3. Principle of distributed Brillouin sensing

According to the DES of SBS, the Brillouin gain in each fiber section is accumulated in an SBS interaction between two continuous waves (CW). This accumulation along the fiber leads to a relative high energy conversion at the detector but makes it difficult to distinguish the information of local interactions. Therefore, distributed Brillouin sensing uses other techniques.

#### 3.1 Temperature and strain-dependent Brillouin frequency shift

According to the theory of material science, the velocity of the longitudinal acoustic mode in the fiber depends on material properties such as Young's moduli and the density [39]. This high sensitivity to the temperature and tensile strain makes the BFS also temperature [40] and strain [41] dependent. The linear dependence has been proved and measured in several papers [40–42], as illustrated in Figure 2 and can be expressed as:

$$
\omega\_B(T, \varepsilon) - \nu\_B(T\_0, \varepsilon\_0) = \mathbf{C}\_\varepsilon \cdot \delta \varepsilon + \mathbf{C}\_T \cdot \delta T \tag{7}
$$

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Figure 2. BFS dependence on (a) temperature and (b) strain in a SMF for a pump wavelength of 1550 nm [42].

where νBð Þ T; ε represents the BFS at a temperature T and strain ε, CT and C<sup>ε</sup> are the temperature and strain coefficients. Although both temperature and strain contribute to the BFS shift, the physical difficulty in discriminating the response from these two factors can be solved with specific strategies [43]. For standard SMF, CT and C<sup>ε</sup> are measured to be 1.081 MHz/°C and 42.93 kHz/με, respectively [42]. The slope of the linearity has also been studied intensively and optimized with different doping concentrations [44].

#### 3.2 Overview of SBS sensing techniques

Since the first demonstration of the most widely used distributed Brillouin sensing scheme in time domain [4], which is now called Brillouin optical time domain analyzer (BOTDA), several different schemes have been proposed and developed with their own advantages and disadvantages.

#### 3.2.1 BOTDA

The full width at half maximum (FWHM) of the BGS Δν<sup>B</sup> ¼ ΓB=ð Þ 2π , also known as the natural Brillouin linewidth, is estimated to be several tens of MHz for SMF, as shown in Figure 1(b) for a 20 km SMF. The Brillouin linewidth can be engineered to several GHz with a broadened pump for applications such as SBSbased filters [18–20] and slow light [21–23] while it can also be narrowed to a record

It is also worth to mention that the complex SBS gain changes not only the probe wave in amplitude, but also in phase by its imaginary part. As shown in Figure 1(b), the SBS phase shift has a linear dependence on the frequency detuning in the vicinity of the BFS and zero-phase shift directly at the BFS, that is, the peak Brillouin gain. These properties are important for applications such as SBS-based microwave

Since the state of polarization (SOP) of the probe and pump waves hover randomly in the fiber due to the weak birefringence of SMF and only an averaged interaction can be detected at the output, the dependence of the SBS gain on the SOP has been neglected for long. However, with the rise of the polarization maintaining technique [31], the polarization effect of SBS has been investigated, and it has been found that the SBS efficiency of the pump-probe interaction with

2

pump waves in the Poincaré sphere. As shown in Eq. (6), the SBS efficiencies of a

both of the pump and Stokes are orthogonally linear polarized (s<sup>3</sup> ¼ 0). This behavior

According to the DES of SBS, the Brillouin gain in each fiber section is accumulated in an SBS interaction between two continuous waves (CW). This accumulation along the fiber leads to a relative high energy conversion at the detector but makes it difficult to distinguish the information of local interactions. Therefore,

According to the theory of material science, the velocity of the longitudinal acoustic mode in the fiber depends on material properties such as Young's moduli and the density [39]. This high sensitivity to the temperature and tensile strain makes the BFS also temperature [40] and strain [41] dependent. The linear dependence has been proved and measured in several papers [40–42], as illustrated in

νBð Þ� T; ε νBð Þ¼ T0; ε<sup>0</sup> C<sup>ε</sup> � δε þ CT � δT (7)

2 <sup>3</sup> and s 2

can be used for many different applications from filters [19, 32, 33] via highresolution spectrum analyzers [34–36] to the generation of THz waves [37, 38].

1 þ s1p<sup>1</sup> þ s2p<sup>2</sup> � s3p<sup>3</sup>

represent the unit vectors of Stokes and

(6)

3. The SBS efficiency reaches zero when

photonic filters [29] and distributed Brillouin dynamic sensing [30].

ð Þ¼ <sup>1</sup> <sup>þ</sup> ^<sup>s</sup> � <sup>p</sup>^ <sup>1</sup>

of 3.4 MHz with specific techniques [24–28].

Fiber Optic Sensing - Principle, Measurement and Applications

arbitrary polarization states is governed by [7]:

<sup>η</sup>SBS <sup>¼</sup> <sup>1</sup> 2

3. Principle of distributed Brillouin sensing

distributed Brillouin sensing uses other techniques.

