## Analysis of optical pulse coding in spontaneous Brillouin-based distributed temperature sensors

Optics Express, Vol. 16, Issue 23, pp. 19097-19111 (2008)

http://dx.doi.org/10.1364/OE.16.019097

Acrobat PDF (283 KB)

### Abstract

A theoretical and experimental analysis of optical pulse coding techniques applied to distributed optical fiber temperature sensors based on spontaneous Brillouin scattering using the Landau-Placzek ratio (LPR) scheme is presented, quantifying in particular the impact of Simplex coding on stimulated Brillouin and Raman power thresholds. The signal-to-noise ratio (SNR) enhancement and temperature resolution improvement provided by coding are also characterized. Experimental results confirm that, differently from Raman-based sensors, pulse coding affects the stimulated Brillouin threshold, resulting in lower optimal input power levels; these features allow one to achieve high sensing performance avoiding the use of high peak power pulses.

© 2008 Optical Society of America

## 1. Introduction

2. H. H. Kee, G. P. Lees, and T. P. Newson, “1.65 µm Raman-based distributed temperature sensor,” Electron. Lett. **35**, 1869–1871 (1999). [CrossRef]

3. M. Niklès, L. Thévenaz, and P. A. Robert, “Simple distributed fiber sensor based on Brillouin gain spectrum analysis,” Opt. Lett. **21**, 758–760 (1996). [CrossRef] [PubMed]

5. Y. T. Cho, M. Alahbabi, M. J. Gunning, and T. P. Newson, “50-km single-ended spontaneous-Brillouinbased distributed-temperature sensor exploiting pulsed Raman amplification,” Opt. Lett. **28**, pp. 1651–1653 (2003). [CrossRef] [PubMed]

6. X. Bao, D. J. Webb, and D. A. Jackson, “Combined distributed temperature and strain sensor based on Brillouin loss in an optical fiber,” Opt. Lett. **19**, 141–143 (1994). [CrossRef] [PubMed]

7. K. Hotate and M. Tanaka, “Distributed fiber Brillouin strain sensing with 1-cm spatial resolution by correlation-cased continuous-wave technique,” IEEE Photon. Technol. Lett. **14**, 197–199 (2002). [CrossRef]

8. A. Minardo*et al.*, “A reconstruction technique for long-range stimulated Brillouin scattering distributed fibre-optic sensors: experimental results,” Meas. Sci. Technol.16, 900–908 (2005). [CrossRef]

5. Y. T. Cho, M. Alahbabi, M. J. Gunning, and T. P. Newson, “50-km single-ended spontaneous-Brillouinbased distributed-temperature sensor exploiting pulsed Raman amplification,” Opt. Lett. **28**, pp. 1651–1653 (2003). [CrossRef] [PubMed]

9. M. A. Soto, P. K. Sahu, G. Bolognini, and F. Di Pasquale, “Brillouin-based distributed temperature sensor employing pulse coding,” IEEE Sens. J. **8**, 225–226 (2008). [CrossRef]

## 2. Basic theory

### 2.1 Brillouin-based sensing using the Landau-Placzek ratio

5. Y. T. Cho, M. Alahbabi, M. J. Gunning, and T. P. Newson, “50-km single-ended spontaneous-Brillouinbased distributed-temperature sensor exploiting pulsed Raman amplification,” Opt. Lett. **28**, pp. 1651–1653 (2003). [CrossRef] [PubMed]

10. P. C. Wait and T. P. Newson, “Landau Placzek ratio applied to distributed fiber sensing,” Opt. Commun. **122**, 141–146 (1996). [CrossRef]

*β*

*is the isothermal compressibility,*

_{T}*ρ*

_{0}the density,

*T*

*the fictive temperature,*

_{f}*ν*

_{s}the acoustic velocity, and

*I*

*,*

_{RS}*I*

*are the intensities of Rayleigh scattering and spontaneous Brillouin scattering respectively. Note that, unlike in Raman-based distributed temperature sensors, the LPR does not require any correction factor for wavelength-dependent losses due to the small frequency separation between Rayleigh scattering and Brillouin-scattered signals (~11 GHz for silica fibers).*

_{SpBS}*T*is typically compared with one LPR curve obtained with the fiber at a reference temperature

