photonic crystal fibres and wavelength modulation spectroscopy,” J. Sens. 2009, 1–10 (2009).
[Crossref]

Li, Z.

Lin, Y.

Liu, F.

Liu, T.

T. Liu, S. Wang, and M. Zhu, “Predicting acoustic relaxation absorption in gas mixtures for extraction of composition relaxation contributions,” Proc. R. Soc. London, Ser. A 473(2208), 20170496 (2017).
[Crossref]

M. Zhu, T. Liu, S. Wang, and K. Zhang, “Capturing molecular multimode relaxation processes in excitable gases based on decomposition of acoustic relaxation spectra,” Meas. Sci. Technol. 28(8), 085008 (2017).
[Crossref]

Liu, Yang

Y. Lin, Wei Jin, Fan Yang, Jun Ma, Chao Wang, Hoi Lut Ho, and Yang Liu, “Pulsed photothermal interferometry for spectroscopic gas detection with hollow-core optical fibre,” Sci. Rep. 6(1), 1–12 (2016).
[Crossref]

Lut, H.

Ma, Jun

Y. Lin, Wei Jin, Fan Yang, Jun Ma, Chao Wang, Hoi Lut Ho, and Yang Liu, “Pulsed photothermal interferometry for spectroscopic gas detection with hollow-core optical fibre,” Sci. Rep. 6(1), 1–12 (2016).
[Crossref]

Magalhães, F.

J. P. Carvalho, H. Lehmann, H. Bartelt, F. Magalhães, R. Amezcua-Correa, J. L. Santos, J. Van Roosbroeck, F. M. Araújo, L. A. Ferreira, and J. C. Knight, “Remote system for detection of low-levels of methane based on photonic crystal fibres and wavelength modulation spectroscopy,” J. Sens. 2009, 1–10 (2009).
[Crossref]

Mason, E. A.

E. A. Mason and S. C. Saxena, “Approximate formula for the thermal conductivity of gas mixtures,” Phys. Fluids 1(5), 361–369 (1958).
[Crossref]

Moodie, D.

B. Culshaw, G. Stewart, F. Dong, C. Tandy, and D. Moodie, “Fibre optic techniques for remote spectroscopic methane detection—from concept to system realisation,” Sens. Actuators, B 51(1-3), 25–37 (1998).
[Crossref]

Petuchowski, S. J.

Qi, Y.

Ren, W.

Santos, J. L.

J. P. Carvalho, H. Lehmann, H. Bartelt, F. Magalhães, R. Amezcua-Correa, J. L. Santos, J. Van Roosbroeck, F. M. Araújo, L. A. Ferreira, and J. C. Knight, “Remote system for detection of low-levels of methane based on photonic crystal fibres and wavelength modulation spectroscopy,” J. Sens. 2009, 1–10 (2009).
[Crossref]

Saxena, S. C.

E. A. Mason and S. C. Saxena, “Approximate formula for the thermal conductivity of gas mixtures,” Phys. Fluids 1(5), 361–369 (1958).
[Crossref]

Stewart, G.

B. Culshaw, G. Stewart, F. Dong, C. Tandy, and D. Moodie, “Fibre optic techniques for remote spectroscopic methane detection—from concept to system realisation,” Sens. Actuators, B 51(1-3), 25–37 (1998).
[Crossref]

Tan, Y.

Tandy, C.

B. Culshaw, G. Stewart, F. Dong, C. Tandy, and D. Moodie, “Fibre optic techniques for remote spectroscopic methane detection—from concept to system realisation,” Sens. Actuators, B 51(1-3), 25–37 (1998).
[Crossref]

Van Roosbroeck, J.

J. P. Carvalho, H. Lehmann, H. Bartelt, F. Magalhães, R. Amezcua-Correa, J. L. Santos, J. Van Roosbroeck, F. M. Araújo, L. A. Ferreira, and J. C. Knight, “Remote system for detection of low-levels of methane based on photonic crystal fibres and wavelength modulation spectroscopy,” J. Sens. 2009, 1–10 (2009).
[Crossref]

Wang, C.

Wang, Chao

Y. Lin, Wei Jin, Fan Yang, Jun Ma, Chao Wang, Hoi Lut Ho, and Yang Liu, “Pulsed photothermal interferometry for spectroscopic gas detection with hollow-core optical fibre,” Sci. Rep. 6(1), 1–12 (2016).
[Crossref]

Wang, P.

