Abstract

The polarization dependent fluctuation of Brillouin frequency shift (BFS) of stimulated Brillouin scattering (SBS) in practical single mode fibers (SMFs) is reported. The phenomenon is actually caused by the interference of the low birefringence in SMF with the SBS spectral polarization spreading of the signal light. The performance of the polarization dependent BFS fluctuation is studied by simulation and confirmed with agreeable experimental results.

© 2017 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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Vector analysis of stimulated Brillouin scattering amplification in standard single-mode fibers

Avi Zadok, Elad Zilka, Avishay Eyal, Luc Thévenaz, and Moshe Tur
Opt. Express 16(26) 21692-21707 (2008)

References

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  1. O. Shlomovits and M. Tur, “Vector analysis of depleted stimulated Brillouin scattering amplification in standard single-mode fibers with nonzero birefringence,” Opt. Lett. 38(6), 836–838 (2013).
    [PubMed]
  2. A. Zadok, S. Chin, L. Thévenaz, E. Zilka, A. Eyal, and M. Tur, “Polarization-induced distortion in stimulated Brillouin scattering slow-light systems,” Opt. Lett. 34(16), 2530–2532 (2009).
    [PubMed]
  3. S. Xie, M. Pang, X. Bao, and L. Chen, “Polarization dependence of Brillouin linewidth and peak frequency due to fiber inhomogeneity in single mode fiber and its impact on distributed fiber Brillouin sensing,” Opt. Express 20(6), 6385–6399 (2012).
    [PubMed]
  4. X. Bao and L. Chen, “Recent progress in optical fiber sensors based on Brillouin scattering at university of Ottawa,” Photonics Sens. 1(2), 102–117 (2011).
  5. D. Zhou, Y. Dong, B. Wang, T. Jiang, D. Ba, P. Xu, H. Zhang, Z. Lu, and H. Li, “Slope-assisted BOTDA based on vector SBS and frequency-agile technique for wide-strain-range dynamic measurements,” Opt. Express 25(3), 1889–1902 (2017).
  6. S. Preussler and T. Schneider, “Attometer resolution spectral analysis based on polarization pulling assisted Brillouin scattering merged with heterodyne detection,” Opt. Express 23(20), 26879–26887 (2015).
    [PubMed]
  7. L. Thévenaz, S. F. Mafang, and J. Lin, “Effect of pulse depletion in a Brillouin optical time-domain analysis system,” Opt. Express 21(12), 14017–14035 (2013).
    [PubMed]
  8. Y. Dong, L. Chen, and X. Bao, “System optimization of a long-range Brillouin-loss-based distributed fiber sensor,” Appl. Opt. 49(27), 5020–5025 (2010).
    [PubMed]
  9. W. Zou, Z. He, and K. Hotate, “Two-Dimensional Finite-Element Modal Analysis of Brillouin Gain Spectra in Optical Fibers,” IEEE Photonics Technol. Lett. 18(23), 2487–2489 (2006).
  10. C. Wang, Q. Zhang, C. Mou, L. Chen, and X. Bao, “Spectral Polarization Spreading Behaviors in Stimulated Brillouin Scattering of Fibers,” IEEE Photonics J. 9(1), 6100111 (2017).
  11. A. Zadok, E. Zilka, A. Eyal, L. Thévenaz, and M. Tur, “Vector analysis of stimulated Brillouin scattering amplification in standard single-mode fibers,” Opt. Express 16(26), 21692–21707 (2008).
    [PubMed]

2017 (2)

D. Zhou, Y. Dong, B. Wang, T. Jiang, D. Ba, P. Xu, H. Zhang, Z. Lu, and H. Li, “Slope-assisted BOTDA based on vector SBS and frequency-agile technique for wide-strain-range dynamic measurements,” Opt. Express 25(3), 1889–1902 (2017).

C. Wang, Q. Zhang, C. Mou, L. Chen, and X. Bao, “Spectral Polarization Spreading Behaviors in Stimulated Brillouin Scattering of Fibers,” IEEE Photonics J. 9(1), 6100111 (2017).

2015 (1)

2013 (2)

2012 (1)

2011 (1)

X. Bao and L. Chen, “Recent progress in optical fiber sensors based on Brillouin scattering at university of Ottawa,” Photonics Sens. 1(2), 102–117 (2011).

