## Effect of pulse depletion in a Brillouin optical time-domain analysis system |

Optics Express, Vol. 21, Issue 12, pp. 14017-14035 (2013)

http://dx.doi.org/10.1364/OE.21.014017

Acrobat PDF (1327 KB)

### Abstract

Energy transfer between the interacting waves in a distributed Brillouin sensor can result in a distorted measurement of the local Brillouin gain spectrum, leading to systematic errors. It is demonstrated that this depletion effect can be precisely modelled. This has been validated by experimental tests in an excellent quantitative agreement. Strict guidelines can be enunciated from the model to make the impact of depletion negligible, for any type and any length of fiber.

© 2013 OSA

## 1. Introduction

1. L. Thévenaz, “Brillouin distributed time-domain sensing in optical fibers: state of the art and perspectives,” Front. Optoelectron. China **3**(1), 13–21 (2010). [CrossRef]

2. M. A. Soto, G. Bolognini, F. Di Pasquale, and L. Thévenaz, “Long-range Brillouin optical time-domain analysis sensor employing pulse coding techniques,” Meas. Sci. Technol. **21**(9), 094024 (2010). [CrossRef]

4. X. Angulo-Vinuesa, S. Martin-Lopez, J. Nuno, P. Corredera, J. D. Ania-Castanon, L. Thevenaz, and M. Gonzalez-Herraez, “Raman-assisted Brillouin distributed temperature sensor over 100 km featuring 2 meter resolution and 1.2°C uncertainty,” J. Lightwave Technol. **30**(8), 1060–1065 (2012). [CrossRef]

6. S. M. Foaleng and L. Thevenaz, “Impact of Raman scattering and modulation instability on the performances of Brillouin sensors,” Proc. SPIE **7753**, 77539V, 77539V-4 (2011). [CrossRef]

7. M. N. Alahbabi, Y. T. Cho, T. P. Newson, P. C. Wait, and A. H. Hartog, “Influence of modulation instability on distributed optical fiber sensors based on spontaneous Brillouin scattering,” J. Opt. Soc. Am. B **21**(6), 1156–1160 (2004). [CrossRef]

8. D. Alasia, M. Gonzalez Herraez, L. Abrardi, S. Martin-Lopez, and L. Thevenaz, “Detrimental effect of modulation instability on distributed optical fiber sensors using stimulated Brillouin scattering,” Proc. SPIE **5855**, 587–590 (2005). [CrossRef]

9. T. Horiguchi, K. Shimizu, T. Kurashima, M. Tateda, and Y. Koyamada, “Development of a distributed sensing technique using Brillouin scattering,” J. Lightwave Technol. **13**(7), 1296–1302 (1995). [CrossRef]

10. E. Geinitz, S. Jetschke, U. Röpke, S. Schröter, R. Willsch, and H. Bartelt, “The influence of pulse amplification on distributed fibre-optic Brillouin sensing and a method to compensate for systematic errors,” Meas. Sci. Technol. **10**(2), 112–116 (1999). [CrossRef]

11. A. Minardo, R. Bernini, L. Zeni, L. Thevenaz, and F. Briffod, “A reconstruction technique for long-range stimulated Brillouin scattering distributed fibre-optic sensors: Experimental results,” Meas. Sci. Technol. **16**(4), 900–908 (2005). [CrossRef]

2. M. A. Soto, G. Bolognini, F. Di Pasquale, and L. Thévenaz, “Long-range Brillouin optical time-domain analysis sensor employing pulse coding techniques,” Meas. Sci. Technol. **21**(9), 094024 (2010). [CrossRef]

12. S. Martin-Lopez, M. Alcon-Camas, F. Rodriguez, P. Corredera, J. D. Ania-Castañon, L. Thévenaz, and M. Gonzalez-Herraez, “Brillouin optical time-domain analysis assisted by second-order Raman amplification,” Opt. Express **18**(18), 18769–18778 (2010). [CrossRef] [PubMed]

13. 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). [CrossRef] [PubMed]

9. T. Horiguchi, K. Shimizu, T. Kurashima, M. Tateda, and Y. Koyamada, “Development of a distributed sensing technique using Brillouin scattering,” J. Lightwave Technol. **13**(7), 1296–1302 (1995). [CrossRef]