*T*

*, as shown by the following equation [11]:*

_{R}*K*

*is the temperature sensitivity of the sensor.*

_{T}*P*

*), which can be expressed by [12*

_{th}12. P. C. Wait, K. De Souza, and T. P. Newson, “A theoretical comparison of spontaneous Raman and Brillouin based fibre optic distributed temperature sensors,” Opt. Commun. **144**, 17–23 (1997). [CrossRef]

*g*

_{R,B}are the Raman and Brillouin gain coefficients,

*C*

_{R,B}are dimensionless constants for Raman and Brillouin scattering respectively,

*A*

*is the fiber effective area, and*

_{eff}*L*

*is the effective interaction length. Note that the threshold power values for light pulses are very different in case of stimulated Raman and Brillouin scattering. In particular, for Raman scattering of pulsed light, the threshold power is dictated by the effective length considering the Raman-scattered light co-propagating with the pump [12*

_{eff}12. P. C. Wait, K. De Souza, and T. P. Newson, “A theoretical comparison of spontaneous Raman and Brillouin based fibre optic distributed temperature sensors,” Opt. Commun. **144**, 17–23 (1997). [CrossRef]

*L*

*corresponding to one pulsewidth (*

_{p}*αL*

*≪1*

_{p}*)*, then the effective length is equal to half the pulse length (

*L*

*=*

_{eff}*L*

*/*

_{p}*2*) [12

12. P. C. Wait, K. De Souza, and T. P. Newson, “A theoretical comparison of spontaneous Raman and Brillouin based fibre optic distributed temperature sensors,” Opt. Commun. **144**, 17–23 (1997). [CrossRef]

13. K. De Souza and T. P. Newson, “Brillouin-based fiber-optic distributed temperature sensor with optical preamplification,” Opt. Lett. **25**, 1331–1333 (2000). [CrossRef]

14. Y. T. Cho, M. N. Alahbabi, M. J. Gunning, and T. P. Newson, “Enhanced performance of long range Brillouin intensity based temperature sensors using remote Raman amplification,” Meas. Sci. Technol. **15**, 1548–1552 (2004). [CrossRef]

15. Y. T. Cho, M. N. Alahbabi, G. Brambilla, and T. P. Newson, “Distributed Raman Amplification Combined With a Remotely Pumped EDFA Utilized to Enhance the Performance of Spontaneous Brillouin-Based Distributed Temperature Sensors,” IEEE Photon. Technol. Lett. **17**, 1256–1258 (2005). [CrossRef]

16. J. Park*et al*, “Raman-based distributed temperature sensor with Simplex coding and link optimization,” IEEE Photon. Technol. Lett.18, 1879–1881 (2006). [CrossRef]

*L*

*=*

_{eff}*L*

*/*

_{p}*2*) cannot unfortunately be used in case of pulse coding, especially for long codewords. This is because the basic assumptions required to obtain this expression for

*L*

*are not valid anymore with pulse coding. In that case the effective length and Brillouin threshold power must be directly derived from time-space propagation equations, as it will be shown in detail in Section 3.*

_{eff}## 2.2 Optical coding techniques in sensing applications

18. M. D. Jones, “Using Simplex codes to improve OTDR Sensitivity,” IEEE Photon. Technol. Lett. **15**, 822–824 (1993). [CrossRef]

18. M. D. Jones, “Using Simplex codes to improve OTDR Sensitivity,” IEEE Photon. Technol. Lett. **15**, 822–824 (1993). [CrossRef]

18. M. D. Jones, “Using Simplex codes to improve OTDR Sensitivity,” IEEE Photon. Technol. Lett. **15**, 822–824 (1993). [CrossRef]

*A*-optimal [20] within its class for a given code length. This means that the root mean square (

*rms*) noise at the receiver is minimized when using Simplex coding, allowing for the best achievable performance.

