Frequency uncertainty improvement in a STFT-BOTDR using highly nonlinear optical fibers

Linqing Luo; Francesca Parmigiani; Yifei Yu; Bo Li; Kenichi Soga; Jize Yan

doi:10.1364/OE.26.003870

Optics Express
Vol. 26,
Issue 4,
pp. 3870-3881
(2018)
•https://doi.org/10.1364/OE.26.003870

Frequency uncertainty improvement in a STFT-BOTDR using highly nonlinear optical fibers

Linqing Luo, Francesca Parmigiani, Yifei Yu, Bo Li, Kenichi Soga, and Jize Yan

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Linqing Luo, Francesca Parmigiani, Yifei Yu, Bo Li, Kenichi Soga, and Jize Yan, "Frequency uncertainty improvement in a STFT-BOTDR using highly nonlinear optical fibers," Opt. Express 26, 3870-3881 (2018)

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Table of Contents Category
- Sensors
Optics & Photonics Topics
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The topics in this list come from the Optics and Photonics Topics applied to this article.
Previously assigned OCIS codes
- Fiber optics sensors (060.2370)
- Nonlinear optics, fibers (060.4370)

About this Article
History
- Original Manuscript: November 16, 2017
- Revised Manuscript: December 24, 2017
- Manuscript Accepted: December 31, 2017
- Published: February 6, 2018

Abstract

The sensitivity of a sensor to strain or the temperature variations due to distributed Brillouin scattering are partially related to the type of fibers used and the Brillouin scattering induced effective index. In this paper, a highly nonlinear fiber that can generate a higher Brillouin scattering signal is compared to a standard single mode fiber in a short-time-Fourier-transform Brillouin optical time domain reflectometer (STFT-BOTDR). The results show that much higher signal to noise ratios of the Brillouin scattering spectrum and smaller frequency uncertainties in the sensing measurement can be achieved in the highly nonlinear fiber for comparable launched powers. With a measurement speed of 4 Hz, the frequency uncertainty can be 0.43 MHz, corresponding to 10 με in strain or 0.43°C in temperature uncertainty for the highly nonlinear fiber. In contrast, for the standard single mode fiber case, the value would increase to about 1.02 MHz (25 με or 1.02°C), demonstrating the advantage of the highly nonlinear fiber for distributed strain/temperature sensing.

Published by The Optical Society under the terms of the Creative Commons Attribution 4.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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References

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Article Order
Year
Author
Publication

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[Crossref] [PubMed]
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[Crossref] [PubMed]
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[Crossref]
Y. Yu, L. Luo, B. Li, K. Soga, and J. Yan, “Quadratic time-frequency transforms-based Brillouin optical time-domain reflectometry,” IEEE Sens. J. 17(20), 6622–6626 (2017).
[Crossref]
O. Aso, M. Tadakuma, and S. Namiki, “Four-wave mixing in optical fibers and its applications,” Furukawa Review 19, 63–68 (2000).
R. H. Stolen and C. Lin, “Self-phase-modulation in silica optical fibers,” Phys. Rev. A 17(4), 1448–1453 (1978).
[Crossref]
G. Agrawal and A. Olsson, “Self-phase modulation and spectral broadening of optical pulses in Semiconductor Laser Amplifiers,” IEEE J. Quantum Electron. 25(11), 2297–2306 (1989).
[Crossref]

2017 (2)

B. Li, L. Luo, Y. Yu, K. Soga, and J. Yan, “Dynamic strain measurement using small gain stimulated Brillouin scattering in STFT-BOTDR,” IEEE Sens. J. 17(9), 2718–2724 (2017).
[Crossref]

Y. Yu, L. Luo, B. Li, K. Soga, and J. Yan, “Quadratic time-frequency transforms-based Brillouin optical time-domain reflectometry,” IEEE Sens. J. 17(20), 6622–6626 (2017).
[Crossref]

2016 (3)