10. E. Geinitz, S. Jetschke, U. Röpke, S. Schröter, R. Willsch, and H. Bartelt, “The influence of pulse amplification on distributed fibre-optic Brillouin sensing and a method to compensate for systematic errors,” Meas. Sci. Technol. **10**(2), 112–116 (1999). [CrossRef]

## 2. Model for the evaluation of the error due to pump depletion

*z*= 0), while the CW probe signal enters at the far end (

*z*=

*L*), as sketched in Fig. 1. The pump pulse will be gradually depleted by the continuous probe after propagating along the long uniform fiber, eventually causing a drop in the pump power when the frequency difference between the pump and the probe closely matches the Brillouin shift, as depicted in Fig. 1. The amount of depletion can be characterized by a dimensionless coefficient

*d*:where

*P*is the pump power in the absence of Brillouin interaction (no gain or no probe wave), and

_{Po}*P*is the pump power in the presence of the maximum interaction at the Brillouin peak gain frequency of the long uniform section. Note that the effect on the pump in a loss configuration can be identically represented by opting for a negative value of the coefficient

_{P}*d*.

*δν*with respect to the long preceding uniform section, the situation is like depicted in Fig. 2. The actual measured gain spectrum shows some asymmetric distortion, resulting in a shifted peak value and leading to a systematic error

*ν*in the determination of the real maximum Brillouin gain frequency. It must be noted that the systematic error vanishes in 2 situations: 1) when the Brillouin gain spectrum in the distant segment shows no overlap with the dip present in the pump power frequency dependence, i.e. when the 2 sections are under very different environmental conditions; 2) when the 2 sections present the same Brillouin shift, resulting in a symmetric distortion of the measured gain spectrum that nullifies the systematic error. This error will therefore be maximized for a particular frequency difference

_{e}*δν*between the Brillouin shifts in the 2 sections, which will be determined by the model.

- 1. For a given tolerable systematic error
*ν*on the measured value of the maximum Brillouin gain frequency, determination of the maximum acceptable depletion coefficient_{e}*d*, assuming a perfectly Lorentzian distribution of the original Brillouin gain spectrum. - 2. Determination of the relation between the pump pulse input power
*P*, the CW signal input power_{P}*P*and the depletion coefficient_{S}*d*in the worst case depicted in Fig. 1, for given fiber characteristics and length.

### 2.1. Determination of the tolerable depletion d for a given error ν_{e}

*ν*′ is the frequency difference between pump and probe,

*ν*is the Brillouin shift corresponding to the maximal gain in the short section, and

_{B}*Δν*is the FWHM width of this gain spectrum. To simplify the expressions, the frequency origin is shifted to

*ν*=

*ν*′-

*ν*, (maximum gain at the frequency origin) without loss of generality.

_{B}*δν*and the FWHM width

*Δν*is identical to the short segment, it is reasonable to assume that the short segment is made either of the same fiber or of at least a fairly identical one. The pump intensity follows this distribution:where the linear approximation holds when the depletion is small (

*d*<0.2), in which case it only results in a minor error on the pump power within 2% of its real value. This small depletion approximation is necessary to obtain expressions simple enough to lead to analytical solutions. It will be later checked that the tolerable depletion does not exceed 0.2 for standard acceptable systematic errors

*ν*.

_{e}*T*and propagating at the group velocity

*V*, the net signal gain can be reasonably expressed by a first order expansion of the exponential amplification:

_{g}*d = 0*. The amount of shifting depends on the magnitude of depletion

*d*and on the relative shift

*δν*between the maximum gain frequencies of the two segments. The gain FWHM spectral width

*Δν*turns out to be a simple scaling factor, so that all results can actually be normalized to

*Δν*. The error is found by searching the frequency

*ν*giving the maximum gain in Eq. (4), by simply nulling the derivative of this expression.

^{6}:

*ν*/

_{e}*Δν*as a function of the normalized relative frequency shift

*δν*/

*Δν*between the peak gains in the 2 sections, for 3 fixed depletion values

*d*. The systematic error reaches its maximum value when the relative frequency shift is approximately 1/4 of the FWHM gain spectral width, while as expected it vanishes if there is no shift or a much larger shift than the gain spectral width (no overlap).