**15**, 822–824 (1993). [CrossRef]

16. J. Park*et al*, “Raman-based distributed temperature sensor with Simplex coding and link optimization,” IEEE Photon. Technol. Lett.18, 1879–1881 (2006). [CrossRef]

## 3. Effective length of coded signals and SBS threshold calculation

*L*

*reported in Section 2 cannot be used. In fact, for long codewords (e.g. 127 bit or higher) the spatial extent of the optical coded pulses within the fiber becomes large, and the fiber absorption effect cannot be neglected. In this case, the solution of the time-space model of Brillouin scattering is required, leading to a set of differential equations describing the interaction between electric fields and acoustic waves [21]. In a quasi-CW regime (i.e. the optical intensities and the nonlinear phase temporal changes are considered slow compared to the photon lifetime*

_{eff}*τ*

*=*

_{B}*1*/

*Γ*

*), the dynamics of the acoustic wave can be neglected [21]. Under these assumptions, the evolution of optical intensities over time,*

_{B}*t*, and space,

*z*, for the forward-propagating pump light

*I*

*(*

_{P}*z*,

*t*) and backward-propagating Stokes Brillouin light

*I*

*(*

_{B}*z*,

*t*) can be described by the following equations [21]:

*n*is the effective index of the fiber mode,

*c*is the speed of light in the vacuum,

*g*

*is the Brillouin gain coefficient, and*

_{B}*α*is the fiber attenuation coefficient (considered as identical at pump and Stokes Brillouin wavelengths).

*I*

*(*

_{Po}*t*) represents the time dependence of the pump pulses at the fiber input, and

*I*

*(*

_{Bo}*t*) represents the spontaneous Brillouin intensity at a distance

*z*

*(*

_{L}*t*) from which SBS is originated. Note that the boundary condition for

*I*

*(*

_{B}*z*,

*t*) in Eq. (7) represents the occurrence of SBS from the initial spontaneous Brillouin scattering generated in a small section of the fiber near the rear edge of the pulse at distance

*z*

*(*

_{L}*t*), which depends on the position of the pump pulse at a given time

*t*.

*t*, and distance,

*z*. In such a method, the solution of the system of equations is found through suitable changes of variables and integration over a given

*z*-

*t*subspace defined by the characteristic curves (i.e. coordinate transformation systems, which in our case consist essentially in two reference frames moving along opposite directions along the optical fiber with the speed of light). The characteristic curves suitable for the solution of the system (5)-(6), defining the new variables

*χ*

*and*

_{P}*χ*

*, result to be:*

_{B}*Γ*

_{1}) physically represents the evolution of pump pulses along the fiber, while the second set of characteristics (

*Γ*

_{2}) describes the backward propagation evolution of the Brillouin light scattered from different fiber locations with the same arrival time

*t*

*at the fiber input.*

_{R}*I*

*(*

_{P}*z*,

*t*) in Eq. (5) can be simply found through integration over the

*Γ*

_{1}characteristic curve, giving:

*I*

*(*

_{B}*z*=

*0*,

*t*), then Eq. (6) must be solved by integration over the

*Γ*

_{2}characteristic curve frame. In case of input light pulses with a finite temporal duration, this integration can be expressed with a semi-analytical expression:

*I*

*(*

_{P}*ξ*,

*t*-

*nξ*/

*c*) is given by Eq. (10). Note that the integration is performed only from

*z*

*(*

_{i}*t*) to

*z*

*(*

_{L}*t*), positions which define the interaction length of the optical waves as represented in Fig. 1a. This length of fiber corresponds to half the pulse duration (

*Δz*≡

*z*

*-*

_{L}*z*

*=*

_{i}*cT*/

*2n*), because the two fields do not interact along the characteristic curve

*Γ*

_{2}when they are not spatially overlapping (i.e. at times

*t*<

*t*

*/*

_{R}*2*and t>

*t*

*/*

_{R}*2*+

*T*/

*2*).

*z*

*(*

_{i}*t*) and

*z*

*(*

_{L}*t*), for a given time t, can then be expressed as [22]:

*t*is maximum. In case of Simplex coding scheme, this worst-case scenario essentially consists in considering an input codeword where all the ‘1’ pulses are adjacent, thus producing a longer continuous optical pulse (such a worst-case codeword is indeed defined within the S-matrix and has a number of adjacent ‘1’ bits equal to (

*L*

*+*

_{c}*1*)/

*2*).

*t*corresponding to the overall duration of the adjacent optical pulses generated within the worst-case codeword mentioned above. Under this condition, we can then infer that the highest Brillouin backscattered signal at the fiber input for the worst-case codeword occurs at

*t*

*=*

_{MAX}*T*

*(*

_{B}*L*

*+*

_{c}*1*)/

*2*, where

*T*

*is the bit duration. Thus, the integral in Eq. (11) can be calculated as:*

_{B}*I*

*is the input peak pulse intensity and*

_{Po}*z*

^{’}

*L*is the maximum interaction length given by

*L*

*is given by:*

_{eff}*L*

*(=*

_{p}*c*·

*T*

*/*

_{B}*n*) is the single bit length in a codeword.

