Abstract

We report a phase-coded Brillouin optical correlation-domain analysis (BOCDA) based on phase-shift keying (PSK), in which the pseudo-random binary sequence (PRBS) phase coding is realized using a Mach-Zehnder modulator (MZM). Unlike the conventional phase-coded BOCDA using a phase modulator, which suffers from the non-rectangular transition in the encoded phase, the PSK can realize perfect phase switches between 0 and π with zero-width edges. It is not sensitive to the bandwidth of the modulator and the power of the radio-frequency modulation signal. Numerical simulations and experimental results prove that it can effectively suppress the Brillouin amplification in the off-peak positions. In experiment, a 2-mm spatial resolution sensing is realized using only a 20-GHz bandwidth MZM.

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

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References

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    [Crossref]
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    [Crossref]
  3. A. Denisov, M. A. Soto, and L. Thevenaz, “Going beyond 1000000 resolved points in a Brillouin distributed fiber sensor: theoretical analysis and experimental demonstration,” Light: Sci. Appl. 5(5), e16074 (2016).
    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
  29. J. Zhang, C. Feng, M. Zhang, Y. Liu, C. Wu, and Y. Wang, “Brillouin optical correlation domain analysis based on chaotic laser with suppressed time delay signature,” Opt. Express 26(6), 6962–6972 (2018).
    [Crossref]
  30. Y. Wang, M. Zhang, J. Zhang, L. Qiao, T. Wang, Q. Zhang, L. Zhao, and Y. Wang, “Millimeter-Level-Spatial-Resolution Brillouin Optical Correlation-Domain Analysis Based on Broadband Chaotic Laser,” J. Lightwave Technol. 37(15), 3706–3712 (2019).
    [Crossref]

2019 (3)

2018 (9)

J. Zhang, M. Zhang, M. Zhang, Y. Liu, C. Feng, Y. Wang, and Y. Wang, “Chaotic Brillouin optical correlation-domain analysis,” Opt. Lett. 43(8), 1722–1725 (2018).
[Crossref]

J. Zhang, Y. Wang, M. Zhang, Q. Zhang, M. Li, C. Wu, L. Qiao, and Y. Wang, “Time-gated chaotic Brillouin optical correlation domain analysis,” Opt. Express 26(13), 17597–17607 (2018).
[Crossref]

J. Zhang, C. Feng, M. Zhang, Y. Liu, C. Wu, and Y. Wang, “Brillouin optical correlation domain analysis based on chaotic laser with suppressed time delay signature,” Opt. Express 26(6), 6962–6972 (2018).
[Crossref]

A. Zarifi, B. Stiller, M. Merklein, Y. Liu, B. Morrison, A. Casas-Bedoya, G. Ren, T. G. Nguyen, K. Vu, D.-Y. Choi, A. Mitchell, S. J. Madden, and B. J. Eggleton, “Brillouin spectroscopy of a hybrid silicon-chalcogenide waveguide with geometrical variations,” Opt. Lett. 43(15), 3493–3496 (2018).
[Crossref]

A. Zarifi, B. Stiller, M. Merklein, N. Li, K. Vu, D.-Y. Choi, P. Ma, S. J. Madden, and B. J. Eggleton, “Highly localized distributed Brillouin scattering response in a photonic integrated circuit,” APL Photonics 3(3), 036101 (2018).
[Crossref]

B. Wang, X. Fan, Y. Fu, and Z. He, “Dynamic strain measurement with kHz-level repetition rate and centimeter-level spatial resolution based on Brillouin optical correlation domain analysis,” Opt. Express 26(6), 6916–6928 (2018).
[Crossref]

D. Zhou, Y. Dong, B. Wang, C. Pang, D. Ba, H. Zhang, Z. Lu, H. Li, and X. Bao, “Single-shot BOTDA based on an optical chirp chain probe wave for distributed ultrafast measurement,” Light: Sci. Appl. 7(1), 32 (2018).
[Crossref]

A. Zadok, E. Preter, and Y. London, “Phase-Coded and Noise-Based Brillouin Optical Correlation-Domain Analysis,” Appl. Sci. 8(9), 1482 (2018).
[Crossref]

Y. Mizuno, H. Lee, and K. Nakamura, “Recent Advances in Brillouin Optical Correlation-Domain Reflectometry,” Appl. Sci. 8(10), 1845 (2018).
[Crossref]

