Abstract

We experimentally investigate the dynamics of backscattered light due to stimulated Brillouin scattering (SBS) in a narrow-linewidth continuous wave (CW) fiber amplifier. We observe the onset of sharp intensity variations in the backscattered radiation as we increase the pump power, which when analyzed using Karl-Pearson’s correlation coefficient reveals a distinct structure. We find that such structure is associated with the onset of stimulated Brillouin scattering (SBS) in the fiber amplifier. Moreover, at higher pump power levels we observe a periodic signature in the Karl-Pearson correlation trace that precedes an observation of kW pulses in the backscattered radiation. Based on controlled experiments, we conclude that the formation of the above kW pulses in our system is preceded by the onset of SBS.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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  1. R. Su, P. Zhou, X. Wang, Y. Ma, and X. Xu, “Active coherent beam combination of two high-power single-frequency nanosecond fiber amplifiers,” Opt. Lett. 37, 497–499 (2012).
    [Crossref] [PubMed]
  2. J. Shi, G. Li, W. Gong, J. Bai, Y. Huang, Y. Liu, S. Li, and D. Liu, “A lidar system based on stimulated Brillouin scattering,” Appl. Phys. B 86, 177–179 (2007).
    [Crossref]
  3. R. Su, P. Zhou, X. Wang, H. Lü, and X. Xu, “Nanosecond pulse pumped, narrow linewidth all-fiber Raman amplifier with stimulated Brillouin scattering suppression,” J. Opt. 16, 015201 (2014).
    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref]

2018 (1)

Y. Panbiharwala, A. Ghosh, J. Nilsson, D. Venkitesh, and B. Srinivasan, “Experimental investigation of the onset of modulation instability as a precursor for the stimulated Brillouin scattering in Yb-doped fiber amplifiers,” Proc. SPIE 10512, 105122X (2018).

2017 (1)

P. Hanzard, M. Talbi, D. Mallek, A. Kellou, H. Leblond, F. Sanchez, T. Godin, and A. Hideur, “Brillouin scattering-induced rogue waves in self-pulsing fiber lasers,” Scientific Reports 7, 45868 (2017).
[Crossref]

2015 (1)

Y. Tang and J. Xu, “A random Q-switched fiber laser,” Scientific Reports 5, 9338 (2015).
[Crossref] [PubMed]

2014 (1)

R. Su, P. Zhou, X. Wang, H. Lü, and X. Xu, “Nanosecond pulse pumped, narrow linewidth all-fiber Raman amplifier with stimulated Brillouin scattering suppression,” J. Opt. 16, 015201 (2014).
[Crossref]

2013 (2)

M. Melo, M. O. Berendt, and J. M. Sousa, “Destructive random backscattering pulses showing Brillouin signature in MOPA fiber laser systems,” Proc. SPIE 8601, 86011P (2013).
[Crossref]

A. V Kiryanov, Y. O. Barmenkov, and M. V Andres, “An experimental analysis of self-Q-switching via stimulated Brillouin scattering in an ytterbium doped fiber laser,” Laser Phys. Lett. 10, 055112 (2013).
[Crossref]

2012 (2)

2011 (1)

2010 (3)

2007 (1)

J. Shi, G. Li, W. Gong, J. Bai, Y. Huang, Y. Liu, S. Li, and D. Liu, “A lidar system based on stimulated Brillouin scattering,” Appl. Phys. B 86, 177–179 (2007).
[Crossref]

2003 (1)

1995 (1)

R. G. Harrison, D. Yu, W. Lu, and P. M. Ripley, “Chaotic stimulated Brillouin scattering: theory and experiment,” Physica D: Nonlinear Phenomena 86, 182188 (1995).
[Crossref]

1991 (1)

A. L. Gaeta and R. W. Boyd, “Stochastic Dynamics of Stimulated Brillouin Scattering in an Optical Fiber,” Phys. Rev. A 44, 3205–3209 (1991).
[Crossref] [PubMed]

1990 (2)

R. G. Harrison, J. S. Uppal, A. Johnstone, and J. V. Moloney, “Evidence of chaotic stimulated Brillouin scattering in optical fibers,” Phys. Rev. Lett. 65, 167–170 (1990).
[Crossref] [PubMed]

R. W. Boyd, K. Rzaewski, and P. Narum, “Noise initiation of stimulated Brillouin scattering,” Phys. Rev. A 42, 5514–5521 (1990).
[Crossref] [PubMed]

1972 (2)

Andres, M. V

A. V Kiryanov, Y. O. Barmenkov, and M. V Andres, “An experimental analysis of self-Q-switching via stimulated Brillouin scattering in an ytterbium doped fiber laser,” Laser Phys. Lett. 10, 055112 (2013).
[Crossref]

Augst, S. J.