2010 (1)

2009 (1)

2008 (1)

2006 (1)

W. Zou, Z. He, and K. Hotate, “Two-Dimensional Finite-Element Modal Analysis of Brillouin Gain Spectra in Optical Fibers,” IEEE Photonics Technol. Lett. 18(23), 2487–2489 (2006).

Ba, D.

Bao, X.

C. Wang, Q. Zhang, C. Mou, L. Chen, and X. Bao, “Spectral Polarization Spreading Behaviors in Stimulated Brillouin Scattering of Fibers,” IEEE Photonics J. 9(1), 6100111 (2017).

S. Xie, M. Pang, X. Bao, and L. Chen, “Polarization dependence of Brillouin linewidth and peak frequency due to fiber inhomogeneity in single mode fiber and its impact on distributed fiber Brillouin sensing,” Opt. Express 20(6), 6385–6399 (2012).
[PubMed]

X. Bao and L. Chen, “Recent progress in optical fiber sensors based on Brillouin scattering at university of Ottawa,” Photonics Sens. 1(2), 102–117 (2011).

Y. Dong, L. Chen, and X. Bao, “System optimization of a long-range Brillouin-loss-based distributed fiber sensor,” Appl. Opt. 49(27), 5020–5025 (2010).
[PubMed]

Chen, L.

C. Wang, Q. Zhang, C. Mou, L. Chen, and X. Bao, “Spectral Polarization Spreading Behaviors in Stimulated Brillouin Scattering of Fibers,” IEEE Photonics J. 9(1), 6100111 (2017).

S. Xie, M. Pang, X. Bao, and L. Chen, “Polarization dependence of Brillouin linewidth and peak frequency due to fiber inhomogeneity in single mode fiber and its impact on distributed fiber Brillouin sensing,” Opt. Express 20(6), 6385–6399 (2012).
[PubMed]

X. Bao and L. Chen, “Recent progress in optical fiber sensors based on Brillouin scattering at university of Ottawa,” Photonics Sens. 1(2), 102–117 (2011).

Y. Dong, L. Chen, and X. Bao, “System optimization of a long-range Brillouin-loss-based distributed fiber sensor,” Appl. Opt. 49(27), 5020–5025 (2010).
[PubMed]

Chin, S.

Dong, Y.

Eyal, A.

He, Z.

W. Zou, Z. He, and K. Hotate, “Two-Dimensional Finite-Element Modal Analysis of Brillouin Gain Spectra in Optical Fibers,” IEEE Photonics Technol. Lett. 18(23), 2487–2489 (2006).

Hotate, K.

W. Zou, Z. He, and K. Hotate, “Two-Dimensional Finite-Element Modal Analysis of Brillouin Gain Spectra in Optical Fibers,” IEEE Photonics Technol. Lett. 18(23), 2487–2489 (2006).

Jiang, T.

Li, H.

Lin, J.

Lu, Z.

Mafang, S. F.

Mou, C.

C. Wang, Q. Zhang, C. Mou, L. Chen, and X. Bao, “Spectral Polarization Spreading Behaviors in Stimulated Brillouin Scattering of Fibers,” IEEE Photonics J. 9(1), 6100111 (2017).

Pang, M.

Preussler, S.

Schneider, T.

Shlomovits, O.

Thévenaz, L.

Tur, M.

Wang, B.

Wang, C.

C. Wang, Q. Zhang, C. Mou, L. Chen, and X. Bao, “Spectral Polarization Spreading Behaviors in Stimulated Brillouin Scattering of Fibers,” IEEE Photonics J. 9(1), 6100111 (2017).

Xie, S.

Xu, P.

Zadok, A.

Zhang, H.

Zhang, Q.

C. Wang, Q. Zhang, C. Mou, L. Chen, and X. Bao, “Spectral Polarization Spreading Behaviors in Stimulated Brillouin Scattering of Fibers,” IEEE Photonics J. 9(1), 6100111 (2017).

Zhou, D.

Zilka, E.

Zou, W.

W. Zou, Z. He, and K. Hotate, “Two-Dimensional Finite-Element Modal Analysis of Brillouin Gain Spectra in Optical Fibers,” IEEE Photonics Technol. Lett. 18(23), 2487–2489 (2006).

Appl. Opt. (1)

IEEE Photonics J. (1)

C. Wang, Q. Zhang, C. Mou, L. Chen, and X. Bao, “Spectral Polarization Spreading Behaviors in Stimulated Brillouin Scattering of Fibers,” IEEE Photonics J. 9(1), 6100111 (2017).