Y. Yu, L. Luo, B. Li, K. Soga, and J. Yan, “Frequency resolution quantification of Brillouin distributed optical fiber sensors,” IEEE Photonics Technol. Lett. 28(21), 2367–2370 (2016).
[Crossref]

A. Motil, A. Bergman, and M. Tur, “State of the art of Brillouin fiber-optic distributed sensing,” Opt. Laser Technol. 78(A), 81–103 (2016).
[Crossref]

L. Luo, B. Li, Y. Yu, X. Xu, K. Soga, and J. Yan, “Time and frequency localized pulse shape for resolution enhancement in STFT-BOTDR,” J. Sens. 2016, 10 (2016).
[Crossref]

2012 (1)

C. A. Galindez-Jamioy and J. M. López-Higuera, “Brillouin distributed fiber sensors: an overview and applications,” J. Sens. 2012, 1–17 (2012).
[Crossref]

2011 (2)

X. Bao and L. Chen, “Recent progress in Brillouin scattering based fiber sensors,” Sensors (Basel) 11(12, 4152–4187 (2011).
[Crossref] [PubMed]

X. Liu and X. Bao, “Brillouin spectrum in LEAF and simultaneous temperature and strain measurement,” J. Lightwave Technol. 30(8), 1053–1059 (2011).
[Crossref]

2010 (2)

L. Thévenaz, “Brillouin distributed time-domain sensing in optical fibers: State of the art and perspectives,” Front. Optoelectron. China 3(1), 13–21 (2010).
[Crossref]

A. Kobyakov, M. Sauer, and D. Chowdhury, “Stimulated Brillouin scattering in optical fibers,” Adv. Opt. Photonics 2(1), 1–59 (2010).
[Crossref]

2005 (3)

J. H. Lee, T. Tanemura, K. Kikuchi, T. Nagashima, T. Hasegawa, S. Ohara, and N. Sugimoto, “Experimental comparison of a Kerr nonlinearity figure of merit including the stimulated Brillouin scattering threshold for state-of-the-art nonlinear optical fibers,” Opt. Lett. 30(13), 1698–1700 (2005).
[Crossref] [PubMed]

J. M. Chavez Boggio, J. D. Marconi, and H. L. Fragnito, “Experimental and numerical investigation of the SBS-threshold increase in an optical fiber by applying strain distributions,” J. Lightwave Technol. 23(11), 3808–3814 (2005).
[Crossref]

S.-B. Cho, Y.-G. Kim, J.-S. Heo, and J.-J. Lee, “Pulse width dependence of Brillouin frequency in single mode optical fibers,” Opt. Express 13(23), 9472–9479 (2005).
[Crossref] [PubMed]

2003 (1)

J. H. Lee, W. Belardi, K. Furusawa, P. Petropoulos, P. Yusoff, T. Monro, and D. Richardson, “Four-wave mixing based 10-Gb/s tunable wavelength conversion using a holey fiber with a high SBS threshold,” IEEE Photonics Technol. Lett. 15(3), 440–442 (2003).
[Crossref]

2001 (1)

J. Hansryd, F. Dross, M. Westlund, P. A. Andrekson, and S. Knudsen, “Increase of the SBS threshold in a short highly nonlinear fiber by applying a temperature distribution,” J. Lightwave Technol. 19(11), 1691–1697 (2001).
[Crossref]

2000 (1)

O. Aso, M. Tadakuma, and S. Namiki, “Four-wave mixing in optical fibers and its applications,” Furukawa Review 19, 63–68 (2000).

