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Optics Express

Optics Express

  • Editor: Michael Duncan
  • Vol. 14, Iss. 6 — Mar. 20, 2006
  • pp: 2071–2078
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How to obtain high spectral resolution of SBS-based distributed sensing by using nanosecond pulses

V. P. Kalosha, E. A. Ponomarev, Liang Chen, and Xiaoyi Bao  »View Author Affiliations


Optics Express, Vol. 14, Issue 6, pp. 2071-2078 (2006)
http://dx.doi.org/10.1364/OE.14.002071


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Abstract

The ultimate spectral and spatial resolutions of distributed sensing based on stimulated Brillouin scattering (SBS) in optical fibers is shown for several-nanosecond Stokes pulses. Precise measurements of the local Brillouin frequency, with a spectral resolution close to the natural linewidth and, simultaneously, the spatial resolution of the pulse length are provided by AC detection of the output pump in the case of a finite cw component (base) of the Stokes pulse. Simulation examples of SBS-based sensing for fibers containing sections with different Brillouin frequencies are presented, demonstrating the high resolution of the sensing.

© 2006 Optical Society of America

1. Introduction

Stimulated Brillouin scattering (SBS) in optical fibers has attracted considerable attention recently because of its very important application for the sensing of distributed strain and temperature profiles along extended objects [1

1. X. Bao, D. J. Webb, and D. A. Jackson, “22-km distributed temperature sensor using Brillouin gain in an optical fiber,” Opt. Lett. 18, 552–554 (1993). [CrossRef] [PubMed]

, 2

2. M. Nikles, L. Thevenaz, and P. A. Robert, “Brillouin gain spectrum characterization in single-mode optical fibers,” J. Lightwave Technol. 15, 1841–1851 (1997). [CrossRef]

, 3

3. T. R. Parker, M. Farhadiroushan, R. Feced, V. A. Handerek, and A. J. Rogers, “Simultaneous distributed measurement of strain and temperature from noise-initiated Brillouin scattering in optical fibers,” IEEE J. Quantum Electron. 34, 645–659 (1998). [CrossRef]

, 4

4. A. Yeniay, J.-M. Delavaux, and J. Toulouse, “Spontaneous and stimulated Brillouin scattering gain spectra in optical fibers,” J. Lightwave Technol. 20, 1425–1432 (2002). [CrossRef]

]. SBS occurs due to coupling of a counter-propagating cw pump wave and a Stokes-shifted probe pulse via an induced acoustic wave [5

5. R. W. Boyd, Nonlinear Optics (Academic Press, San Diego, 2003).

]. Sensing is obtained by temporally resolved Brillouin spectra, i.e. the depleted output pump as a function of the detuning from the Brillouin frequency. The Brillouin frequency gives the strain and/or temperature along the fiber. To obtain precise values of the strain/temperature and their locations the following contradictory conditions should be compromised: to get accurate frequency measurements, the spectra should be as narrow as possible implying the application of long Stokes pulses; however, to get an accurate spatial resolution, the short pulses should be used.

In tens km-long fibers the Stokes pulses of several-nanosecond duration provide the high spatial resolution, which is defined by the pulse length and is a few tens of centimeters, with a significant signal-to-noise ratio [1

1. X. Bao, D. J. Webb, and D. A. Jackson, “22-km distributed temperature sensor using Brillouin gain in an optical fiber,” Opt. Lett. 18, 552–554 (1993). [CrossRef] [PubMed]

]. At the same time, the Brillouin spectrum linewidth defined by the spectral width of nanosecond Stokes pulses is expected to be larger than the natural Brillouin linewidth. The latter is defined by the phonon lifetime, τ ph ≈ 10 ns for silica fibers, and corresponds to the stationary interaction of cw pump and cw Stokes waves. Surprisingly, it was experimentally shown that the Brillouin spectrum linewidth could be close to the natural for nanosecond Stokes pulses [6

6. X. Bao, A. Brown, M. DeMerchant, and J. Smith, “Characterization of the Brillouin-loss spectrum of single-mode fibers by use of very short (< 10-ns) pulses,” Opt. Lett. 24, 510–512 (1999). [CrossRef]

]. This was explained by the fact that in a real experiment the Stokes pulses have a small cw component (base) due to unavoidable leakage of any optical amplitude modulator used to generate nanosecond pulses. In this case the linewidth could still be defined by the stationary interaction of the cw pump and cw base and could therefore be close to the natural linewidth, provided the relative contribution of the transient regime on the output pump depletion is weak [7

7. V. Lecoeuche, D. J. Webb, C. N. Pannell, and D. A. Jackson, “Transient response in high-resolution Brillouin-based distributed sensing using probe pulses shorter than the acoustic relaxation time,” Opt. Lett. 25, 156–158 (2000). [CrossRef]

].