2016 (2)

A. Denisov, M. A. Soto, and L. Thevenaz, “Going beyond 1000000 resolved points in a Brillouin distributed fiber sensor: theoretical analysis and experimental demonstration,” Light: Sci. Appl. 5(5), e16074 (2016).
[Crossref]

Y. London, Y. Antman, E. Preter, N. Levanon, and A. Zadok, “Brillouin Optical Correlation Domain Analysis Addressing 440 000 Resolution Points,” J. Lightwave Technol. 34(19), 4421–4429 (2016).
[Crossref]

2014 (2)

2012 (3)

A. Zadok, Y. Antman, N. Primerov, A. Denisov, J. Sancho, and L. Thevenaz, “Random-access distributed fiber sensing,” Laser Photonics Rev. 6(5), L1–L5 (2012).
[Crossref]

Y. Dong, H. Zhang, L. Chen, and X. Bao, “2 cm spatial-resolution and 2 km range Brillouin optical fiber sensor using a transient differential pulse pair,” Appl. Opt. 51(9), 1229–1235 (2012).
[Crossref]

X. Bao and L. Chen, “Recent Progress in Distributed Fiber Optic Sensors,” Sensors 12(7), 8601–8639 (2012).
[Crossref]

2008 (2)

W. Li, X. Bao, Y. Li, and L. Chen, “Differential pulse-width pair BOTDA for high spatial resolution sensing,” Opt. Express 16(26), 21616–21625 (2008).
[Crossref]

K.-Y. Song and K. Hotate, “Brillouin Optical Correlation Domain Analysis in Linear Configuration,” IEEE Photonics Technol. Lett. 20(24), 2150–2152 (2008).
[Crossref]

2007 (1)

K. Y. Song and K. Hotate, “Distributed fiber strain sensor with 1-kHz sampling rate based on Brillouin optical correlation domain analysis,” IEEE Photonics Technol. Lett. 19(23), 1928–1930 (2007).
[Crossref]

2006 (1)

2005 (1)

A. W. Brown, B. G. Colpitts, and K. Brown, “Distributed sensor based on dark-pulse Brillouin scattering,” IEEE Photonics Technol. Lett. 17(7), 1501–1503 (2005).
[Crossref]

2000 (1)

K. Hotate and T. Hasegawa, “Measurement of Brillouin gain spectrum distribution along an optical fiber using a correlation-based technique - Proposal, experiment and simulation,” IEICE Trans. Electron. E83C, 405–412 (2000).

1990 (2)

M. Tateda, T. Horiguchi, T. Kurashima, and K. Ishihara, “1st Measurement of Strain Distribution Along Field-Installed Optical Fibers Using Brillouin Spectroscopy,” J. Lightwave Technol. 8(9), 1269–1272 (1990).
[Crossref]

T. Kurashima, T. Horiguchi, and M. Tateda, “Distributed-Temperature Sensing Using Stimulated Brillouin-Scattering in Optical Silica Fibers,” Opt. Lett. 15(18), 1038–1040 (1990).
[Crossref]

Ahmad, R.

D. M. Chow, J. C. Tchahame, A. Denisov, J.-C. Beugnot, T. Sylvestre, L. Li, R. Ahmad, M. Rochette, K. H. Tow, M. A. Soto, and L. Thévenaz, “Mapping the Uniformity of Optical Microwires Using Phase-Correlation Brillouin Distributed Measurements,” in Frontiers in Optics 2015 (2015), Paper FW4F.4 (Optical Society of America, 2015), p. FW4F.4.

Antman, Y.

Ba, D.

D. Zhou, Y. Dong, B. Wang, C. Pang, D. Ba, H. Zhang, Z. Lu, H. Li, and X. Bao, “Single-shot BOTDA based on an optical chirp chain probe wave for distributed ultrafast measurement,” Light: Sci. Appl. 7(1), 32 (2018).
[Crossref]

Bao, X.