*ν*is much smaller than

_{e}*Δν*:

*d*, this expression is maximal when:Since

*d*is a subtractive term on the plain number 2 and is assumed to be at least 10 times smaller, it has a small impact on the result and the rightmost approximate term in the expression is evaluated for the median value

*d*= 0.1. This result shows that the error is maximal when the spectral shift between the peak gains in the two segments is about a quarter of the full width at half maximum, which is fully consistent with the graphical information shown in Fig. 3(left).

*d*that would ensure an error not exceeding a given value

_{max}*ν*. Inspecting Eq. (5) shows it is a linear function of the depletion factor

_{e}*d.*An exact solution can be therefore obtained for

*d*, assuming the approximation made to establish Eq. (4):

*ν*is much smaller than the gain spectral width

_{e}*Δν*in a weak depletion regime, this expression can be simplified and a robust 2nd order approximate relation can be easily deduced:

*d*for a given normalized error

_{max}*ν*/

_{e}*Δν*using Eq. (8) and (9), in the situation of the relative frequency shift

*δν*leaving the maximum systematic error as given by Eq. (7). Some important points are represented, corresponding to standard accuracies in Brillouin distributed sensors (1 MHz, 0.5 MHz, 0.1 MHz) using a gain FWHM spectral width of 27 MHz, which is a standard value according to our experience in the commonly used ITU-T G.652 fibers at a wavelength of 1550 nm. These standard accuracies require a maximum tolerable depletion of 0.194 for a maximum error of 1 MHz, while it must be reduced to 0.105 for an error of 0.5 MHz and to 0.023 for 0.1 MHz. This confirms the relevance of the approximation used for establishing the model (

*d*<0.2) and its validity in real situations.

*d*has to be inserted in all expressions, leading to similar errors for small

*d*. It should also be pointed out that depletion induces a distortion of the gain spectrum, which gives a biased evaluation of the peak gain frequency and thus leads to a systematic error that is not subject to statistical variations. When a sensing system is subject to depletion, the estimation of the accuracy calculated from the standard deviation over repeated measurements does not actually inform on the real total error. Instead, the error can be increased by the systematic non-stochastic contribution due to depletion.

### 2.2. The 1st order maximum probe power in a gain configuration

*P*(small gain condition), the probe launched at the far end (

_{S}*z*=

*L*) will essentially experience an exponential decay due to the linear attenuation

*α*, so that

*P*(

_{P}*z*) can be calculated by solving the basic equation for the Brillouin interaction, including the linear attenuation term:where

*g*and

_{B}*A*are the Brillouin linear gain and the nonlinear effective area of the propagating mode, respectively. It must be pointed out that

_{eff}*g*is considered here as position-independent, since the maximal depletion effect will be observed for the worst case scenario when the gain is maximal at any position and this is the situation addressed here.

_{B}*P*(

_{P}*z*) can be found under the small gain assumption, given here by the following expression at

*z*=

*L,*for the residual output pump power

*P*(

_{P}*L*) with the initial condition

*P*=

_{iP}*P*(0):

_{P}*d*can be easily derived from Eq. (1) and Eq. (11):Hence the maximum input probe signal power

*P*for a given tolerable depletion factor

_{iS}*d*can be expressed as:

*P*is totally independent of the power

_{iS}*P*and the pulse width of the pump. For a given depletion factor

_{P}*d*it solely depends on the fiber properties. This may hurt at first glance the good sense, but this is a direct consequence of the small gain approximation and the consecutive linear dependence between gain and pump power: the power transfer between pump and probe power is for sure larger for a higher pump power, but this power transfer scales in the exact same proportion as the pump power. The fractional depletion

*d*is therefore independent of the pump power

*P*and, as demonstrated in the previous sub-section, the systematic error

_{P}*ν*is only function of

_{e}*d*. In standard conditions (

*g*= 2 × 10

_{B}^{−11}m/W,

*A*= 80 × 10

_{eff}^{−12}m

^{2},

*α*= 22 × 10

^{−1}^{3}m), for a depletion factor

*d*= 0.20, the input probe power

*P*must not exceed 40 μW, which is a fairly low value, far from being respected by the vast majority – if not the entirety - of existing sensors.