Bai, J.

J. Shi, G. Li, W. Gong, J. Bai, Y. Huang, Y. Liu, S. Li, and D. Liu, “A lidar system based on stimulated Brillouin scattering,” Appl. Phys. B 86, 177–179 (2007).
[Crossref]

Barmenkov, Y. O.

A. V Kiryanov, Y. O. Barmenkov, and M. V Andres, “An experimental analysis of self-Q-switching via stimulated Brillouin scattering in an ytterbium doped fiber laser,” Laser Phys. Lett. 10, 055112 (2013).
[Crossref]

Berendt, M. O.

M. Melo, M. O. Berendt, and J. M. Sousa, “Destructive random backscattering pulses showing Brillouin signature in MOPA fiber laser systems,” Proc. SPIE 8601, 86011P (2013).
[Crossref]

Boyd, R. W.

A. L. Gaeta and R. W. Boyd, “Stochastic Dynamics of Stimulated Brillouin Scattering in an Optical Fiber,” Phys. Rev. A 44, 3205–3209 (1991).
[Crossref] [PubMed]

R. W. Boyd, K. Rzaewski, and P. Narum, “Noise initiation of stimulated Brillouin scattering,” Phys. Rev. A 42, 5514–5521 (1990).
[Crossref] [PubMed]

Calia, D. B.

Chowdhury, D.

Clarkson, W. A.

Dajani, I.

Derickson, D.

D. Derickson, Fiber Optic Test and Measurement(Prentice Hall PTR1998).

Fan, T. Y.

Feng, Y.

Flannery, B.

W. H. Press, S. A. Teukolsky, B. Flannery, and B. P. Flannery, Numerical Recipes in C(Cambridge University1992).

Flannery, B. P.

W. H. Press, S. A. Teukolsky, B. Flannery, and B. P. Flannery, Numerical Recipes in C(Cambridge University1992).

Gaeta, A. L.

A. L. Gaeta and R. W. Boyd, “Stochastic Dynamics of Stimulated Brillouin Scattering in an Optical Fiber,” Phys. Rev. A 44, 3205–3209 (1991).
[Crossref] [PubMed]

Ghosh, A.

Y. Panbiharwala, A. Ghosh, J. Nilsson, D. Venkitesh, and B. Srinivasan, “Experimental investigation of the onset of modulation instability as a precursor for the stimulated Brillouin scattering in Yb-doped fiber amplifiers,” Proc. SPIE 10512, 105122X (2018).

Godin, T.

P. Hanzard, M. Talbi, D. Mallek, A. Kellou, H. Leblond, F. Sanchez, T. Godin, and A. Hideur, “Brillouin scattering-induced rogue waves in self-pulsing fiber lasers,” Scientific Reports 7, 45868 (2017).
[Crossref]

Goldizen, K. C.

Gong, W.

J. Shi, G. Li, W. Gong, J. Bai, Y. Huang, Y. Liu, S. Li, and D. Liu, “A lidar system based on stimulated Brillouin scattering,” Appl. Phys. B 86, 177–179 (2007).
[Crossref]

Hanzard, P.

P. Hanzard, M. Talbi, D. Mallek, A. Kellou, H. Leblond, F. Sanchez, T. Godin, and A. Hideur, “Brillouin scattering-induced rogue waves in self-pulsing fiber lasers,” Scientific Reports 7, 45868 (2017).
[Crossref]

Harrison, R. G.

R. G. Harrison, D. Yu, W. Lu, and P. M. Ripley, “Chaotic stimulated Brillouin scattering: theory and experiment,” Physica D: Nonlinear Phenomena 86, 182188 (1995).
[Crossref]

R. G. Harrison, J. S. Uppal, A. Johnstone, and J. V. Moloney, “Evidence of chaotic stimulated Brillouin scattering in optical fibers,” Phys. Rev. Lett. 65, 167–170 (1990).
[Crossref] [PubMed]

Hideur, A.