D. Zhou, Y. Dong, B. Wang, C. Pang, D. Ba, H. Zhang, Z. Lu, H. Li, and X. Bao, “Single-shot BOTDA based on an optical chirp chain probe wave for distributed ultrafast measurement,” Light: Sci. Appl. 7(1), 32 (2018).
[Crossref]

X. Bao and L. Chen, “Recent Progress in Distributed Fiber Optic Sensors,” Sensors 12(7), 8601–8639 (2012).
[Crossref]

Y. Dong, H. Zhang, L. Chen, and X. Bao, “2 cm spatial-resolution and 2 km range Brillouin optical fiber sensor using a transient differential pulse pair,” Appl. Opt. 51(9), 1229–1235 (2012).
[Crossref]

W. Li, X. Bao, Y. Li, and L. Chen, “Differential pulse-width pair BOTDA for high spatial resolution sensing,” Opt. Express 16(26), 21616–21625 (2008).
[Crossref]

Beugnot, J.-C.

D. M. Chow, J. C. Tchahame, A. Denisov, J.-C. Beugnot, T. Sylvestre, L. Li, R. Ahmad, M. Rochette, K. H. Tow, M. A. Soto, and L. Thévenaz, “Mapping the Uniformity of Optical Microwires Using Phase-Correlation Brillouin Distributed Measurements,” in Frontiers in Optics 2015 (2015), Paper FW4F.4 (Optical Society of America, 2015), p. FW4F.4.

Brown, A. W.

A. W. Brown, B. G. Colpitts, and K. Brown, “Distributed sensor based on dark-pulse Brillouin scattering,” IEEE Photonics Technol. Lett. 17(7), 1501–1503 (2005).
[Crossref]

Brown, K.

A. W. Brown, B. G. Colpitts, and K. Brown, “Distributed sensor based on dark-pulse Brillouin scattering,” IEEE Photonics Technol. Lett. 17(7), 1501–1503 (2005).
[Crossref]

Casas-Bedoya, A.

Chen, L.

Choi, D.-Y.

Chow, D. M.

D. M. Chow, J. C. Tchahame, A. Denisov, J.-C. Beugnot, T. Sylvestre, L. Li, R. Ahmad, M. Rochette, K. H. Tow, M. A. Soto, and L. Thévenaz, “Mapping the Uniformity of Optical Microwires Using Phase-Correlation Brillouin Distributed Measurements,” in Frontiers in Optics 2015 (2015), Paper FW4F.4 (Optical Society of America, 2015), p. FW4F.4.

Cohen, R.

Colpitts, B. G.

A. W. Brown, B. G. Colpitts, and K. Brown, “Distributed sensor based on dark-pulse Brillouin scattering,” IEEE Photonics Technol. Lett. 17(7), 1501–1503 (2005).
[Crossref]

Denisov, A.

A. Denisov, M. A. Soto, and L. Thevenaz, “Going beyond 1000000 resolved points in a Brillouin distributed fiber sensor: theoretical analysis and experimental demonstration,” Light: Sci. Appl. 5(5), e16074 (2016).
[Crossref]

A. Zadok, Y. Antman, N. Primerov, A. Denisov, J. Sancho, and L. Thevenaz, “Random-access distributed fiber sensing,” Laser Photonics Rev. 6(5), L1–L5 (2012).
[Crossref]

D. M. Chow, J. C. Tchahame, A. Denisov, J.-C. Beugnot, T. Sylvestre, L. Li, R. Ahmad, M. Rochette, K. H. Tow, M. A. Soto, and L. Thévenaz, “Mapping the Uniformity of Optical Microwires Using Phase-Correlation Brillouin Distributed Measurements,” in Frontiers in Optics 2015 (2015), Paper FW4F.4 (Optical Society of America, 2015), p. FW4F.4.

Dong, Y.

D. Zhou, Y. Dong, B. Wang, C. Pang, D. Ba, H. Zhang, Z. Lu, H. Li, and X. Bao, “Single-shot BOTDA based on an optical chirp chain probe wave for distributed ultrafast measurement,” Light: Sci. Appl. 7(1), 32 (2018).
[Crossref]

Y. Dong, H. Zhang, L. Chen, and X. Bao, “2 cm spatial-resolution and 2 km range Brillouin optical fiber sensor using a transient differential pulse pair,” Appl. Opt. 51(9), 1229–1235 (2012).
[Crossref]

Eggleton, B. J.

Elooz, D.

Fan, X.

Feng, C.

Fu, Y.

Fukuda, H.

Y. Mizuno, N. Hayashi, H. Fukuda, K. Y. Song, and K. Nakamura, “Ultrahigh-speed distributed Brillouin reflectometry,” Light: Sci. Appl. 5, e16184 (2016).

Hasegawa, T.

