Abstract

We report a novel, pump-power dependent, linewidth broadening effect in stimulated Brillouin amplification of a continuous-wave probe by a pulsed pump. This behavior is different from the case of two interacting continuous-wave pump and probe fields, where the shape of the logarithmic Brillouin gain spectrum is independent of the pump power. Studying this effect numerically and experimentally and also analytically, we find that for a given width of the pump pulse the Brillouin linewidth grows linearly with the Brillouin logarithmic gain with a slope, which inversely depends on the pulse width. Thus, for example, in a standard single-mode fiber, a 15ns pump pulse, strong enough to generate a gain of 0.5dB, broadens the logarithmic lineshape by ~1.5MHz, while a 45ns pulse, providing the same gain, increases the linewidth by only ~0.5MHz. Since the rising and falling slopes of the shape of the Brillouin gain spectrum are also gain dependent, this effect might challenge the calibration of Brillouin distributed slope-assisted sensing techniques.

© 2014 Optical Society of America

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References

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  1. R. W. Boyd, Nonlinear Optics, 3rd ed. (Acedemic, 2008).
  2. L. Thévenaz, Advanced Fiber Optics - Concepts and Technology (EPFL, 2011).
  3. X. Bao and L. Chen, “Recent progress in distributed fiber optic sensors,” Sensors 12(7), 8601–8639 (2012).
    [Crossref] [PubMed]
  4. 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).
    [Crossref] [PubMed]
  5. S. M. Foaleng, F. Rodríguez-Barrios, S. Martin-Lopez, M. González-Herráez, and L. Thévenaz, “Detrimental effect of self-phase modulation on the performance of Brillouin distributed fiber sensors,” Opt. Lett. 36(2), 97–99 (2011).
    [Crossref] [PubMed]
  6. S. Foaleng and L. Thévenaz, “Impact of Raman scattering and modulation instability on the performances of Brillouin sensors,” in 21st International Conference on Optical Fibre Sensors (OFS21), International Society for Optics and Photonics (2011).
    [Crossref]
  7. Y. Peled, A. Motil, L. Yaron, and M. Tur, “Slope-assisted fast distributed sensing in optical fibers with arbitrary Brillouin profile,” Opt. Express 19(21), 19845–19854 (2011).
    [Crossref] [PubMed]
  8. A. Motil, O. Danon, Y. Peled, and M. Tur, “Pump-power-independent double slope-assisted distributed and fast Brillouin fiber-optic sensor,” IEEE Photon. Technol. Lett. 26(8), 797–800 (2014).
    [Crossref]
  9. J. Urricelqui, A. Zornoza, M. Sagues, and A. Loayssa, “Dynamic BOTDA measurements based on Brillouin phase-shift and RF demodulation,” Opt. Express 20(24), 26942–26949 (2012).
    [Crossref] [PubMed]
  10. A. David and M. Horowitz, “Low-frequency transmitted intensity noise induced by stimulated Brillouin scattering in optical fibers,” Opt. Express 19(12), 11792–11803 (2011).
    [Crossref] [PubMed]
  11. L. Chen and X. Bao, “Analytical and numerical solutions for steady state stimulated Brillouin scattering in a single-mode fiber,” Opt. Commun. 152(1–3), 65–70 (1998).
    [Crossref]
  12. J.-C. Beugnot, M. Tur, S. F. Mafang, and L. Thévenaz, “Distributed Brillouin sensing with sub-meter spatial resolution: modeling and processing,” Opt. Express 19(8), 7381–7397 (2011).
    [Crossref] [PubMed]
  13. Y. Peled, A. Motil, and M. Tur, “Fast Brillouin optical time domain analysis for dynamic sensing,” Opt. Express 20(8), 8584–8591 (2012).
    [Crossref] [PubMed]
  14. G. L. Keaton, M. J. Leonardo, M. W. Byer, and D. J. Richard, “Stimulated Brillouin scattering of pulses in optical fibers,” Opt. Express 22(11), 13351–13365 (2014).
    [Crossref] [PubMed]

2014 (2)

A. Motil, O. Danon, Y. Peled, and M. Tur, “Pump-power-independent double slope-assisted distributed and fast Brillouin fiber-optic sensor,” IEEE Photon. Technol. Lett. 26(8), 797–800 (2014).
[Crossref]

G. L. Keaton, M. J. Leonardo, M. W. Byer, and D. J. Richard, “Stimulated Brillouin scattering of pulses in optical fibers,” Opt. Express 22(11), 13351–13365 (2014).
[Crossref] [PubMed]

2013 (1)

2012 (3)

2011 (4)

1998 (1)

L. Chen and X. Bao, “Analytical and numerical solutions for steady state stimulated Brillouin scattering in a single-mode fiber,” Opt. Commun. 152(1–3), 65–70 (1998).
[Crossref]

Bao, X.

X. Bao and L. Chen, “Recent progress in distributed fiber optic sensors,” Sensors 12(7), 8601–8639 (2012).
[Crossref] [PubMed]

L. Chen and X. Bao, “Analytical and numerical solutions for steady state stimulated Brillouin scattering in a single-mode fiber,” Opt. Commun. 152(1–3), 65–70 (1998).
[Crossref]

Beugnot, J.-C.

Byer, M. W.