*L*

*=1) where the fiber attenuation is negligible (*

_{c}*αL*

*/*

_{p}*2*≪1) due to the short used pulse duration, the effective length in Eq. (16) is reduced to

*L*

*/*

_{p}*2*, which corresponds to the well-known expression for OTDR and conventional-BDTS [12

**144**, 17–23 (1997). [CrossRef]

*g*

*=10*

_{R}^{-13}m

^{-1},

*g*

*=5×10*

_{B}^{-11}m

^{-1},

*α*=0.25 dB/km,

*Δλ*

*=113 nm [12*

_{Raman}**144**, 17–23 (1997). [CrossRef]

**144**, 17–23 (1997). [CrossRef]

**144**, 17–23 (1997). [CrossRef]

*G*

*>4.58 dB, and spatial resolution ≥2 m). However, for code length <32 bit, the limiting effect can be either SBS or SRS, depending of the spatial resolution as shown in Fig. 2.*

_{COD}23. Y. Aoki, K. Tajima, and I. Mito, “Input Power Limits of Single-Mode Optical Fibers due to Stimulated Brillouin Scattering in Optical Communication Systems,” J. Lightwave Technol. **6**, 710–719 (1988). [CrossRef]

*ν*

*is the effective linewidth of the laser, and Δ*

_{p}*ν*

*is the SBS gain linewidth. Therefore, SBS thresholds shown in Fig. 2 may be increased as described in Eq. (17). Laser dithering inducing a broadening in the effective linewidth of the laser also allows for a reduction of coherent Rayleigh noise (CRN) in Rayleigh trace used in LPR [24*

_{B}24. K. De Souza, “Significance of coherent Rayleigh noise in fibre-optic distributed temperature sensing based on spontaneous Brillouin scattering,” Meas. Sci. Technol. **17**, 1065–1069 (2006). [CrossRef]

## 4. Experimental setup for Simplex coded-BDTS

24. K. De Souza, “Significance of coherent Rayleigh noise in fibre-optic distributed temperature sensing based on spontaneous Brillouin scattering,” Meas. Sci. Technol. **17**, 1065–1069 (2006). [CrossRef]

24. K. De Souza, “Significance of coherent Rayleigh noise in fibre-optic distributed temperature sensing based on spontaneous Brillouin scattering,” Meas. Sci. Technol. **17**, 1065–1069 (2006). [CrossRef]

*V*

*is the group velocity,*

_{g}*Δz*is the spatial resolution of the sensor and

*Δf*is the sweeping band of the laser.

**17**, 1065–1069 (2006). [CrossRef]

## 5. Results

### 5.1 Temperature measurements

*rms*of the difference between the estimated and the real temperatures, as shown in Fig. 6. For the single-pulse case the achieved temperature resolution is ~30 K near fiber end (30 km distance), and it is enhanced down to 5.0 K with the use of 127-bit Simplex coding.

## 5.2 Impact of stimulated Brillouin scattering threshold

*P*

_{th}, before the onset of nonlinear effects, is strongly affected by the use of coding, as correctly predicted by theory. Actually, the SBS threshold power with single-pulsed BDTS is about 25 dBm, while with Simplex-coding

*P*

*is about 10 dBm. This is occurring since the coding process leads to a longer pulse effective length (at the same spatial resolution) with respect to single pulses. Therefore Simplex-BDTS allows one to achieve the optimum at an input peak power which is ~15 dB lower than in case of conventional-BDTS, allowing one to avoid optical pulse amplification. Thus, SBS threshold can limit the ability of pulse coding to achieve an overall better temperature resolution with respect to the single pulse case; such a drawback is not present in distributed Raman temperature sensors, where this effect has never been observed for practical code lengths.*

_{th}## 6. Conclusions

## References and links

1. | “Optical-fibre Sensors,” Tech. Focus Nature Photon.2, 143–158 (2008). |

2. | H. H. Kee, G. P. Lees, and T. P. Newson, “1.65 µm Raman-based distributed temperature sensor,” Electron. Lett. |

3. | M. Niklès, L. Thévenaz, and P. A. Robert, “Simple distributed fiber sensor based on Brillouin gain spectrum analysis,” Opt. Lett. |