Wang, Q.

Wang, S.

M. Zhu, T. Liu, S. Wang, and K. Zhang, “Capturing molecular multimode relaxation processes in excitable gases based on decomposition of acoustic relaxation spectra,” Meas. Sci. Technol. 28(8), 085008 (2017).
[Crossref]

T. Liu, S. Wang, and M. Zhu, “Predicting acoustic relaxation absorption in gas mixtures for extraction of composition relaxation contributions,” Proc. R. Soc. London, Ser. A 473(2208), 20170496 (2017).
[Crossref]

Wang, Y.

Wang, Y.-Y.

Wang, Z.

Xiao, L.

Yang, F.

Yang, Fan

Y. Lin, Wei Jin, Fan Yang, Jun Ma, Chao Wang, Hoi Lut Ho, and Yang Liu, “Pulsed photothermal interferometry for spectroscopic gas detection with hollow-core optical fibre,” Sci. Rep. 6(1), 1–12 (2016).
[Crossref]

Yao, C.

Zhang, K.

M. Zhu, T. Liu, S. Wang, and K. Zhang, “Capturing molecular multimode relaxation processes in excitable gases based on decomposition of acoustic relaxation spectra,” Meas. Sci. Technol. 28(8), 085008 (2017).
[Crossref]

Zhang, M.

Zhu, M.

T. Liu, S. Wang, and M. Zhu, “Predicting acoustic relaxation absorption in gas mixtures for extraction of composition relaxation contributions,” Proc. R. Soc. London, Ser. A 473(2208), 20170496 (2017).
[Crossref]

M. Zhu, T. Liu, S. Wang, and K. Zhang, “Capturing molecular multimode relaxation processes in excitable gases based on decomposition of acoustic relaxation spectra,” Meas. Sci. Technol. 28(8), 085008 (2017).
[Crossref]

Appl. Opt. (1)

J. Lightwave Technol. (3)

J. Sens. (1)

J. P. Carvalho, H. Lehmann, H. Bartelt, F. Magalhães, R. Amezcua-Correa, J. L. Santos, J. Van Roosbroeck, F. M. Araújo, L. A. Ferreira, and J. C. Knight, “Remote system for detection of low-levels of methane based on photonic crystal fibres and wavelength modulation spectroscopy,” J. Sens. 2009, 1–10 (2009).
[Crossref]

Meas. Sci. Technol. (1)

M. Zhu, T. Liu, S. Wang, and K. Zhang, “Capturing molecular multimode relaxation processes in excitable gases based on decomposition of acoustic relaxation spectra,” Meas. Sci. Technol. 28(8), 085008 (2017).
[Crossref]

Nat. Commun. (1)

W. Jin, Y. Cao, F. Yang, and H. L. Ho, “Ultra-sensitive all-fibre photothermal spectroscopy with large dynamic range,” Nat. Commun. 6(1), 6767 (2015).
[Crossref]

Opt. Express (1)

Opt. Lett. (5)

Phys. Fluids (1)

E. A. Mason and S. C. Saxena, “Approximate formula for the thermal conductivity of gas mixtures,” Phys. Fluids 1(5), 361–369 (1958).
[Crossref]

Proc. R. Soc. London, Ser. A (1)

T. Liu, S. Wang, and M. Zhu, “Predicting acoustic relaxation absorption in gas mixtures for extraction of composition relaxation contributions,” Proc. R. Soc. London, Ser. A 473(2208), 20170496 (2017).
[Crossref]

Sci. Rep. (1)

Y. Lin, Wei Jin, Fan Yang, Jun Ma, Chao Wang, Hoi Lut Ho, and Yang Liu, “Pulsed photothermal interferometry for spectroscopic gas detection with hollow-core optical fibre,” Sci. Rep. 6(1), 1–12 (2016).
[Crossref]

Sens. Actuators, B (1)

B. Culshaw, G. Stewart, F. Dong, C. Tandy, and D. Moodie, “Fibre optic techniques for remote spectroscopic methane detection—from concept to system realisation,” Sens. Actuators, B 51(1-3), 25–37 (1998).
[Crossref]

Other (1)

S. E. Bialkowski, Photothermal Spectroscopy Methods for Chemical Analysis, vol. 177. John Wiley & Sons, 1996.

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Figures (12)