1995 (2)

M. J. Holmes, D. Williams, and R. Manning, “Highly nonlinear optical fiber for all optical processing applications,” IEEE Photonics Technol. Lett. 7(9), 1045–1047 (1995).
[Crossref]

T. Horiguchi, K. Shimizu, T. Kurashima, M. Tateda, and Y. Koyamada, “Development of a distributed sensing technique using Brillouin scattering,” J. Lightwave Technol. 13(7), 1296–1302 (1995).
[Crossref]

1993 (1)

P. Benassi, V. Mazzacurati, G. Ruocco, and G. Signorelli, “Elasto-optic constants in silicate glasses: Experiment and theory,” Phys. Rev. B Condens. Matter 48(9), 5987–5996 (1993).
[Crossref] [PubMed]

1989 (1)

G. Agrawal and A. Olsson, “Self-phase modulation and spectral broadening of optical pulses in Semiconductor Laser Amplifiers,” IEEE J. Quantum Electron. 25(11), 2297–2306 (1989).
[Crossref]

1978 (1)

R. H. Stolen and C. Lin, “Self-phase-modulation in silica optical fibers,” Phys. Rev. A 17(4), 1448–1453 (1978).
[Crossref]

1972 (1)

R. G. Smith, “Optical power handling capacity of low loss optical fibers as determined by stimulated Raman and brillouin scattering,” Appl. Opt. 11(11), 2489–2494 (1972).
[Crossref] [PubMed]

1965 (1)

I. Malitson, “Interspecimen comparison of the refractive index of fused silica,” J. Opt. Soc. Am. 55(11), 1205–1208 (1965).
[Crossref]

Agrawal, G.

G. Agrawal and A. Olsson, “Self-phase modulation and spectral broadening of optical pulses in Semiconductor Laser Amplifiers,” IEEE J. Quantum Electron. 25(11), 2297–2306 (1989).
[Crossref]

Andrekson, P. A.

Aso, O.

O. Aso, M. Tadakuma, and S. Namiki, “Four-wave mixing in optical fibers and its applications,” Furukawa Review 19, 63–68 (2000).

Bao, X.

X. Bao and L. Chen, “Recent progress in Brillouin scattering based fiber sensors,” Sensors (Basel) 11(12, 4152–4187 (2011).
[Crossref] [PubMed]

X. Liu and X. Bao, “Brillouin spectrum in LEAF and simultaneous temperature and strain measurement,” J. Lightwave Technol. 30(8), 1053–1059 (2011).
[Crossref]

Belardi, W.

Benassi, P.

Bergman, A.

A. Motil, A. Bergman, and M. Tur, “State of the art of Brillouin fiber-optic distributed sensing,” Opt. Laser Technol. 78(A), 81–103 (2016).
[Crossref]

Chavez Boggio, J. M.

Chen, L.

X. Bao and L. Chen, “Recent progress in Brillouin scattering based fiber sensors,” Sensors (Basel) 11(12, 4152–4187 (2011).
[Crossref] [PubMed]

Cho, S.-B.

S.-B. Cho, Y.-G. Kim, J.-S. Heo, and J.-J. Lee, “Pulse width dependence of Brillouin frequency in single mode optical fibers,” Opt. Express 13(23), 9472–9479 (2005).
[Crossref] [PubMed]

Chowdhury, D.

A. Kobyakov, M. Sauer, and D. Chowdhury, “Stimulated Brillouin scattering in optical fibers,” Adv. Opt. Photonics 2(1), 1–59 (2010).
[Crossref]

Dross, F.

Fragnito, H. L.

Furusawa, K.

Galindez-Jamioy, C. A.

C. A. Galindez-Jamioy and J. M. López-Higuera, “Brillouin distributed fiber sensors: an overview and applications,” J. Sens. 2012, 1–17 (2012).
[Crossref]

Hansryd, J.

Hasegawa, T.

Heo, J.-S.

S.-B. Cho, Y.-G. Kim, J.-S. Heo, and J.-J. Lee, “Pulse width dependence of Brillouin frequency in single mode optical fibers,” Opt. Express 13(23), 9472–9479 (2005).
[Crossref] [PubMed]

Holmes, M. J.

M. J. Holmes, D. Williams, and R. Manning, “Highly nonlinear optical fiber for all optical processing applications,” IEEE Photonics Technol. Lett. 7(9), 1045–1047 (1995).
[Crossref]

Horiguchi, T.