K. Hotate and T. Hasegawa, “Measurement of Brillouin gain spectrum distribution along an optical fiber using a correlation-based technique - Proposal, experiment and simulation,” IEICE Trans. Electron. E83C, 405–412 (2000).

Hayashi, N.

Y. Mizuno, N. Hayashi, H. Fukuda, K. Y. Song, and K. Nakamura, “Ultrahigh-speed distributed Brillouin reflectometry,” Light: Sci. Appl. 5, e16184 (2016).

He, Z.

Horiguchi, T.

M. Tateda, T. Horiguchi, T. Kurashima, and K. Ishihara, “1st Measurement of Strain Distribution Along Field-Installed Optical Fibers Using Brillouin Spectroscopy,” J. Lightwave Technol. 8(9), 1269–1272 (1990).
[Crossref]

T. Kurashima, T. Horiguchi, and M. Tateda, “Distributed-Temperature Sensing Using Stimulated Brillouin-Scattering in Optical Silica Fibers,” Opt. Lett. 15(18), 1038–1040 (1990).
[Crossref]

Hotate, K.

K.-Y. Song and K. Hotate, “Brillouin Optical Correlation Domain Analysis in Linear Configuration,” IEEE Photonics Technol. Lett. 20(24), 2150–2152 (2008).
[Crossref]

K. Y. Song and K. Hotate, “Distributed fiber strain sensor with 1-kHz sampling rate based on Brillouin optical correlation domain analysis,” IEEE Photonics Technol. Lett. 19(23), 1928–1930 (2007).
[Crossref]

K. Y. Song, Z. He, and K. Hotate, “Distributed strain measurement with millimeter-order spatial resolution based on Brillouin optical correlation domain analysis,” Opt. Lett. 31(17), 2526–2528 (2006).
[Crossref]

K. Hotate and T. Hasegawa, “Measurement of Brillouin gain spectrum distribution along an optical fiber using a correlation-based technique - Proposal, experiment and simulation,” IEICE Trans. Electron. E83C, 405–412 (2000).

Ishihara, K.

M. Tateda, T. Horiguchi, T. Kurashima, and K. Ishihara, “1st Measurement of Strain Distribution Along Field-Installed Optical Fibers Using Brillouin Spectroscopy,” J. Lightwave Technol. 8(9), 1269–1272 (1990).
[Crossref]

Kim, G.-T.

Kishida, K.

K. Kishida, C. H. Li, and K. Nishiguchi, “Pulse pre-pump method for cm-order spatial resolution of BOTDA,” in 17th International Conference on Optical Fibre Sensors, Pts 1 and 2, M. Voet, R. Willsch, W. Ecke, J. Jones, and B. Culshaw, eds. (Spie-Int Soc Optical Engineering, 2005), Vol. 5855, pp. 559–562.

Kurashima, T.

M. Tateda, T. Horiguchi, T. Kurashima, and K. Ishihara, “1st Measurement of Strain Distribution Along Field-Installed Optical Fibers Using Brillouin Spectroscopy,” J. Lightwave Technol. 8(9), 1269–1272 (1990).
[Crossref]

T. Kurashima, T. Horiguchi, and M. Tateda, “Distributed-Temperature Sensing Using Stimulated Brillouin-Scattering in Optical Silica Fibers,” Opt. Lett. 15(18), 1038–1040 (1990).
[Crossref]

Lee, H.

Y. Mizuno, H. Lee, and K. Nakamura, “Recent Advances in Brillouin Optical Correlation-Domain Reflectometry,” Appl. Sci. 8(10), 1845 (2018).
[Crossref]

Lee, K.

Lee, S. B.

Levanon, N.

Li, C. H.

K. Kishida, C. H. Li, and K. Nishiguchi, “Pulse pre-pump method for cm-order spatial resolution of BOTDA,” in 17th International Conference on Optical Fibre Sensors, Pts 1 and 2, M. Voet, R. Willsch, W. Ecke, J. Jones, and B. Culshaw, eds. (Spie-Int Soc Optical Engineering, 2005), Vol. 5855, pp. 559–562.

Li, H.

D. Zhou, Y. Dong, B. Wang, C. Pang, D. Ba, H. Zhang, Z. Lu, H. Li, and X. Bao, “Single-shot BOTDA based on an optical chirp chain probe wave for distributed ultrafast measurement,” Light: Sci. Appl. 7(1), 32 (2018).
[Crossref]

Li, L.