Fig. 1.
Fig. 1. Schematic of the FPI for PT gas detection with a hollow-core fiber. The pump and probe beam are copropagating in the HCF. $I_{probe}^{r1}$ and $I_{probe}^{r2}$ are the reflected probe beams.
Fig. 2.
Fig. 2. A hollow capillary used as to model the gas-filled HCF.
Fig. 3.
Fig. 3. (a) The calculated frequency-dependent PT modulation for HCFs with different core radius and with R/w fixed to 1.25. (b) The calculated PT phase modulation with w = 4.5 µm and the pump modulation frequency of 0.1 Hz. The dots are calculated using COMSOL Multiphysics while the line is the result from Eq. (4) with R/w raging from 1.25 to ∼10. (c) The calculated -3-dB roll-off frequencies for HCFs with different core radius and with R/w = 1.25. The dots are calculated using COMSOL Multiphysics while the line is the result from Eq. (5) with 1 ppm acetylene balanced in air. The acetylene concentration of 1 ppm is used for computation in (a), (b) and (c).
Fig. 4.
Fig. 4. The cross-sectional images of (a) the HC-1550-06 HC-PCF and (b) the AR-HCF.
Fig. 5.
Fig. 5. Experimental setup to measure the frequency-dependent PT phase modulation of a HC-PCF and an AR-HCF. LPF: low pass filter which is used as part of the servo-loop for FPI stabilization; DAQ: data acquisition and PD: Photodetector.
Fig. 6.
Fig. 6. The measured and calculated frequency response of PT modulation in AR-HCF and HC-PCF. The blue triangles are measured with the AR-HCF and the blue line is calculated using COMSOL Multiphysics based on the simplified capillary model with radius of the hollow core equals to 32 µm. The red dots are measured with the HC-PCF and the red line is calculated using COMSOL Multiphysics based on the simplified capillary model with radius of the hollow core equals to 6.3 µm.
Fig. 7.
Fig. 7. Experimental setup for gas detection with PT spectroscopy in AR-HCF.
Fig. 8.
Fig. 8. (a) The measured PT signals with different pump power with a 5.5-cm-long AR-HCF. (b) The peak-to-peak value of the PT signal and the standard deviation (s. d.) of the noise as functions of pump power level with 1000 ppm acetylene balanced in nitrogen. Error bars show the s.d. of the PT signal from five measurements and the magnitudes of the error bars are scaled up by 10-fold for clarity reason.
Fig. 9.
Fig. 9. (a) Measured PT signals when pump laser is tuned across the P(13) absorption line of acetylene for 10, 50 and 142 ppm acetylene in nitrogen with ∼125 mW pump power delivered to the AR-HCF. (b) Peak-to-peak amplitude of the PT signal as a function of gas concentration with ∼125 mW pump power delivered to the AR-HCF. Error bars show the s.d. of the PT signal from five measurements.
Fig. 10.
Fig. 10. Time trace (upper panel) and Allan deviation analysis (lower panel) of the baseline noise over a period of 6 hours. The time constant of the lock-in amplifier is 100 ms.
Fig. 11.
Fig. 11. The time trace (upper panel) and the Allan plot (lower panel) of the relative PT signal over 24 hours with 1000 ppm acetylene in nitrogen and 125 mW pump power in the AR-HCF. The time constant of the lock-in amplifier is 1 s.
Fig. 12.
Fig. 12. The measured 2f-signal as a function of time during gas loading and unloading process.

Tables (1)

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Table 1. Detection limit of some state-of-the-art gas sensors based HCFs

Equations (5)

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1 r d d r ( r d T ( r ) d r ) + Q ( r ) k = 0
Q ( r ) = α C P p u m p / ( π w p u m p 2 ) exp ( r 2 / w p u m p 2 )
Δ ϕ =  -  4 π ( n 0 1 ) L λ p r o b e 0 R ( T T a b s ) T a b s exp ( r 2 / w p r o b e 2 ) / ( π w p r o b e 2 ) 2 π r d r
Δ ϕ = α C P p u m p ( n 0 1 ) L k λ p r o b e T a b s { μ E u l e r + E n [ 1 , 2 R 2 w 2 ] + 2 E i [ 2 R 2 w 2 ] 2 E i [ R 2 w 2 ] + l n [ R 2 w 2 ] }
f 3 d B = 2 ln ( 2 ) β R 2

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