_{iS}### 2.3. 1st order and 2nd order maximum probe power in general condition

14. M. Niklès, L. Thévenaz, and P. A. Robert, “Simple distributed fiber sensor based on Brillouin gain spectrum analysis,” Opt. Lett. **21**(10), 758–760 (1996). [CrossRef] [PubMed]

16. A. Minardo, R. Bernini, and L. Zeni, “A simple technique for reducing pump depletion in long-range distributed Brillouin fiber sensors,” IEEE Sens. J. **9**(6), 633–634 (2009). [CrossRef]

14. M. Niklès, L. Thévenaz, and P. A. Robert, “Simple distributed fiber sensor based on Brillouin gain spectrum analysis,” Opt. Lett. **21**(10), 758–760 (1996). [CrossRef] [PubMed]

*P*and the upper sideband with power

_{SL}*P*. It is straightforward to generalize the simple expression given by Eq. (13) to this case, by adding the contribution of the 2 probe waves in Eq. (10):from which the depletion factor

_{SU}*d*can be easily determined following the same procedure:where

*P*and

_{iSL}*P*are the respective input powers of the 2 probe waves at position

_{iSU}*z*=

*L*. This generalized expression can be indistinctively used to describe sensors operating in the gain regime (

*P*= 0) or in the loss regime (

_{iSU}*P*= 0), as well as sensors in presence of two CW probe waves equally spectrally separated from the pump.

_{iSL}*P*-

_{iSL}*P*= 0). This was soon identified as a clear merit of the double sideband configuration and it is here fully proved by this model. However, one of the probe waves must be spectrally filtered out before detection due to the opposite but equal amplitude Brillouin response of each pump-probe interaction, which consequently exactly compensate in the linear small gain approximation. Equation (21) simply expresses that the power of the 2 probe waves has no real limit and the only condition is that their power difference must not exceed the limit given for a single probe wave in Eq. (13). Practically the CW probe waves power is limited to several milliwatts by the onset of intense amplified spontaneous Brillouin scattering.

_{iSU}*P*≅□

_{iSL}*P*. It is easy to prove that, in presence of a single probe wave (

_{iSU}*P*or

_{iSL}*P*only), this second order term is negligible since equal to the previous first-order term multiplied by the gain during the interaction with the pump pulse, assumed to be <<1. However, if the two probe waves have equal amplitudes, the 1st order term vanishes and the effect of depletion is entirely given by this 2nd order correction.

_{iSU}*P*and

_{iSL}*P*can lead to a compensation of the second order term by the no longer vanishing first order term [17

_{iSU}17. R. Bernini, A. Minardo, and L. Zeni, “Long-range distributed Brillouin fiber sensors by use of an unbalanced double sideband probe,” Opt. Express **19**(24), 23845–23856 (2011). [CrossRef] [PubMed]

*z*=

*L*, can be expressed as:

*P*=

_{iSL}*P*). The 2nd order correction must be taken into account. However, many terms vanish in Eq. (26) in this particular case, so that the pump power at the far end can be expressed as:The depletion factor

_{iSU}*d*can then be calculated using:where the expression Eq. (14) for the gain at the fiber input has been inserted. After inspecting this expression it turns out that the depletion factor

*d*is maximum when the fiber length is exactly

*L*= 1/

*α*. This can be explained as follows: the depletion naturally increases with the fiber length when the effect of attenuation is small, so for short fiber lengths. But, for longer fibers, the attenuation experienced by the signal and the pump limits the product of their power at any location along the fiber, which is the relevant quantity scaling the energy transfer between the interacting waves, as established by Eqs. (10) and (24). The distance

*L*= 1/

*α*– note this is the actual distance

*L*and not the nonlinear effective length

*L*– corresponds to the intermediate situation maximizing the effect of depletion.

_{eff}*P*=

_{iSL}*P*) an expression similar to Eq. (13), the tolerable signal power for a given depletion

_{iSU}*d*can be expressed as:

*d*.