Kikuchi, K.

Kim, Y.-G.

S.-B. Cho, Y.-G. Kim, J.-S. Heo, and J.-J. Lee, “Pulse width dependence of Brillouin frequency in single mode optical fibers,” Opt. Express 13(23), 9472–9479 (2005).
[Crossref] [PubMed]

Knudsen, S.

Kobyakov, A.

A. Kobyakov, M. Sauer, and D. Chowdhury, “Stimulated Brillouin scattering in optical fibers,” Adv. Opt. Photonics 2(1), 1–59 (2010).
[Crossref]

Koyamada, Y.

Kurashima, T.

Lee, J. H.

Lee, J.-J.

S.-B. Cho, Y.-G. Kim, J.-S. Heo, and J.-J. Lee, “Pulse width dependence of Brillouin frequency in single mode optical fibers,” Opt. Express 13(23), 9472–9479 (2005).
[Crossref] [PubMed]

Li, B.

B. Li, L. Luo, Y. Yu, K. Soga, and J. Yan, “Dynamic strain measurement using small gain stimulated Brillouin scattering in STFT-BOTDR,” IEEE Sens. J. 17(9), 2718–2724 (2017).
[Crossref]

Y. Yu, L. Luo, B. Li, K. Soga, and J. Yan, “Quadratic time-frequency transforms-based Brillouin optical time-domain reflectometry,” IEEE Sens. J. 17(20), 6622–6626 (2017).
[Crossref]

L. Luo, B. Li, Y. Yu, X. Xu, K. Soga, and J. Yan, “Time and frequency localized pulse shape for resolution enhancement in STFT-BOTDR,” J. Sens. 2016, 10 (2016).
[Crossref]

Lin, C.

R. H. Stolen and C. Lin, “Self-phase-modulation in silica optical fibers,” Phys. Rev. A 17(4), 1448–1453 (1978).
[Crossref]

Liu, X.

X. Liu and X. Bao, “Brillouin spectrum in LEAF and simultaneous temperature and strain measurement,” J. Lightwave Technol. 30(8), 1053–1059 (2011).
[Crossref]

López-Higuera, J. M.

C. A. Galindez-Jamioy and J. M. López-Higuera, “Brillouin distributed fiber sensors: an overview and applications,” J. Sens. 2012, 1–17 (2012).
[Crossref]

Luo, L.

B. Li, L. Luo, Y. Yu, K. Soga, and J. Yan, “Dynamic strain measurement using small gain stimulated Brillouin scattering in STFT-BOTDR,” IEEE Sens. J. 17(9), 2718–2724 (2017).
[Crossref]

Y. Yu, L. Luo, B. Li, K. Soga, and J. Yan, “Quadratic time-frequency transforms-based Brillouin optical time-domain reflectometry,” IEEE Sens. J. 17(20), 6622–6626 (2017).
[Crossref]

L. Luo, B. Li, Y. Yu, X. Xu, K. Soga, and J. Yan, “Time and frequency localized pulse shape for resolution enhancement in STFT-BOTDR,” J. Sens. 2016, 10 (2016).
[Crossref]

Malitson, I.

I. Malitson, “Interspecimen comparison of the refractive index of fused silica,” J. Opt. Soc. Am. 55(11), 1205–1208 (1965).
[Crossref]

Manning, R.

M. J. Holmes, D. Williams, and R. Manning, “Highly nonlinear optical fiber for all optical processing applications,” IEEE Photonics Technol. Lett. 7(9), 1045–1047 (1995).
[Crossref]

Marconi, J. D.

Mazzacurati, V.

Monro, T.

Motil, A.

A. Motil, A. Bergman, and M. Tur, “State of the art of Brillouin fiber-optic distributed sensing,” Opt. Laser Technol. 78(A), 81–103 (2016).
[Crossref]

Nagashima, T.

Namiki, S.