Based on this fact, in the present paper we have explored the transient SBS regime for nanosecond Stokes pulses with a base and have shown how to achieve the narrowest linewidth and, simultaneously, the smallest spatial resolution of SBS-based sensing. An important issue regarding the sensing, which was not addressed so far to the best of our knowledge, is the influence of AC or DC detection of the output pump power on the spectral measurements. We report that both high spectral and high spatial resolution can be obtained by time-domain analysis of AC-detected Brillouin spectra in the case of nanosecond Stokes pulses with a finite base. It is demonstrated by simulation of SBS-based sensing of longitudinally inhomogeneous distributions of the Brillouin frequency along the fiber.

2. Theoretical model

The theoretical model used to simulate the sensing in single-mode fiber is based on the wave equations for the pump and Stokes waves with the slowly-varying field amplitudes E p(z,t) and E s(z,t), respectively, which interact nonlinearly by the excitation of the acoustic wave Q(z,t) [5

5. R. W. Boyd, Nonlinear Optics (Academic Press, San Diego, 2003).

]:

E˙pvEp'=QEs,
(1a)
E˙s+vEs'=Q*Ep,
(1b)

where dot and prime stand for the derivatives over time and longitudinal coordinates t and z, respectively, and v is the phase velocity of the fiber’s fundamental mode. In the case of several-nanosecond optical pulses participating in SBS, the slowly-varying amplitude approximation normally used may no longer be valid for the acoustic field [8

8. I. Velchev, D. Neshev, W. Hogervorst, and W. Ubachs, “Pulse compression to the subphonon lifetime region by half-cycle gain in transient stimulated Brillouin scattering,” IEEE J. Quantum Electron. 35, 1812–1816 (1999). [CrossRef]

]. Therefore, from the acoustic wave equation [5

5. R. W. Boyd, Nonlinear Optics (Academic Press, San Diego, 2003).

] we have obtained the equation for the field Q(z,t) with second-order time derivative as follows:

Q¨+2(ΓiΩ)Q˙+(ΩB2Ω22iΓΩ)Q=igEpEs*,
(2)

where Γ = 1/τ ph is the relaxation rate, Ω = ω p - ω s, ω p, ω s are the acoustic field, pump, and Stokes frequencies, respectively, ΩB is the Brillouin frequency, g = vΓΩgB, and gB is the SBS gain factor.

Taking into account the existence of the base, we model the boundary input Stokes pulse as

Es(z=0,t)=(EsEb)A(t)+Eb,
(3)

where E s,b = (P s,b/A eff)1/2 for the field normalization used in Eqs. (1)-(2), P s and P b are the peak and cw base powers of the Stokes pulse, respectively, and A eff is the fiber effective area. We characterize the base level of the Stokes pulse by the extinction ratio ER = 10log(P s/Pb).

Equations (1)-(2) were solved by the time update [9

9. W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes in Fortran (Cambridge University Academic Press, 1986).

] of the initial distribution of the pump, Stokes and acoustic waves obtained from the corresponding stationary equations of the SBS for cw pump and cw base. Our results below do not depend on the time moment, when the Stokes pulse enters the fiber (cf. [7

7. V. Lecoeuche, D. J. Webb, C. N. Pannell, and D. A. Jackson, “Transient response in high-resolution Brillouin-based distributed sensing using probe pulses shorter than the acoustic relaxation time,” Opt. Lett. 25, 156–158 (2000). [CrossRef]

]). This time moment was assumed to be equal to t 0 = 5 ns in respect to the pulse leading edge for any pulse duration τ s.

All the simulations presented here were performed with Brillouin parameters typical for the single-mode silica fibers at the wavelength 1.3 μm: τ ph = 10 ns, ν B = 12.8 GHz, g B = 5 × 10-11 m/W, A eff = 50 μm2, v = 0.2 m/ns.