*g*= 2 × 10

_{B}^{−11}m/W,

*A*= 80 × 10

_{eff}^{−12}m

^{2},

*α*= 22 × 10

^{−1}^{3}m), with a peak pump power

*P*= 100 mW – the maximum power before modulation instability depletes the pump [6

_{ip}6. S. M. Foaleng and L. Thevenaz, “Impact of Raman scattering and modulation instability on the performances of Brillouin sensors,” Proc. SPIE **7753**, 77539V, 77539V-4 (2011). [CrossRef]

*l*= 1 m, the power for each probe wave must not exceed 4.9 mW for a depletion factor

*d*= 0.2. This is approximately 100X larger than for a single probe and this limit is getting even higher for longer fiber lengths. It must be pointed out that a longer spatial resolution requires a lower probe power in the exact same proportions.

## 3. Experimental validation of the model

### 3.1. Measurements of the amount of depletion

*d*. The measurement is scaled by normalizing the output pump power at the peak gain frequency to its off-gain value, obtained far from the gain central frequency. Figure 7 (left) represents the measured depletion factor

*d*for various probe powers, where the solid curve is the prediction obtained using Eq. (12). The experimental values are only slightly smaller than the prediction and the discrepancy can be explained by the residual non-uniformity along the fiber and the gain spectral offset between the hot spot and the long uniform segment, which is not exactly ideal to maximize the error. Figure 7 (right) represents the depletion factor

*d*for a varying pump power while keeping the probe power constant. The depletion does not change while the gain experienced by the probe is very substantially modified. This experimentally confirms the remarkable fact that the depletion is independent of the pump power in a first-order small gain approximation.

*λ*= 1550 nm. This tiny difference makes a full compensation by gain and loss at all frequencies impossible and explains the derivative aspect of the depletion spectral dependence in Fig. 8. For a complete compensation at all frequencies, the 2 probe waves must be slightly asymmetrically positioned with respect to the pump wave, by some ½ × 600 = 300 Hz. The more pronounced asymmetry observed for high probe powers is a direct consequence of the large pump gain-loss integrated all over the fiber in this situation, so that the small gain linear approximation no longer holds and the asymmetry results from the exponential dependence of the pump gain-loss on the probe power.

*d*from these measurements, the peak excursion of the output pump power from the off-gain value was considered, which is not necessarily corresponding to the peak gain frequency but is representation of the worst case situation. The experimentaldepletion factor

*d*is graphed as a function of the probe powers in Fig. 9 (left). The solid line corresponds to the estimated values from Eq. (26), which slightly underestimates the real depletion as a result of the peak gain frequency mismatch. It must be pointed out that depletion in this case is much smaller than in the case of a single probe wave, while the signal waves power is much higher. The difference can be observed by comparing Fig. 7 (left) and Fig. 9 (left). The 2 signal waves were synthesized from the pump source using the sidebands generated by an intensity electro-optic modulator in a suppressed carrier configuration, so that they were automatically symmetrically positioned. The residual phase modulation in the modulator resulted in 2.2% power difference in the two sidebands. Due to this difference, the complete Eq. (26) was used instead of the simplified Eq. (28) for the estimation of depletion in Fig. 9 (left). Equation (26) also predicts a small dependence on the peak pump power

*P*for the depletion factor

_{ip}*d*, that is confirmed by the measurement shown in Fig. 9 (right), in excellent agreement with the model.

### 3.2. Measurement of the frequency error as a function of depletion

*ν*on the evaluated Brillouin frequency shifts to that predicted by the model using Eq. (6), as a function of the actual measured depletion

_{e}*d*. This comparison is shown in Fig. 12. The excellent agreement gives a solid confidence in the robustness of the model.