O. Aso, M. Tadakuma, and S. Namiki, “Four-wave mixing in optical fibers and its applications,” Furukawa Review 19, 63–68 (2000).

Ohara, S.

Olsson, A.

G. Agrawal and A. Olsson, “Self-phase modulation and spectral broadening of optical pulses in Semiconductor Laser Amplifiers,” IEEE J. Quantum Electron. 25(11), 2297–2306 (1989).
[Crossref]

Petropoulos, P.

Richardson, D.

Ruocco, G.

Sauer, M.

A. Kobyakov, M. Sauer, and D. Chowdhury, “Stimulated Brillouin scattering in optical fibers,” Adv. Opt. Photonics 2(1), 1–59 (2010).
[Crossref]

Shimizu, K.

Signorelli, G.

Smith, R. G.

R. G. Smith, “Optical power handling capacity of low loss optical fibers as determined by stimulated Raman and brillouin scattering,” Appl. Opt. 11(11), 2489–2494 (1972).
[Crossref] [PubMed]

Soga, K.

B. Li, L. Luo, Y. Yu, K. Soga, and J. Yan, “Dynamic strain measurement using small gain stimulated Brillouin scattering in STFT-BOTDR,” IEEE Sens. J. 17(9), 2718–2724 (2017).
[Crossref]

Y. Yu, L. Luo, B. Li, K. Soga, and J. Yan, “Quadratic time-frequency transforms-based Brillouin optical time-domain reflectometry,” IEEE Sens. J. 17(20), 6622–6626 (2017).
[Crossref]

L. Luo, B. Li, Y. Yu, X. Xu, K. Soga, and J. Yan, “Time and frequency localized pulse shape for resolution enhancement in STFT-BOTDR,” J. Sens. 2016, 10 (2016).
[Crossref]

Stolen, R. H.

R. H. Stolen and C. Lin, “Self-phase-modulation in silica optical fibers,” Phys. Rev. A 17(4), 1448–1453 (1978).
[Crossref]

Sugimoto, N.

Tadakuma, M.

O. Aso, M. Tadakuma, and S. Namiki, “Four-wave mixing in optical fibers and its applications,” Furukawa Review 19, 63–68 (2000).

Tanemura, T.

Tateda, M.

Thévenaz, L.

L. Thévenaz, “Brillouin distributed time-domain sensing in optical fibers: State of the art and perspectives,” Front. Optoelectron. China 3(1), 13–21 (2010).
[Crossref]

Tur, M.

A. Motil, A. Bergman, and M. Tur, “State of the art of Brillouin fiber-optic distributed sensing,” Opt. Laser Technol. 78(A), 81–103 (2016).
[Crossref]

Westlund, M.

Williams, D.

M. J. Holmes, D. Williams, and R. Manning, “Highly nonlinear optical fiber for all optical processing applications,” IEEE Photonics Technol. Lett. 7(9), 1045–1047 (1995).
[Crossref]

Xu, X.

L. Luo, B. Li, Y. Yu, X. Xu, K. Soga, and J. Yan, “Time and frequency localized pulse shape for resolution enhancement in STFT-BOTDR,” J. Sens. 2016, 10 (2016).
[Crossref]

Yan, J.

B. Li, L. Luo, Y. Yu, K. Soga, and J. Yan, “Dynamic strain measurement using small gain stimulated Brillouin scattering in STFT-BOTDR,” IEEE Sens. J. 17(9), 2718–2724 (2017).
[Crossref]

Y. Yu, L. Luo, B. Li, K. Soga, and J. Yan, “Quadratic time-frequency transforms-based Brillouin optical time-domain reflectometry,” IEEE Sens. J. 17(20), 6622–6626 (2017).
[Crossref]

L. Luo, B. Li, Y. Yu, X. Xu, K. Soga, and J. Yan, “Time and frequency localized pulse shape for resolution enhancement in STFT-BOTDR,” J. Sens. 2016, 10 (2016).
[Crossref]

Yu, Y.