3. Brillouin spectrum detection for the several-nanosecond pulses with base

Due to existence of the cw component of the Stokes waves, the pump depletion takes place at any time moment before the pulse arrival. The spectral properties of the output pump are different in the stationary regime, when the pump and the Stokes base interact, and in the transient regime, when the Stokes pulse comes into play. Therefore, it is important to clarify which value is represented in the time-domain analysis of the Brillouin spectra. The actual time-dependent output pump power or the time-dependent deviation from the stationary output power, induced by the Stokes pulse, can be measured in the experiment. Then the pump loss defined as

αDC=PpPp(z=0,t)
(4a)

or

αAC=Pp(z=0,t=0)Pp(z=0,t),
(4b)

each as a function of the time and frequency detuning ΔΩ = Ω - ΩB, can represent the Brillouin spectrum. Here P p is the boundary input pump power at z = L, P p (z = 0, t) is the time-dependent output pump power at z = 0, P p(z = 0,t = 0) is the output pump power at the initial time moment, defined by the stationary pump-base SBS before the Stokes pulse arrives in the fiber, and P p (z,t) = |E p (z, t)|2 A eff. Hereafter we refer to these two possibilities of pump loss definition by Eq. (4a) and Eq. (4b) as DC or AC detection, respectively. We note that AC detection is most likely to be used in the experiment to measure the small relative variations of the output pump signal in the case of several-nanosecond Stokes pulses.

Fig. 1. Brillouin spectra resolved in the time domain by DC (a) and AC (b) detection for the pump power P p = 5 mW and the Stokes pulse with duration τ s = 3 ns, peak power P s = 10 mW, extinction ratio ER = 15 dB, and for the fiber length L = 10 m.

Fig. 2. Brillouin spectrum linewidth vs Stokes pulse duration for DC (a) and AC (b) detection at t = 100 ns, different extinction ratio and the same pump and Stokes pulse parameters as in Fig. 1. Dashed line shows the natural Brillouin linewidth.

4. SBS-based sensing of longitudinally inhomogeneous fibers

Now we address the SBS-based sensing for longitudinally inhomogeneous distribution of the Brillouin frequency along the fiber and give two examples showing that several-nanosecond Stokes pulses with finite base level provide a possibility to precisely detect different Brillouin frequencies along fibers. First we consider DC- and AC-detected Brillouin spectra of the fiber consisting of two 10-m long sections with Brillouin frequencies 12.800 and 12.875 GHz for the case of a 1-ns Stokes pulse (Fig. 3). We verify how the sections and especially the boundary between them are identified by both types of detection for two different base levels of 15 and 50 dB. The figure is limited by the time interval of the output pump corresponding to the time moments, when the Stokes pulse propagates in the vicinity of the boundary. The thick dashed curve is drawn at the time t = 105.5 ns, when the pulse peak center is passing through the middle of the fiber, and this point should be identified by sensing as a boundary between the sections.

Fig. 3. SBS-based sensing of the boundary between two 10-m fibers with 75 MHz-shifted Brillouin frequencies by a 1-ns Stokes pulse with 15-dB (a,b) and 50-dB (c) base for DC (a) and AC (b,c) detection, and the same other parameters as in Fig. 1. The thick dashed curve is at time moment t = 105.5 ns and corresponds to the boundary between the fiber sections.

Fig. 4. SBS-based sensing of a 10-cm section with 75 MHz-shifted Brillouin frequency in the middle of a 10-m fiber by a 1-ns Stokes pulse with 15-dB (a) and 50-dB (b) base for AC detection and the same other parameters as in Fig. 1. Thick dashed curves are at the time moment t = 55.5 ns and the frequency detuning Δν= 75 MHz.

5. Conclusion

In summary, we have shown the possibility to obtain the high spectral resolution along with the high spatial resolution in SBS-based sensors for 1-ns Stokes pulses with finite cw component (base). The precise identification of the local Brillouin frequency is provided by AC detection of the output pump, i.e. detection of the time-dependent deviation of the output pump induced by the pulse from the output pump induced by the stationary pump-base SBS. In this case the spectral resolution is close to the natural Brillouin linewidth and, simultaneously, the spatial resolution is defined by the Stokes pulse length. This was illustrated by the examples of the SBS-based detection of the two-section fiber and the fiber with the Brillouin frequency-shifted small section. Neither DC detection for a substantial base, nor both DC and AC detection for a low base makes possible precise sensing of longitudinally inhomogeneous fibers.

Acknowledgment

This work was supported by the Intelligent Sensing for Innovative Structures, Natural Science and Engineering Research Council, and Research Chair Program, Canada. One of the authors (V.P.K.) would like to thank Dr. S. Afshar V. for the fruitful discussions on SBS in the optical fibers.

References and links

1.

X. Bao, D. J. Webb, and D. A. Jackson, “22-km distributed temperature sensor using Brillouin gain in an optical fiber,” Opt. Lett. 18, 552–554 (1993). [CrossRef] [PubMed]

2.