4. | X. Bao, L. Zou, Q. Yu, and L. Chen, “Development and applications of the distributed temperature and strain sensors based on Brillouin scattering,” |

5. | Y. T. Cho, M. Alahbabi, M. J. Gunning, and T. P. Newson, “50-km single-ended spontaneous-Brillouinbased distributed-temperature sensor exploiting pulsed Raman amplification,” Opt. Lett. |

6. | X. Bao, D. J. Webb, and D. A. Jackson, “Combined distributed temperature and strain sensor based on Brillouin loss in an optical fiber,” Opt. Lett. |

7. | K. Hotate and M. Tanaka, “Distributed fiber Brillouin strain sensing with 1-cm spatial resolution by correlation-cased continuous-wave technique,” IEEE Photon. Technol. Lett. |

8. | A. Minardo |

9. | M. A. Soto, P. K. Sahu, G. Bolognini, and F. Di Pasquale, “Brillouin-based distributed temperature sensor employing pulse coding,” IEEE Sens. J. |

10. | P. C. Wait and T. P. Newson, “Landau Placzek ratio applied to distributed fiber sensing,” Opt. Commun. |

11. | K. De. Souza |

12. | P. C. Wait, K. De Souza, and T. P. Newson, “A theoretical comparison of spontaneous Raman and Brillouin based fibre optic distributed temperature sensors,” Opt. Commun. |

13. | K. De Souza and T. P. Newson, “Brillouin-based fiber-optic distributed temperature sensor with optical preamplification,” Opt. Lett. |

14. | Y. T. Cho, M. N. Alahbabi, M. J. Gunning, and T. P. Newson, “Enhanced performance of long range Brillouin intensity based temperature sensors using remote Raman amplification,” Meas. Sci. Technol. |

15. | Y. T. Cho, M. N. Alahbabi, G. Brambilla, and T. P. Newson, “Distributed Raman Amplification Combined With a Remotely Pumped EDFA Utilized to Enhance the Performance of Spontaneous Brillouin-Based Distributed Temperature Sensors,” IEEE Photon. Technol. Lett. |

16. | J. Park |

17. | M. Nazarathy et al., “Real-time long-range complementary correlation optical time-domain reflectometer,” J. Lightwave Technol. |

18. | M. D. Jones, “Using Simplex codes to improve OTDR Sensitivity,” IEEE Photon. Technol. Lett. |

19. | D. Lee |

20. | M. Harwit and N. J. A. Sloane, |

21. | G. P. Agrawal, |

22. | R. Courant and D. Hilbert, |

23. | Y. Aoki, K. Tajima, and I. Mito, “Input Power Limits of Single-Mode Optical Fibers due to Stimulated Brillouin Scattering in Optical Communication Systems,” J. Lightwave Technol. |

24. | K. De Souza, “Significance of coherent Rayleigh noise in fibre-optic distributed temperature sensing based on spontaneous Brillouin scattering,” Meas. Sci. Technol. |

**OCIS Codes**

(060.2370) Fiber optics and optical communications : Fiber optics sensors

(290.5830) Scattering : Scattering, Brillouin

(120.4825) Instrumentation, measurement, and metrology : Optical time domain reflectometry

**ToC Category:**

Fiber Optics and Optical Communications

**History**

Original Manuscript: September 12, 2008

Revised Manuscript: October 17, 2008

Manuscript Accepted: October 17, 2008

Published: November 4, 2008

**Citation**

Marcelo A. Soto, Gabriele Bolognini, and Fabrizio Di Pasquale, "Analysis of optical pulse coding in spontaneous Brillouin-based distributed temperature sensors," Opt. Express **16**, 19097-19111 (2008)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-23-19097