D. M. Chow, J. C. Tchahame, A. Denisov, J.-C. Beugnot, T. Sylvestre, L. Li, R. Ahmad, M. Rochette, K. H. Tow, M. A. Soto, and L. Thévenaz, “Mapping the Uniformity of Optical Microwires Using Phase-Correlation Brillouin Distributed Measurements,” in Frontiers in Optics 2015 (2015), Paper FW4F.4 (Optical Society of America, 2015), p. FW4F.4.

Li, M.

Li, N.

A. Zarifi, B. Stiller, M. Merklein, N. Li, K. Vu, D.-Y. Choi, P. Ma, S. J. Madden, and B. J. Eggleton, “Highly localized distributed Brillouin scattering response in a photonic integrated circuit,” APL Photonics 3(3), 036101 (2018).
[Crossref]

Li, W.

Li, Y.

Liu, Y.

London, Y.

Lu, Z.

D. Zhou, Y. Dong, B. Wang, C. Pang, D. Ba, H. Zhang, Z. Lu, H. Li, and X. Bao, “Single-shot BOTDA based on an optical chirp chain probe wave for distributed ultrafast measurement,” Light: Sci. Appl. 7(1), 32 (2018).
[Crossref]

Ma, P.

A. Zarifi, B. Stiller, M. Merklein, N. Li, K. Vu, D.-Y. Choi, P. Ma, S. J. Madden, and B. J. Eggleton, “Highly localized distributed Brillouin scattering response in a photonic integrated circuit,” APL Photonics 3(3), 036101 (2018).
[Crossref]

Madden, S. J.

Merklein, M.

Mitchell, A.

Mizuno, Y.

Y. Mizuno, H. Lee, and K. Nakamura, “Recent Advances in Brillouin Optical Correlation-Domain Reflectometry,” Appl. Sci. 8(10), 1845 (2018).
[Crossref]

Y. Mizuno, N. Hayashi, H. Fukuda, K. Y. Song, and K. Nakamura, “Ultrahigh-speed distributed Brillouin reflectometry,” Light: Sci. Appl. 5, e16184 (2016).

Morrison, B.

Nakamura, K.

Y. Mizuno, H. Lee, and K. Nakamura, “Recent Advances in Brillouin Optical Correlation-Domain Reflectometry,” Appl. Sci. 8(10), 1845 (2018).
[Crossref]

Y. Mizuno, N. Hayashi, H. Fukuda, K. Y. Song, and K. Nakamura, “Ultrahigh-speed distributed Brillouin reflectometry,” Light: Sci. Appl. 5, e16184 (2016).

Nguyen, T. G.

Nishiguchi, K.

K. Kishida, C. H. Li, and K. Nishiguchi, “Pulse pre-pump method for cm-order spatial resolution of BOTDA,” in 17th International Conference on Optical Fibre Sensors, Pts 1 and 2, M. Voet, R. Willsch, W. Ecke, J. Jones, and B. Culshaw, eds. (Spie-Int Soc Optical Engineering, 2005), Vol. 5855, pp. 559–562.

Pang, C.

D. Zhou, Y. Dong, B. Wang, C. Pang, D. Ba, H. Zhang, Z. Lu, H. Li, and X. Bao, “Single-shot BOTDA based on an optical chirp chain probe wave for distributed ultrafast measurement,” Light: Sci. Appl. 7(1), 32 (2018).
[Crossref]

Preter, E.

A. Zadok, E. Preter, and Y. London, “Phase-Coded and Noise-Based Brillouin Optical Correlation-Domain Analysis,” Appl. Sci. 8(9), 1482 (2018).
[Crossref]

Y. London, Y. Antman, E. Preter, N. Levanon, and A. Zadok, “Brillouin Optical Correlation Domain Analysis Addressing 440 000 Resolution Points,” J. Lightwave Technol. 34(19), 4421–4429 (2016).
[Crossref]

Primerov, N.

A. Zadok, Y. Antman, N. Primerov, A. Denisov, J. Sancho, and L. Thevenaz, “Random-access distributed fiber sensing,” Laser Photonics Rev. 6(5), L1–L5 (2012).
[Crossref]

Qiao, L.

Ren, G.

Rochette, M.