Chen, L.

X. Bao and L. Chen, “Recent progress in distributed fiber optic sensors,” Sensors 12(7), 8601–8639 (2012).
[Crossref] [PubMed]

L. Chen and X. Bao, “Analytical and numerical solutions for steady state stimulated Brillouin scattering in a single-mode fiber,” Opt. Commun. 152(1–3), 65–70 (1998).
[Crossref]

Danon, O.

A. Motil, O. Danon, Y. Peled, and M. Tur, “Pump-power-independent double slope-assisted distributed and fast Brillouin fiber-optic sensor,” IEEE Photon. Technol. Lett. 26(8), 797–800 (2014).
[Crossref]

David, A.

Foaleng, S. M.

González-Herráez, M.

Horowitz, M.

Keaton, G. L.

Leonardo, M. J.

Lin, J.

Loayssa, A.

Mafang, S. F.

Martin-Lopez, S.

Motil, A.

Peled, Y.

Richard, D. J.

Rodríguez-Barrios, F.

Sagues, M.

Thévenaz, L.

Tur, M.

Urricelqui, J.

Yaron, L.

Zornoza, A.

IEEE Photon. Technol. Lett. (1)

A. Motil, O. Danon, Y. Peled, and M. Tur, “Pump-power-independent double slope-assisted distributed and fast Brillouin fiber-optic sensor,” IEEE Photon. Technol. Lett. 26(8), 797–800 (2014).
[Crossref]

Opt. Commun. (1)

L. Chen and X. Bao, “Analytical and numerical solutions for steady state stimulated Brillouin scattering in a single-mode fiber,” Opt. Commun. 152(1–3), 65–70 (1998).
[Crossref]

Opt. Express (7)

Opt. Lett. (1)

Sensors (1)

X. Bao and L. Chen, “Recent progress in distributed fiber optic sensors,” Sensors 12(7), 8601–8639 (2012).
[Crossref] [PubMed]

Other (3)

S. Foaleng and L. Thévenaz, “Impact of Raman scattering and modulation instability on the performances of Brillouin sensors,” in 21st International Conference on Optical Fibre Sensors (OFS21), International Society for Optics and Photonics (2011).
[Crossref]

R. W. Boyd, Nonlinear Optics, 3rd ed. (Acedemic, 2008).

L. Thévenaz, Advanced Fiber Optics - Concepts and Technology (EPFL, 2011).

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Figures (4)

Fig. 1
Fig. 1 Experimental setup: DFB-LD: A 1550nm narrow linewidth (<10kHz) laser diode, AWG: arbitrary waveform generator, VSG: vector signal generator, EOM: electro-optic modulator, EDFA: Erbium-doped fiber amplifier, ATT: attenuator, PC: polarization controller, IS: isolator, FUT: fiber under test, CIR: circulator, PD: photodiode, A2D: analog to digital converter. Pol.: in-line polarizer, FBG: fiber Bragg grating optical filter.
Fig. 2
Fig. 2 Experimentally obtained normalized Brillouin logarithmic gain spectrum of a 45ns wide pump pulse for different Brillouin gains (i.e., different pump powers). Brillouin frequency shift = 10.867GHz.
Fig. 3
Fig. 3 The Brillouin-gain-dependent broadening of the Brillouin Gain Spectrum, δ(Δ ν B )Δ ν B (T,P)Δ ν B (T,P0) , Eq. (2), for pump pulses having different widths. Solid lines represent the numerical solutions of Eqs. (3) while the X's stand for experimentally obtained results. The reported gains for the 45, 30 and 15ns pump pulses were obtained using peak powers of up to 1.78, 3, and 4.5W, respectively.
Fig. 4
Fig. 4 A Logarithmic scale plot of the dependence of the slopes, d[δ(Δ ν B )]/d[Gain] , of the lines in Fig. 3 on the pump pulse width,T. The black circles represent the gradients of the numerically calculated curves of Fig. 3 while the black X's represent experimentally obtained values. The dashed line describes the 0.055·10−6/T (in units of MHz/dB) dependence of the gain-slope of Eq. (6), Sec. 5.

Equations (8)

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g(ν ν B )= g B (Δ ν B,CW /2) 2 (ν ν B ) 2 + (Δ ν B,CW /2) 2 ,
δ(Δ ν B )Δ ν B (T,P)Δ ν B (T,P0),
A Pump (z,t) z + n c A Pump (z,t) t =i 1 2 g 2 A Probe (z,t)Q(z,t)
A Probe (z,t) z n c A Probe (z,t) t =i 1 2 g 2 A Pump (z,t) Q * (z,t)
Q(z,t) t + Γ A Q(z,t)=i g 1 A Pump (z,t) A Probe * (z,t);( Γ A =i 2π( ν B 2 ν 2 )iν Γ B 2ν ).
g T (ν)= T 4 τ A { (1+iδ) 2 +γ + (1iδ) 2 +γ 2 },
Δ ν B = 1 2π τ A ( 1+ τ A g T,max T ) 1+ 2 τ A g T,max /T 2+ τ A g T,max /T 1 2π τ A + 3 g T,max 4πT ,
δ(Δ ν B ) | GainBroadening = 3 4πT g T,max [Neper]= 0.055 T g T,max [dB].

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