P. Hanzard, M. Talbi, D. Mallek, A. Kellou, H. Leblond, F. Sanchez, T. Godin, and A. Hideur, “Brillouin scattering-induced rogue waves in self-pulsing fiber lasers,” Scientific Reports 7, 45868 (2017).
[Crossref]

Huang, Y.

J. Shi, G. Li, W. Gong, J. Bai, Y. Huang, Y. Liu, S. Li, and D. Liu, “A lidar system based on stimulated Brillouin scattering,” Appl. Phys. B 86, 177–179 (2007).
[Crossref]

Ippen, E.P.

E.P. Ippen and R.H. Stolen, “Stimulated Brillouin scattering in optical fibers,” Appl. Phys. Lett. 21, 539 (1972).
[Crossref]

Johnstone, A.

R. G. Harrison, J. S. Uppal, A. Johnstone, and J. V. Moloney, “Evidence of chaotic stimulated Brillouin scattering in optical fibers,” Phys. Rev. Lett. 65, 167–170 (1990).
[Crossref] [PubMed]

Kellou, A.

P. Hanzard, M. Talbi, D. Mallek, A. Kellou, H. Leblond, F. Sanchez, T. Godin, and A. Hideur, “Brillouin scattering-induced rogue waves in self-pulsing fiber lasers,” Scientific Reports 7, 45868 (2017).
[Crossref]

Kiryanov, A. V

A. V Kiryanov, Y. O. Barmenkov, and M. V Andres, “An experimental analysis of self-Q-switching via stimulated Brillouin scattering in an ytterbium doped fiber laser,” Laser Phys. Lett. 10, 055112 (2013).
[Crossref]

Kobyakov, A.

Leblond, H.

P. Hanzard, M. Talbi, D. Mallek, A. Kellou, H. Leblond, F. Sanchez, T. Godin, and A. Hideur, “Brillouin scattering-induced rogue waves in self-pulsing fiber lasers,” Scientific Reports 7, 45868 (2017).
[Crossref]

Li, G.

J. Shi, G. Li, W. Gong, J. Bai, Y. Huang, Y. Liu, S. Li, and D. Liu, “A lidar system based on stimulated Brillouin scattering,” Appl. Phys. B 86, 177–179 (2007).
[Crossref]

Li, S.

J. Shi, G. Li, W. Gong, J. Bai, Y. Huang, Y. Liu, S. Li, and D. Liu, “A lidar system based on stimulated Brillouin scattering,” Appl. Phys. B 86, 177–179 (2007).
[Crossref]

Liem, A.

Limpert, J.

Liu, D.

J. Shi, G. Li, W. Gong, J. Bai, Y. Huang, Y. Liu, S. Li, and D. Liu, “A lidar system based on stimulated Brillouin scattering,” Appl. Phys. B 86, 177–179 (2007).
[Crossref]

Liu, Y.

J. Shi, G. Li, W. Gong, J. Bai, Y. Huang, Y. Liu, S. Li, and D. Liu, “A lidar system based on stimulated Brillouin scattering,” Appl. Phys. B 86, 177–179 (2007).
[Crossref]

Lu, W.

R. G. Harrison, D. Yu, W. Lu, and P. M. Ripley, “Chaotic stimulated Brillouin scattering: theory and experiment,” Physica D: Nonlinear Phenomena 86, 182188 (1995).
[Crossref]

Lü, H.

R. Su, P. Zhou, X. Wang, H. Lü, and X. Xu, “Nanosecond pulse pumped, narrow linewidth all-fiber Raman amplifier with stimulated Brillouin scattering suppression,” J. Opt. 16, 015201 (2014).
[Crossref]

Ma, Y.

Mallek, D.

P. Hanzard, M. Talbi, D. Mallek, A. Kellou, H. Leblond, F. Sanchez, T. Godin, and A. Hideur, “Brillouin scattering-induced rogue waves in self-pulsing fiber lasers,” Scientific Reports 7, 45868 (2017).
[Crossref]

Melo, M.

M. Melo, M. O. Berendt, and J. M. Sousa, “Destructive random backscattering pulses showing Brillouin signature in MOPA fiber laser systems,” Proc. SPIE 8601, 86011P (2013).
[Crossref]

Moloney, J. V.

R. G. Harrison, J. S. Uppal, A. Johnstone, and J. V. Moloney, “Evidence of chaotic stimulated Brillouin scattering in optical fibers,” Phys. Rev. Lett. 65, 167–170 (1990).
[Crossref] [PubMed]

Moore, G. T.