## 4. Discussion and conclusion

6. S. M. Foaleng and L. Thevenaz, “Impact of Raman scattering and modulation instability on the performances of Brillouin sensors,” Proc. SPIE **7753**, 77539V, 77539V-4 (2011). [CrossRef]

18. Y. Dong, X. Bao, and L. Chen, “High performance Brillouin strain and temperature sensor based on frequency division multiplexing using nonuniform fibers over 75km fiber,” Proc. SPIE **7753**, 77533H, 77533H-4 (2011). [CrossRef]

19. A. Zornoza, A. Minardo, R. Bernini, A. Loayssa, and L. Zeni, “Pulsing the probe wave to reduce nonlocal effects in Brillouin optical time-domain analysis (BOTDA) sensors,” IEEE Sens. J. **11**(4), 1067–1068 (2011). [CrossRef]

20. Y. Dong, L. Chen, and X. Bao, “Time-division multiplexing-based BOTDA over 100 km sensing length,” Opt. Lett. **36**(2), 277–279 (2011). [CrossRef] [PubMed]

*L*that is the distance scaling quantity for depletion. This means that each segment must be fairly shorter than the asymptotic effective length of ~22 km and segmenting the fiber in sections longer than this asymptotic effective length is essentially useless.

_{eff}*ν*on the Brillouin frequency shift can be implemented by using a long uniform fiber having a length equivalent to the claimed distance range. The Brillouin frequency at the far end of this fiber is shifted by locally modifying the temperature or the applied strain over a short section, albeit longer than the spatial resolution. The amount of shift must be

_{e}*δν*=

*Δν*/4 and the measured Brillouin shift must correspond to the real value that can be obtained by measuring the short segment only. This can be actually realized using the procedure described in Section 3.2 to obtain the measurements shown in Fig. 11.

## Acknowledgments

## References and links

1. | L. Thévenaz, “Brillouin distributed time-domain sensing in optical fibers: state of the art and perspectives,” Front. Optoelectron. China |

2. | M. A. Soto, G. Bolognini, F. Di Pasquale, and L. Thévenaz, “Long-range Brillouin optical time-domain analysis sensor employing pulse coding techniques,” Meas. Sci. Technol. |

3. | M. A. Soto, M. Taki, G. Bolognini, and F. D. Pasquale, “Simplex-coded BOTDA sensor over 120-km SMF with 1-m spatial resolution assisted by optimized bidirectional Raman amplification,” IEEE Photon. Technol. Lett. |

4. | X. Angulo-Vinuesa, S. Martin-Lopez, J. Nuno, P. Corredera, J. D. Ania-Castanon, L. Thevenaz, and M. Gonzalez-Herraez, “Raman-assisted Brillouin distributed temperature sensor over 100 km featuring 2 meter resolution and 1.2°C uncertainty,” J. Lightwave Technol. |

5. | A. Fellay, L. Thévenaz, M. Facchini, and P. A. Robert, “Limitation of Brillouin time-domain analysis by Raman scattering,” in |

6. | S. M. Foaleng and L. Thevenaz, “Impact of Raman scattering and modulation instability on the performances of Brillouin sensors,” Proc. SPIE |

7. | M. N. Alahbabi, Y. T. Cho, T. P. Newson, P. C. Wait, and A. H. Hartog, “Influence of modulation instability on distributed optical fiber sensors based on spontaneous Brillouin scattering,” J. Opt. Soc. Am. B |

8. | D. Alasia, M. Gonzalez Herraez, L. Abrardi, S. Martin-Lopez, and L. Thevenaz, “Detrimental effect of modulation instability on distributed optical fiber sensors using stimulated Brillouin scattering,” Proc. SPIE |

9. | T. Horiguchi, K. Shimizu, T. Kurashima, M. Tateda, and Y. Koyamada, “Development of a distributed sensing technique using Brillouin scattering,” J. Lightwave Technol. |

10. | E. Geinitz, S. Jetschke, U. Röpke, S. Schröter, R. Willsch, and H. Bartelt, “The influence of pulse amplification on distributed fibre-optic Brillouin sensing and a method to compensate for systematic errors,” Meas. Sci. Technol. |

11. | A. Minardo, R. Bernini, L. Zeni, L. Thevenaz, and F. Briffod, “A reconstruction technique for long-range stimulated Brillouin scattering distributed fibre-optic sensors: Experimental results,” Meas. Sci. Technol. |

12. | S. Martin-Lopez, M. Alcon-Camas, F. Rodriguez, P. Corredera, J. D. Ania-Castañon, L. Thévenaz, and M. Gonzalez-Herraez, “Brillouin optical time-domain analysis assisted by second-order Raman amplification,” Opt. Express |