IEEE Photonics Technol. Lett. (1)

W. Zou, Z. He, and K. Hotate, “Two-Dimensional Finite-Element Modal Analysis of Brillouin Gain Spectra in Optical Fibers,” IEEE Photonics Technol. Lett. 18(23), 2487–2489 (2006).

Opt. Express (5)

Opt. Lett. (2)

Photonics Sens. (1)

X. Bao and L. Chen, “Recent progress in optical fiber sensors based on Brillouin scattering at university of Ottawa,” Photonics Sens. 1(2), 102–117 (2011).

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Figures (8)

Fig. 1
Fig. 1 (a) The symmetrical distinct SBS pulling force on s ^ ξ when β l =0; (b) The synthetization of the SBS pulling and birefringence evolution forces on s ^ ξ .
Fig. 2
Fig. 2 (a) The simulated Δ ξ B s of 100- p ^ in by 100- s ^ in for a 100 m SMF with a birefringence realization of beat length of 40 m and birefringence correlation length of 10 m. (b) The histogram of the simulated Δ ξ B . (c) The mean and STD of Δ ξ B s for fixing s ^ in and p ^ in with respect to 100- p ^ in and 100- s ^ in , respectively. (d) The scatter of Δ ξ B with respect to the corresponding SBS gain.
Fig. 3
Fig. 3 Simulations for p ^ in max with 6 groups of regularly chosen s ^ in s. (a) Front view of polarization spreadings against s ^ out max , and (b) corresponding Δ ξ B s of the 6-group of s ^ in s. (c) SBS gain spectrums corresponding to s ^ in1 , s ^ in11 , s ^ in9 and s ^ in12 of group #1. (d) The enlarged central region of SBS gain spectrums. (e) Δ ξ B vs. s ^ in s of group #1 for different pump powers. (f) The relationship between the variation range of Δ ξ B and the pump power.
Fig. 4
Fig. 4 Experimental setup, in which, PC: polarization controller; P: polarizer; HWP: half-wave plate; QWP: quarter-wave plate; FBG: fiber Bragg grating; EDFA: Erbium–doped fiber amplifier; ISO: isolator; EOM: electro-optical modulator; PSA: polarization state analyzer.
Fig. 5
Fig. 5 (a) The front view of the measured s ^ -spreadings of six groups of s ^ in s against s ^ out max . (b) Measured Δ ν B s vs. the rotation angle of HWP1. (c) Measured SBS gain spectrums corresponding to s ^ in1 , s ^ in8 , s ^ in10 , and s ^ in12 of group #3. (d) The enlarged central region of (c).
Fig. 6
Fig. 6 (a) Measured Δ ν B curves for s ^ in s of group #3 under different pump powers. (b) Measured relationship between the largest Δ ν B difference and pump power.
Fig. 7
Fig. 7 (a) Simulated PDFs of Δ ξ B for different fiber lengths. (b) Relationships of the mean, STD, and the range of Δ ξ B vs. the fiber length.
Fig. 8
Fig. 8 Measured Δ ν B with a 25 m SMF for (a) p ^ in max and (b) a randomly chosen p ^ in cooperating with 6-group of regularly set s ^ in s. The simulated Δ ξ B with a 25 m fiber with constant Lb = 50 m for (c) p ^ in near p ^ in max by p ^ in p ^ max in =0.979, and (d) p ^ in by p ^ in p ^ max in =0.7632.

Equations (7)

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d I s dz = d I p dz = r 0 I p I s 1+ ξ 2 (1+ s ^ p ^ );
d p ^ dz β p × p ^ ;
d s ^ dz = β s × s ^ + r 0 I p 1+ ξ 2 [ p ^ ( s ^ p ^ ) s ^ ]+ r 0 ξ 1+ ξ 2 I p ( s ^ × p ^ ).
G( ξ )= e r 0 I p 1+ ξ 2 ( L+ 0 L ( s ^ ξ p ^ )dz ) ,
d( s ^ ξ p ^ ) dz =2 β l ( s ^ ξ × p ^ )+ r 0 I p 1+ ξ 2 [ 1 ( s ^ ξ p ^ ) 2 ].
s ^ ξ . p ^ = (1+ u 0 ) e 2 κ ξ L (1 u 0 ) (1+ u 0 ) e 2 κ ξ L +(1 u 0 ) ,
Δ ξ B =2Δ ν B / Γ B .

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