Murphy, D. V.

Naderi, S.

Narum, P.

R. W. Boyd, K. Rzaewski, and P. Narum, “Noise initiation of stimulated Brillouin scattering,” Phys. Rev. A 42, 5514–5521 (1990).
[Crossref] [PubMed]

Nilsson, J.

Y. Panbiharwala, A. Ghosh, J. Nilsson, D. Venkitesh, and B. Srinivasan, “Experimental investigation of the onset of modulation instability as a precursor for the stimulated Brillouin scattering in Yb-doped fiber amplifiers,” Proc. SPIE 10512, 105122X (2018).

D. J. Richardson, J. Nilsson, and W. A. Clarkson, “High power fiber lasers: current status and future perspectives [Invited],” J. Opt. Soc. Am. B 27, B63–B92 (2010).
[Crossref]

Panbiharwala, Y.

Y. Panbiharwala, A. Ghosh, J. Nilsson, D. Venkitesh, and B. Srinivasan, “Experimental investigation of the onset of modulation instability as a precursor for the stimulated Brillouin scattering in Yb-doped fiber amplifiers,” Proc. SPIE 10512, 105122X (2018).

Press, W. H.

W. H. Press, S. A. Teukolsky, B. Flannery, and B. P. Flannery, Numerical Recipes in C(Cambridge University1992).

Redmond, S. M.

Richardson, D. J.

Ripley, P. M.

R. G. Harrison, D. Yu, W. Lu, and P. M. Ripley, “Chaotic stimulated Brillouin scattering: theory and experiment,” Physica D: Nonlinear Phenomena 86, 182188 (1995).
[Crossref]

Robin, C.

Rzaewski, K.

R. W. Boyd, K. Rzaewski, and P. Narum, “Noise initiation of stimulated Brillouin scattering,” Phys. Rev. A 42, 5514–5521 (1990).
[Crossref] [PubMed]

Sanchez, A.

Sanchez, F.

P. Hanzard, M. Talbi, D. Mallek, A. Kellou, H. Leblond, F. Sanchez, T. Godin, and A. Hideur, “Brillouin scattering-induced rogue waves in self-pulsing fiber lasers,” Scientific Reports 7, 45868 (2017).
[Crossref]

Sauer, M.

Shi, J.

J. Shi, G. Li, W. Gong, J. Bai, Y. Huang, Y. Liu, S. Li, and D. Liu, “A lidar system based on stimulated Brillouin scattering,” Appl. Phys. B 86, 177–179 (2007).
[Crossref]

Smith, R. G.

Sousa, J. M.

M. Melo, M. O. Berendt, and J. M. Sousa, “Destructive random backscattering pulses showing Brillouin signature in MOPA fiber laser systems,” Proc. SPIE 8601, 86011P (2013).
[Crossref]

Srinivasan, B.

Y. Panbiharwala, A. Ghosh, J. Nilsson, D. Venkitesh, and B. Srinivasan, “Experimental investigation of the onset of modulation instability as a precursor for the stimulated Brillouin scattering in Yb-doped fiber amplifiers,” Proc. SPIE 10512, 105122X (2018).

Stolen, R.H.

E.P. Ippen and R.H. Stolen, “Stimulated Brillouin scattering in optical fibers,” Appl. Phys. Lett. 21, 539 (1972).
[Crossref]

Su, R.

R. Su, P. Zhou, X. Wang, H. Lü, and X. Xu, “Nanosecond pulse pumped, narrow linewidth all-fiber Raman amplifier with stimulated Brillouin scattering suppression,” J. Opt. 16, 015201 (2014).
[Crossref]

R. Su, P. Zhou, X. Wang, Y. Ma, and X. Xu, “Active coherent beam combination of two high-power single-frequency nanosecond fiber amplifiers,” Opt. Lett. 37, 497–499 (2012).
[Crossref] [PubMed]

Talbi, M.

P. Hanzard, M. Talbi, D. Mallek, A. Kellou, H. Leblond, F. Sanchez, T. Godin, and A. Hideur, “Brillouin scattering-induced rogue waves in self-pulsing fiber lasers,” Scientific Reports 7, 45868 (2017).
[Crossref]

Tang, Y.

Y. Tang and J. Xu, “A random Q-switched fiber laser,” Scientific Reports 5, 9338 (2015).
[Crossref] [PubMed]

Taylor, L. R.