3.1 Temperature and strain-dependent Brillouin frequency shift

where ^s ¼ ð Þ s1; s2; s<sup>3</sup> and p^ ¼ p1; p2; p<sup>3</sup>

parallel and orthogonal SOP are 1 � s

Figure 2 and can be expressed as:

62

2.3 The polarization effect of SBS

The principle of BOTDA is based on the Brillouin interaction between a pulsed pump (or probe) wave and a counterpropagating CW probe (or pump) wave. The acoustic wave is generated locally at the point where the pump pulse and the probe CW meet. The energy transfer via the acoustic wave at each position of the fiber under test (FUT) is determined by the frequency detuning between the two signals in comparison to the phonon frequency, that is, the probe wave is amplified when ν<sup>p</sup> � ν<sup>s</sup> ¼ ν<sup>a</sup> and depleted when ν<sup>s</sup> � ν<sup>p</sup> ¼ ν<sup>a</sup> where νp, νs, and ν<sup>a</sup> are the pump, probe, and phonon frequency, respectively. As shown in Figure 3(a) as a typical example, local Brillouin gain (or loss) can be translated from the time-dependent to the distance-dependent information according to the round trip relation z ¼ ct=ð Þ 2n where z is the fiber position where pump and probe wave interact, t is the propagation time of the pulse, c is the velocity of light in vacuum, and n is the refractive index.

In order to derive the local BFS at each position of the fiber, the reconstruction of the BGS, as illustrated in Figure 3(b), should be carried out by a frequency sweep with every frequency detuning around the phonon frequency. The accurate BFS at each fiber section can be achieved by fitting every measured BGS with the theoretical profile (either Voigt [45] or Lorentzian, dependent on pulse width) as illustrated in Figure 4(a).

Figure 3. (a) Evolution of the Brillouin gain for a given frequency detuning; (b) reconstructed 3D BGS along the fiber.

nodes with the frequency difference properly set in the vicinity of the BFS of the FUT [48]. Since the frequency difference varies much faster than the time to excite an acoustic wave, only negligible Brillouin interactions will take place at the other positions. Therefore, unlike a pulse-based scheme such as BOTDA, the spatial resolution of a BOCDA system is usually high and determined by the modulation

Schematic explanation of BOCDA [48]. The frequency difference between pump and probe wave is constant at

Correlation peaks

<sup>Δ</sup><sup>z</sup> <sup>¼</sup> vg � <sup>ν</sup><sup>B</sup>

where vg is the group velocity, ν<sup>B</sup> is the Brillouin gain linewidth, f <sup>m</sup> and Δf are the modulation frequency and amplitude of the FM. By sweeping the frequency difference between the pump and probe wave, the BGS of the measured fiber position is

It is difficult to determine the contribution of the Brillouin interaction from multiple points of the fiber simultaneously. Therefore, the modulation frequency of both waves and the delay from one side should be carefully set, so that only a single correlation peak along the fiber is measured at a time. Thus, the sensing range of a BOCDA system is usually short and limited by the distance between adjacent cor-

In comparison with other Brillouin sensing techniques, BOCDA has an excellent performance in achieving high spatial resolution, which depends on the FM modulation amplitude and the natural Brillouin linewidth. Besides, since the acoustic wave is excited by CW waves, the BGS linewidth will not be broadened. However, since each point along the fiber must be measured individually, the total measurement time will be linearly proportional to the amount of resolved points, which makes the measure-

The principle of the Brillouin optical frequency domain analyzer (BOFDA) [49]

ment time also longer, compared to the other Brillouin sensing techniques.

is based on the measurement of the complex transfer function that relates the amplitudes of the CW counterpropagating pump and probe wave with the FUT. The probe wave is frequency downshifted to the pump by the BFS and amplitude modulated with a sinusoidal function at a variable frequency. The modulated pump and probe wave intensities are measured at the end of the FUT with two separate photodiodes (PD) that fed to a network analyzer (NWA). By sweeping the modulation frequency, the NWA measures the baseband transfer function of the FUT,

<sup>2</sup>π<sup>f</sup> <sup>m</sup> � <sup>Δ</sup><sup>f</sup> (8)

P ump(f1)

P robe(f2)

P osition

P osition

. The location of the measured correlation peak can be

parameters (amplitude and frequency) written as:

*f*

The State-of-the-Art of Brillouin Distributed Fiber Sensing

DOI: http://dx.doi.org/10.5772/intechopen.84684

Δf

*f*<sup>1</sup> *− f*<sup>2</sup> Δ*f*

shifted by changing the modulation frequency.

scanned.

Figure 5.

the correlation peaks.