D. M. Chow, J. C. Tchahame, A. Denisov, J.-C. Beugnot, T. Sylvestre, L. Li, R. Ahmad, M. Rochette, K. H. Tow, M. A. Soto, and L. Thévenaz, “Mapping the Uniformity of Optical Microwires Using Phase-Correlation Brillouin Distributed Measurements,” in Frontiers in Optics 2015 (2015), Paper FW4F.4 (Optical Society of America, 2015), p. FW4F.4.

Ryu, G.

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D. M. Chow, J. C. Tchahame, A. Denisov, J.-C. Beugnot, T. Sylvestre, L. Li, R. Ahmad, M. Rochette, K. H. Tow, M. A. Soto, and L. Thévenaz, “Mapping the Uniformity of Optical Microwires Using Phase-Correlation Brillouin Distributed Measurements,” in Frontiers in Optics 2015 (2015), Paper FW4F.4 (Optical Society of America, 2015), p. FW4F.4.

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Figures (9)

Fig. 1.
Fig. 1. Schematic diagram of imperfect phase modulation. Because of the bandwidth limitation, the phase coding by phase modulator is imperfect: the phase transition is not instantaneous but with rising and falling edges. The peak-to-peak phase shift is less than ${\pi }$.
Fig. 2.
Fig. 2. Schematic diagram of the phase coding based on phase-shift keying. The RF modulation signal is imperfect due to bandwidth limitation, resulting in imperfect phase coding for conventional BOCDA which employs a phase modulator to encode phase. When using the phase-shift keying (PSK), the phase coding is perfect as shown with red curve.
Fig. 3.
Fig. 3. (a) the limiting case of the transition imperfection, in which all the bit-duration is taken up by the rising (falling) edge. (b) an RF modulation signal with rectangular transition but the peak-to-peak voltage is less than the half-voltage of the modulator.
Fig. 4.
Fig. 4. Normalized simulated acoustic field distributions when the phases of the pump and the probe are encoded using the imperfect RF modulation signal in Fig. 3(a) and Fig. 3(b), respectively. The imperfection of the RF modulation signal in the conventional BOCDA results in the distraction of the acoustic field, which can be suppressed by the PSK technique. Note that the correlation nature of PRBS determines that the acoustic field cannot be zero in off-peak-positions even using perfect phase coding.
Fig. 5.
Fig. 5. Simulated BGS when the imperfect RF signal is used in the phase coding of BOCDA. The BFS of the hot region is 10.95 GHz, while in other positions the BFS is 10.85 GHz. (a) The BGS in the middle of the hot region for the conventional BOCDA which employs a phase modulator. (b) the corresponding BGS of BOCDA using PSK. Because of the use of PSK, there is no fake peak in the BGS.
Fig. 6.
Fig. 6. Experimental setup of the phase-coded BOCDA based on phase-shift keying. PC, polarization controller; AWG, arbitrary waveform generator; AFG, arbitrary function generator; EOM, electro-optic modulator; MZM, Mach-Zehnder modulator; SSBM, single-sideband modulator; MG, microwave generator; EDFA, erbium-doped fiber amplifier; FUT, fiber under test; PD, photodetector; OSC, oscilloscope.
Fig. 7.
Fig. 7. Detected signal trace at different AWG sampling rates for phase coding using (a) a 40-GHz phase modulator and (b) a 20-GHz MZM. The sampling rate of the AWG varied from 10 GS/s to 50 GS/s, corresponding to the theoretical spatial resolution changing from 10 mm to 2 mm. When the sampling rate goes higher, it gets harder to retrieve the Brillouin echo wave (marked with red circles) in the correlation peak when using the phase modulator. But for 50 GS/s, the effective Brillouin signal can be recognized using the BOCDA based on PSK.
Fig. 8.
Fig. 8. (a) Measured Brillouin gain spectrum in the vicinity of the spliced joint of the fiber under test (b) Reconstructed local BFS.
Fig. 9.
Fig. 9. (a) The layout of FUT. (b) The measured BGS distribution. (c) The demodulated BFS distribution.

Equations (3)

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h = cos [ π 2 V m ( t ) V π RF + π 2 V DC V π DC ]
h =  -  sin [ π 2 V m ( t ) V π R F ]
E out = e i ϕ 0 E in h = e i ϕ 0 E in { sin [ π 2 V m ( t ) V π RF ] ,   V m ( t ) 0 e  - i π sin [ π 2 | V m ( t ) | V π RF ] ,   V m ( t ) < 0  

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