Teukolsky, S. A.

W. H. Press, S. A. Teukolsky, B. Flannery, and B. P. Flannery, Numerical Recipes in C(Cambridge University1992).

Tünnermann, A

Uppal, J. S.

R. G. Harrison, J. S. Uppal, A. Johnstone, and J. V. Moloney, “Evidence of chaotic stimulated Brillouin scattering in optical fibers,” Phys. Rev. Lett. 65, 167–170 (1990).
[Crossref] [PubMed]

Venkitesh, D.

Y. Panbiharwala, A. Ghosh, J. Nilsson, D. Venkitesh, and B. Srinivasan, “Experimental investigation of the onset of modulation instability as a precursor for the stimulated Brillouin scattering in Yb-doped fiber amplifiers,” Proc. SPIE 10512, 105122X (2018).

Wang, X.

R. Su, P. Zhou, X. Wang, H. Lü, and X. Xu, “Nanosecond pulse pumped, narrow linewidth all-fiber Raman amplifier with stimulated Brillouin scattering suppression,” J. Opt. 16, 015201 (2014).
[Crossref]

R. Su, P. Zhou, X. Wang, Y. Ma, and X. Xu, “Active coherent beam combination of two high-power single-frequency nanosecond fiber amplifiers,” Opt. Lett. 37, 497–499 (2012).
[Crossref] [PubMed]

Xu, J.

Y. Tang and J. Xu, “A random Q-switched fiber laser,” Scientific Reports 5, 9338 (2015).
[Crossref] [PubMed]

Xu, X.

R. Su, P. Zhou, X. Wang, H. Lü, and X. Xu, “Nanosecond pulse pumped, narrow linewidth all-fiber Raman amplifier with stimulated Brillouin scattering suppression,” J. Opt. 16, 015201 (2014).
[Crossref]

R. Su, P. Zhou, X. Wang, Y. Ma, and X. Xu, “Active coherent beam combination of two high-power single-frequency nanosecond fiber amplifiers,” Opt. Lett. 37, 497–499 (2012).
[Crossref] [PubMed]

Yu, C. X.

Yu, D.

R. G. Harrison, D. Yu, W. Lu, and P. M. Ripley, “Chaotic stimulated Brillouin scattering: theory and experiment,” Physica D: Nonlinear Phenomena 86, 182188 (1995).
[Crossref]

Zellmer, H.

Zeringue, C.

Zhou, P.

R. Su, P. Zhou, X. Wang, H. Lü, and X. Xu, “Nanosecond pulse pumped, narrow linewidth all-fiber Raman amplifier with stimulated Brillouin scattering suppression,” J. Opt. 16, 015201 (2014).
[Crossref]

R. Su, P. Zhou, X. Wang, Y. Ma, and X. Xu, “Active coherent beam combination of two high-power single-frequency nanosecond fiber amplifiers,” Opt. Lett. 37, 497–499 (2012).
[Crossref] [PubMed]

Adv. Opt. Photon. (1)

Appl. Opt. (1)

Appl. Phys. B (1)

J. Shi, G. Li, W. Gong, J. Bai, Y. Huang, Y. Liu, S. Li, and D. Liu, “A lidar system based on stimulated Brillouin scattering,” Appl. Phys. B 86, 177–179 (2007).
[Crossref]

Appl. Phys. Lett. (1)

E.P. Ippen and R.H. Stolen, “Stimulated Brillouin scattering in optical fibers,” Appl. Phys. Lett. 21, 539 (1972).
[Crossref]

J. Opt. (1)

R. Su, P. Zhou, X. Wang, H. Lü, and X. Xu, “Nanosecond pulse pumped, narrow linewidth all-fiber Raman amplifier with stimulated Brillouin scattering suppression,” J. Opt. 16, 015201 (2014).
[Crossref]

J. Opt. Soc. Am. B (1)

Laser Phys. Lett. (1)

A. V Kiryanov, Y. O. Barmenkov, and M. V Andres, “An experimental analysis of self-Q-switching via stimulated Brillouin scattering in an ytterbium doped fiber laser,” Laser Phys. Lett. 10, 055112 (2013).
[Crossref]

Opt. Express (2)

Opt. Lett. (3)

Phys. Rev. A (2)