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### References

- "Optical-fibre Sensors," Tech. Focus Nature Photon. 2, 143-158 (2008).
- H. H. Kee, G. P. Lees, and T. P. Newson, "1.65 ?m Raman-based distributed temperature sensor," Electron. Lett. 35, 1869-1871 (1999). [CrossRef]
- M. Niklès, L. Thévenaz, and P. A. Robert, "Simple distributed fiber sensor based on Brillouin gain spectrum analysis," Opt. Lett. 21, 758-760 (1996). [CrossRef] [PubMed]
- X. Bao, L. Zou, Q. Yu, and L. Chen, "Development and applications of the distributed temperature and strain sensors based on Brillouin scattering," in Proceeding of IEEE Sensors Conf.2004, vol 3, pp. 1210 - 1213.
- Y. T. Cho, M. Alahbabi, M. J. Gunning, and T. P. Newson, "50-km single-ended spontaneous-Brillouin-based distributed-temperature sensor exploiting pulsed Raman amplification," Opt. Lett. 28, pp. 1651-1653 (2003). [CrossRef] [PubMed]
- X. Bao, D. J. Webb, and D. A. Jackson, "Combined distributed temperature and strain sensor based on Brillouin loss in an optical fiber," Opt. Lett. 19, 141-143 (1994). [CrossRef] [PubMed]
- K. Hotate and M. Tanaka, "Distributed fiber Brillouin strain sensing with 1-cm spatial resolution by correlation-cased continuous-wave technique," IEEE Photon. Technol. Lett. 14, 197-199 (2002). [CrossRef]
- A. Minardo et al., "A reconstruction technique for long-range stimulated Brillouin scattering distributed fibre-optic sensors: experimental results," Meas. Sci. Technol. 16, 900-908 (2005). [CrossRef]
- M. A. Soto, P. K. Sahu, G. Bolognini, and F. Di Pasquale, "Brillouin-based distributed temperature sensor employing pulse coding," IEEE Sens. J. 8, 225-226 (2008). [CrossRef]
- P. C. Wait and T. P. Newson, "Landau Placzek ratio applied to distributed fiber sensing," Opt. Commun. 122, 141-146 (1996). [CrossRef]
- K. De. Souza et al, "Improvement of signal-to-noise capabilities of a distributed temperature sensor using optical preamplification," Meas. Sci. Technol. 12, 952- 957 (2001).
- P. C. Wait, K. De Souza, and T. P. Newson, "A theoretical comparison of spontaneous Raman and Brillouin based fibre optic distributed temperature sensors," Opt. Commun. 144, 17-23 (1997). [CrossRef]
- K. De Souza and T. P. Newson, "Brillouin-based fiber-optic distributed temperature sensor with optical preamplification," Opt. Lett. 25, 1331-1333 (2000). [CrossRef]
- Y. T. Cho, M. N. Alahbabi, M. J. Gunning, and T. P. Newson, "Enhanced performance of long range Brillouin intensity based temperature sensors using remote Raman amplification," Meas. Sci. Technol. 15, 1548-1552 (2004). [CrossRef]
- Y. T. Cho, M. N. Alahbabi, G. Brambilla, and T. P. Newson, "Distributed Raman Amplification Combined With a Remotely Pumped EDFA Utilized to Enhance the Performance of Spontaneous Brillouin-Based Distributed Temperature Sensors," IEEE Photon. Technol. Lett. 17, 1256-1258 (2005). [CrossRef]
- J. Park et al, "Raman-based distributed temperature sensor with Simplex coding and link optimization," IEEE Photon. Technol. Lett. 18, 1879-1881 (2006). [CrossRef]
- M. Nazarathy et al., "Real-time long-range complementary correlation optical time-domain reflectometer," J. Lightwave Technol. 7, 24-38 (1989). [CrossRef]
- M. D. Jones, "Using Simplex codes to improve OTDR Sensitivity," IEEE Photon. Technol. Lett. 15, 822-824 (1993). [CrossRef]
- D. Lee et al, "Analysis and Experimental Demonstration of Simplex Coding Technique for SNR Enhancement of OTDR," In Proceeding of IEEE LTIMC, (New York, USA, 2004), pp. 118-122,
- M. Harwit and N. J. A. Sloane, Hadamard Transform Optics (New York: Academic, 1979).
- G. P. Agrawal, Nonlinear Fiber Optics, 2nd ed. (New York: Academic, 1995).
- R. Courant and D. Hilbert, Methods of Mathematical Physics, Vol. II, (Wiley New York, 1962).
- Y. Aoki, K. Tajima, and I. Mito, "Input Power Limits of Single-Mode Optical Fibers due to Stimulated Brillouin Scattering in Optical Communication Systems," J. Lightwave Technol. 6, 710-719 (1988). [CrossRef]
- K. De Souza, "Significance of coherent Rayleigh noise in fibre-optic distributed temperature sensing based on spontaneous Brillouin scattering," Meas. Sci. Technol. 17, 1065-1069 (2006). [CrossRef]

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