Y. Yu, L. Luo, B. Li, K. Soga, and J. Yan, “Quadratic time-frequency transforms-based Brillouin optical time-domain reflectometry,” IEEE Sens. J. 17(20), 6622–6626 (2017).
[Crossref]

B. Li, L. Luo, Y. Yu, K. Soga, and J. Yan, “Dynamic strain measurement using small gain stimulated Brillouin scattering in STFT-BOTDR,” IEEE Sens. J. 17(9), 2718–2724 (2017).
[Crossref]

L. Luo, B. Li, Y. Yu, X. Xu, K. Soga, and J. Yan, “Time and frequency localized pulse shape for resolution enhancement in STFT-BOTDR,” J. Sens. 2016, 10 (2016).
[Crossref]

Yusoff, P.

Adv. Opt. Photonics (1)

A. Kobyakov, M. Sauer, and D. Chowdhury, “Stimulated Brillouin scattering in optical fibers,” Adv. Opt. Photonics 2(1), 1–59 (2010).
[Crossref]

Appl. Opt. (1)

R. G. Smith, “Optical power handling capacity of low loss optical fibers as determined by stimulated Raman and brillouin scattering,” Appl. Opt. 11(11), 2489–2494 (1972).
[Crossref] [PubMed]

Front. Optoelectron. China (1)

L. Thévenaz, “Brillouin distributed time-domain sensing in optical fibers: State of the art and perspectives,” Front. Optoelectron. China 3(1), 13–21 (2010).
[Crossref]

Furukawa Review (1)

O. Aso, M. Tadakuma, and S. Namiki, “Four-wave mixing in optical fibers and its applications,” Furukawa Review 19, 63–68 (2000).

IEEE J. Quantum Electron. (1)

G. Agrawal and A. Olsson, “Self-phase modulation and spectral broadening of optical pulses in Semiconductor Laser Amplifiers,” IEEE J. Quantum Electron. 25(11), 2297–2306 (1989).
[Crossref]

IEEE Photonics Technol. Lett. (3)

M. J. Holmes, D. Williams, and R. Manning, “Highly nonlinear optical fiber for all optical processing applications,” IEEE Photonics Technol. Lett. 7(9), 1045–1047 (1995).
[Crossref]

IEEE Sens. J. (2)

Y. Yu, L. Luo, B. Li, K. Soga, and J. Yan, “Quadratic time-frequency transforms-based Brillouin optical time-domain reflectometry,” IEEE Sens. J. 17(20), 6622–6626 (2017).
[Crossref]

B. Li, L. Luo, Y. Yu, K. Soga, and J. Yan, “Dynamic strain measurement using small gain stimulated Brillouin scattering in STFT-BOTDR,” IEEE Sens. J. 17(9), 2718–2724 (2017).
[Crossref]

J. Lightwave Technol. (4)

X. Liu and X. Bao, “Brillouin spectrum in LEAF and simultaneous temperature and strain measurement,” J. Lightwave Technol. 30(8), 1053–1059 (2011).
[Crossref]

J. Opt. Soc. Am. (1)

I. Malitson, “Interspecimen comparison of the refractive index of fused silica,” J. Opt. Soc. Am. 55(11), 1205–1208 (1965).
[Crossref]

J. Sens. (2)

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Fig. 1 Experimental set-up of the STFT-BOTDR to test the HNLF-1145A and SMF-28. AWG: arbitrary waveform generator; EOM: electro-optic modulator; BPF: DWDM filter; PS: polarization scrambler; PD: photodiode; BPF: bandpass filter; LNA: low noise amplifier; VCO: voltage controlled oscillator ADC: analogue to digital converter

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Fig. 2 Transmitted and back reflected Brillouin powers as a function of input power for HNLF-1145A.

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Fig. 3 Normalized spectra of the Brillouin scatter signal for the two FUT at 10 m, 100 m and 500 m location.