M. Nikles, L. Thevenaz, and P. A. Robert, “Brillouin gain spectrum characterization in single-mode optical fibers,” J. Lightwave Technol. 15, 1841–1851 (1997). [CrossRef]

3.

T. R. Parker, M. Farhadiroushan, R. Feced, V. A. Handerek, and A. J. Rogers, “Simultaneous distributed measurement of strain and temperature from noise-initiated Brillouin scattering in optical fibers,” IEEE J. Quantum Electron. 34, 645–659 (1998). [CrossRef]

4.

A. Yeniay, J.-M. Delavaux, and J. Toulouse, “Spontaneous and stimulated Brillouin scattering gain spectra in optical fibers,” J. Lightwave Technol. 20, 1425–1432 (2002). [CrossRef]

5.

R. W. Boyd, Nonlinear Optics (Academic Press, San Diego, 2003).

6.

X. Bao, A. Brown, M. DeMerchant, and J. Smith, “Characterization of the Brillouin-loss spectrum of single-mode fibers by use of very short (< 10-ns) pulses,” Opt. Lett. 24, 510–512 (1999). [CrossRef]

7.

V. Lecoeuche, D. J. Webb, C. N. Pannell, and D. A. Jackson, “Transient response in high-resolution Brillouin-based distributed sensing using probe pulses shorter than the acoustic relaxation time,” Opt. Lett. 25, 156–158 (2000). [CrossRef]

8.

I. Velchev, D. Neshev, W. Hogervorst, and W. Ubachs, “Pulse compression to the subphonon lifetime region by half-cycle gain in transient stimulated Brillouin scattering,” IEEE J. Quantum Electron. 35, 1812–1816 (1999). [CrossRef]

9.

W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes in Fortran (Cambridge University Academic Press, 1986).

OCIS Codes
(060.2370) Fiber optics and optical communications : Fiber optics sensors
(060.4370) Fiber optics and optical communications : Nonlinear optics, fibers
(290.5830) Scattering : Scattering, Brillouin

ToC Category:
Fiber Optics and Optical Communications

History
Original Manuscript: December 22, 2005
Manuscript Accepted: March 1, 2006
Published: March 20, 2006

Citation
V. P. Kalosha, E. Ponomarev, Liang Chen, and Xiaoyi Bao, "How to obtain high spectral resolution of SBS-based distributed sensing by using nanosecond pulses," Opt. Express 14, 2071-2078 (2006)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-6-2071


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References

  1. X. Bao, D. J. Webb, and D. A. Jackson, "22-km distributed temperature sensor using Brillouin gain in an optical fiber," Opt. Lett. 18, 552-554 (1993). [CrossRef] [PubMed]
  2. M. Nikles, L. Thevenaz, and P. A. Robert, "Brillouin gain spectrum characterization in single-mode optical fibers," J. Lightwave Technol. 15, 1841-1851 (1997). [CrossRef]
  3. T. R. Parker, M. Farhadiroushan, R. Feced, V. A. Handerek, and A. J. Rogers, "Simultaneous distributed measurement of strain and temperature from noise-initiated Brillouin scattering in optical fibers," IEEE J. Quantum Electron. 34, 645 - 659 (1998). [CrossRef]
  4. A. Yeniay, J.-M. Delavaux, and J. Toulouse, "Spontaneous and stimulated Brillouin scattering gain spectra in optical fibers," J. Lightwave Technol. 20, 1425-1432 (2002). [CrossRef]
  5. R. W. Boyd, Nonlinear Optics (Academic Press, San Diego, 2003).
  6. X. Bao, A. Brown, M. DeMerchant, and J. Smith, "Characterization of the Brillouin-loss spectrum of single-mode fibers by use of very short (< 10-ns) pulses," Opt. Lett. 24, 510-512 (1999). [CrossRef]
  7. V. Lecoeuche, D. J. Webb, C. N. Pannell, and D. A. Jackson, "Transient response in high-resolution Brillouinbased distributed sensing using probe pulses shorter than the acoustic relaxation time," Opt. Lett. 25, 156-158 (2000). [CrossRef]
  8. I. Velchev, D. Neshev, W. Hogervorst, and W. Ubachs, "Pulse compression to the subphonon lifetime region by half-cycle gain in transient stimulated Brillouin scattering," IEEE J. Quantum Electron. 35, 1812-1816 (1999). [CrossRef]
  9. W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes in Fortran (Cambridge University Academic Press, 1986).

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