13. | Y. Dong, L. Chen, and X. Bao, “System optimization of a long-range Brillouin-loss-based distributed fiber sensor,” Appl. Opt. |

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

15. | S. Diaz, S. Mafang-Foaleng, M. Lopez-Amo, and L. Thevenaz, “A high-performance optical time-domain Brillouin distributed fiber sensor,” IEEE Sens. J. |

16. | A. Minardo, R. Bernini, and L. Zeni, “A simple technique for reducing pump depletion in long-range distributed Brillouin fiber sensors,” IEEE Sens. J. |

17. | R. Bernini, A. Minardo, and L. Zeni, “Long-range distributed Brillouin fiber sensors by use of an unbalanced double sideband probe,” Opt. Express |

18. | Y. Dong, X. Bao, and L. Chen, “High performance Brillouin strain and temperature sensor based on frequency division multiplexing using nonuniform fibers over 75km fiber,” Proc. SPIE |

19. | A. Zornoza, A. Minardo, R. Bernini, A. Loayssa, and L. Zeni, “Pulsing the probe wave to reduce nonlocal effects in Brillouin optical time-domain analysis (BOTDA) sensors,” IEEE Sens. J. |

20. | Y. Dong, L. Chen, and X. Bao, “Time-division multiplexing-based BOTDA over 100 km sensing length,” Opt. Lett. |

**OCIS Codes**

(060.2310) Fiber optics and optical communications : Fiber optics

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

(060.4370) Fiber optics and optical communications : Nonlinear optics, fibers

(290.5900) Scattering : Scattering, stimulated Brillouin

**ToC Category:**

Fiber Optics and Optical Communications

**History**

Original Manuscript: April 8, 2013

Revised Manuscript: May 25, 2013

Manuscript Accepted: May 27, 2013

Published: June 4, 2013

**Citation**

Luc Thévenaz, Stella Foaleng Mafang, and Jie Lin, "Effect of pulse depletion in a Brillouin optical time-domain analysis system," Opt. Express **21**, 14017-14035 (2013)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-12-14017

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### References

- L. Thévenaz, “Brillouin distributed time-domain sensing in optical fibers: state of the art and perspectives,” Front. Optoelectron. China3(1), 13–21 (2010). [CrossRef]
- M. A. Soto, G. Bolognini, F. Di Pasquale, and L. Thévenaz, “Long-range Brillouin optical time-domain analysis sensor employing pulse coding techniques,” Meas. Sci. Technol.21(9), 094024 (2010). [CrossRef]
- M. A. Soto, M. Taki, G. Bolognini, and F. D. Pasquale, “Simplex-coded BOTDA sensor over 120-km SMF with 1-m spatial resolution assisted by optimized bidirectional Raman amplification,” IEEE Photon. Technol. Lett.24(20), 1823–1826 (2012). [CrossRef]
- X. Angulo-Vinuesa, S. Martin-Lopez, J. Nuno, P. Corredera, J. D. Ania-Castanon, L. Thevenaz, and M. Gonzalez-Herraez, “Raman-assisted Brillouin distributed temperature sensor over 100 km featuring 2 meter resolution and 1.2°C uncertainty,” J. Lightwave Technol.30(8), 1060–1065 (2012). [CrossRef]
- A. Fellay, L. Thévenaz, M. Facchini, and P. A. Robert, “Limitation of Brillouin time-domain analysis by Raman scattering,” in 5th Optical Fibre Measurement Conference, (Université de Nantes, 1999), 110–113.
- S. M. Foaleng and L. Thevenaz, “Impact of Raman scattering and modulation instability on the performances of Brillouin sensors,” Proc. SPIE7753, 77539V, 77539V-4 (2011). [CrossRef]
- M. N. Alahbabi, Y. T. Cho, T. P. Newson, P. C. Wait, and A. H. Hartog, “Influence of modulation instability on distributed optical fiber sensors based on spontaneous Brillouin scattering,” J. Opt. Soc. Am. B21(6), 1156–1160 (2004). [CrossRef]
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