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Fig. 4 The SNR for the HNLF-1145A and the SMF-28 at 10 m, 50 m, 100 m, 400 m, and 500 m locations along the fibers with different input power.

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Fig. 5 The BFS uncertainty versus input average power for the HNLF-1145A and the SMF-28.

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Fig. 6 The Power of the spectra of the HNLF-1145A fiber at position 10m, 100, 400m, 500m, 950m when the incident pump power is (a) 3.5 dBm, (b) 7.87 dBm, and (c) 12.30 dBm, vertical axis unit is relative value in dB.

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Fig. 7 The power difference of the launched power along the HNLF-1145A with input power 3.5 dBm, 7.87 dBm, 9,95 dBm, 11.31 dBm and 12.30 dBm.

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Fig. 8 Transmitted spectra at the end (1 km) of the HNLF-1145A (a) and HNLF-09 (b) when the incident pump power is 3.5 dBm (LDC100), 7.87 dBm (LDC150), 9.95 dBm (LDC200), 11.31 dBm (LDC 250), and 12.30 dBm (LDC300)

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Fig. 9 The SNR along the HNLF-1145A (a) and HNLF-09 (b) when the incident pump power is 3.5 dBm (LDC100), 7.87 dBm (LDC150), 9.95 dBm (LDC200), 11.31 dBm (LDC 250), and 12.30 dBm (LDC300)

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Tables (2)

Table 1 The values of the parameters to calculate Brillouin gain

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Table 2 The parameters of SMF-28 and HNLF-1145A

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Equations (6)

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γ L_{e f f} P_{t h} \propto \frac{n_{2}}{g_{B}}

g_{B} = \frac{4 π n^{8} p_{12}^{2}}{c λ_{p}^{2} ρ_{o} ν_{B} Δ ν_{B}}

P_{T H} = \frac{C K A_{e f f}}{g {}_{B}L_{e f f}}

S N R (d B) = 10 \log_{10} (\frac{2 R^{2} P_{B} P_{O L O} \sqrt{N}}{4 k T B / R_{L} + 2 e R P_{O L O} B + {(R P_{O L O})}^{2} RIN B}) - N F_{E - n o i s e}

Q = \frac{v_{B}}{F W H M}

σ \approx \frac{v_{B} \times δ^{0.05}}{8.5 \times Q \times S N R^{0.25}}

Refractive index silica	n = 1.44 [22]
Elasto-optic constant of SiO₂	$p_{12}$ = 0.285 [23]
Density	$ρ_{o}$ = $2.21 \times 10^{3} k g / m^{3}$ [24]
Wavelength of pump incident light	$λ_{p}$ = 1554.13 nm
Acoustic velocity	$V_{A}$ = 5996 m/s [23]

	SMF	HNLF-1145A
FWHM ( $Δ v_{B}$ )	100 MHz	50 MHz
Effective area ( $A_{e f f}$ )	80 ${μm}^{2}$	10.5 ${μm}^{2}$
Centre frequency for BGS ( $ν_{B}$ )	10.8 GHz	9.6 GHz
Attenuation ( $α$ )	0.2 dB/km	0.59 dB/km

Refractive index silica	n = 1.44 [22]
Elasto-optic constant of SiO₂	$p_{12}$ = 0.285 [23]
Density	$ρ_{o}$ = $2.21 \times 10^{3} k g / m^{3}$ [24]
Wavelength of pump incident light	$λ_{p}$ = 1554.13 nm
Acoustic velocity	$V_{A}$ = 5996 m/s [23]

	SMF	HNLF-1145A
FWHM ( $Δ v_{B}$ )	100 MHz	50 MHz
Effective area ( $A_{e f f}$ )	80 ${μm}^{2}$	10.5 ${μm}^{2}$
Centre frequency for BGS ( $ν_{B}$ )	10.8 GHz	9.6 GHz
Attenuation ( $α$ )	0.2 dB/km	0.59 dB/km