R. W. Boyd, K. Rzaewski, and P. Narum, “Noise initiation of stimulated Brillouin scattering,” Phys. Rev. A 42, 5514–5521 (1990).
[Crossref] [PubMed]

A. L. Gaeta and R. W. Boyd, “Stochastic Dynamics of Stimulated Brillouin Scattering in an Optical Fiber,” Phys. Rev. A 44, 3205–3209 (1991).
[Crossref] [PubMed]

Phys. Rev. Lett. (1)

R. G. Harrison, J. S. Uppal, A. Johnstone, and J. V. Moloney, “Evidence of chaotic stimulated Brillouin scattering in optical fibers,” Phys. Rev. Lett. 65, 167–170 (1990).
[Crossref] [PubMed]

Physica D: Nonlinear Phenomena (1)

R. G. Harrison, D. Yu, W. Lu, and P. M. Ripley, “Chaotic stimulated Brillouin scattering: theory and experiment,” Physica D: Nonlinear Phenomena 86, 182188 (1995).
[Crossref]

Proc. SPIE (2)

Y. Panbiharwala, A. Ghosh, J. Nilsson, D. Venkitesh, and B. Srinivasan, “Experimental investigation of the onset of modulation instability as a precursor for the stimulated Brillouin scattering in Yb-doped fiber amplifiers,” Proc. SPIE 10512, 105122X (2018).

M. Melo, M. O. Berendt, and J. M. Sousa, “Destructive random backscattering pulses showing Brillouin signature in MOPA fiber laser systems,” Proc. SPIE 8601, 86011P (2013).
[Crossref]

Scientific Reports (2)

Y. Tang and J. Xu, “A random Q-switched fiber laser,” Scientific Reports 5, 9338 (2015).
[Crossref] [PubMed]

P. Hanzard, M. Talbi, D. Mallek, A. Kellou, H. Leblond, F. Sanchez, T. Godin, and A. Hideur, “Brillouin scattering-induced rogue waves in self-pulsing fiber lasers,” Scientific Reports 7, 45868 (2017).
[Crossref]

Other (2)

D. Derickson, Fiber Optic Test and Measurement(Prentice Hall PTR1998).

W. H. Press, S. A. Teukolsky, B. Flannery, and B. P. Flannery, Numerical Recipes in C(Cambridge University1992).

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Figures (7)

Fig. 1
Fig. 1 Schematic of the master-oscillator power amplifier (MOPA) showing three stages of signal amplification, i.e. fiber amplifier 1 (FA1), fiber amplifier 2 (FA2) and fiber amplifier 3 (FA3). DFB: distributed feedback laser, PM: phase modulator, I: Isolator, Yb: Ytterbium, CPS: cladding pump stripper.
Fig. 2
Fig. 2 Plot of the output signal power (left axis) and SBS Stokes power (right axis) vs input pump power (FA3) with marking of the initiation of SBS and kW pulsing.
Fig. 3
Fig. 3 Plot of the temporal trace of the backscattered light captured with a fast photodiode for different output signal powers of (a) 12 W, (b) 18 W, and (c) 32 W, (d) plot of Karl Pearson’s co-efficient vs. the lag.
Fig. 4
Fig. 4 Plot of correlation coefficient 3-dB width (left axis) and SBS Stokes power (right axis) vs output signal power (FA3).
Fig. 5
Fig. 5 (a) Plot of backscattered kW peak power pulses against time, the inset shows the zoomed in plot of (a) showing the detector saturation due high peak power and (b) backward spectrum captured with resolution bandwidth of 1 nm showing the increase in the Raman scattering with increasing output signal power.
Fig. 6
Fig. 6 (a) Plot of the backscattered SBS Stokes power against the output signal power for different modulation depths and (b) Karl Pearson correlation coefficient (AL) plotted against the time lag for different output signal power at which the kW peak power pulses are initiated for different modulation depths.
Fig. 7
Fig. 7 (a) Plot of the output signal power (left axis) and backscattered SBS Stokes power (right axis) against the input signal power (Brillouin pump power) for a 18 m long Hi1060 fiber and (b) Temporal trace of the backscattered power in the passive fiber at (b) 2 W and (c) 2.4 W, and (d) Karl Pearson correlation coefficient plotted against the time lag for different input signal power levels.

Equations (1)

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A L = r = 1 N L ( x r x ¯ ) ( x r + L x ¯ ) r = 1 N ( x r x ¯ ) 2