3.2.4 BOFDA

65

relation peaks dm ¼ vg= 2f <sup>m</sup>

#### 3.2.2 BOTDR

The principle of Brillouin optical time domain reflectometry (BOTDR) is a Brillouin scattering-based OTDR [2]. Different from BOTDA, only a pulsed pump is launched into the FUT from one side of the fiber. Since the time-resolved probe signal is back reflected due to SpBS instead of SBS, the signal power is much weaker than for BOTDA [4] and it is of great importance to apply a coherent detection with a strong local oscillator simultaneously [46]. Since an access to the other fiber end is not necessary, BOTDR is advantageous for some applications. However, besides the weak received signal, it suffers from further disadvantages such as limited spatial resolution of around 1 m, the distortion from Rayleigh backscattering, Fresnel reflection from the connector, and a limited sensing range due to fiber attenuation.

#### 3.2.3 BOCDA

The Brillouin optical correlation domain analyzer (BOCDA) is one of the most recently demonstrated Brillouin sensing techniques. Compared to BOTDA and BOTDR, much higher spatial resolutions down to several millimeters can be achieved [47]. Its principle is based on the interaction of two identically frequencymodulated (FM) counterpropagating CW waves. Similar to the principle of a standing wave (see Figure 5), the frequency difference between the counterpropagating pump and probe wave remains constant at specific positions of the fiber, that is, correlation peaks called nodes. Brillouin interactions will take place at these

#### Figure 4.

(a) Measured BGS (solid) at a given fiber section with its Lorentzian fitting (dashed); (b) the reconstructed Brillouin gain mapping with a 20 m long hot spot at the fiber end.

The State-of-the-Art of Brillouin Distributed Fiber Sensing DOI: http://dx.doi.org/10.5772/intechopen.84684

Figure 5.

3.2.2 BOTDR

**0.995 1.000 1.005 1.010 1.015 1.020 1.025 1.030 1.035**

**(a)**

**Brillouin gain (a.u)**

Figure 3.

3.2.3 BOCDA

**1.000 1.005 1.010 1.015 1.020 1.025 1.030**

**(a)**

**Brillouin gain (a.u.)**

Figure 4.

64

The principle of Brillouin optical time domain reflectometry (BOTDR) is a Brillouin scattering-based OTDR [2]. Different from BOTDA, only a pulsed pump is launched into the FUT from one side of the fiber. Since the time-resolved probe signal is back reflected due to SpBS instead of SBS, the signal power is much weaker than for BOTDA [4] and it is of great importance to apply a coherent detection with a strong local oscillator simultaneously [46]. Since an access to the other fiber end is not necessary, BOTDR is advantageous for some applications. However, besides the weak received signal, it suffers from further disadvantages such as limited spatial resolution of around 1 m, the distortion from Rayleigh backscattering, Fresnel reflection from the connector, and a limited sensing range due to fiber attenuation.

(a) Evolution of the Brillouin gain for a given frequency detuning; (b) reconstructed 3D BGS along the fiber.

**-50 0 50 100 150 200 250 300**

**10.75 10.80 10.85 10.90 10.95**

Brillouin gain mapping with a 20 m long hot spot at the fiber end.

**Frequency (GHz)**

**Time ( s)**

**-5 0 5 10 15 20 25 30**

**Distance (km)**

Fiber Optic Sensing - Principle, Measurement and Applications

The Brillouin optical correlation domain analyzer (BOCDA) is one of the most recently demonstrated Brillouin sensing techniques. Compared to BOTDA and BOTDR, much higher spatial resolutions down to several millimeters can be achieved [47]. Its principle is based on the interaction of two identically frequencymodulated (FM) counterpropagating CW waves. Similar to the principle of a standing wave (see Figure 5), the frequency difference between the counterpropagating pump and probe wave remains constant at specific positions of the fiber, that is, correlation peaks called nodes. Brillouin interactions will take place at these

**24.40 24.45 24.50 24.55 24.60**

**Distance (km)**

**Brillouin gain (a.u) (b)**

**0.998 1.000 1.002 1.003 1.005 1.007 1.009 1.010 1.012**

**10.76 10.78 10.80 10.82 10.84 10.86 10.88 10.90 10.92 10.94**

**Frequency**

(a) Measured BGS (solid) at a given fiber section with its Lorentzian fitting (dashed); (b) the reconstructed

 **(GHz)**

Schematic explanation of BOCDA [48]. The frequency difference between pump and probe wave is constant at the correlation peaks.

nodes with the frequency difference properly set in the vicinity of the BFS of the FUT [48]. Since the frequency difference varies much faster than the time to excite an acoustic wave, only negligible Brillouin interactions will take place at the other positions. Therefore, unlike a pulse-based scheme such as BOTDA, the spatial resolution of a BOCDA system is usually high and determined by the modulation parameters (amplitude and frequency) written as:

$$
\Delta z = \frac{\upsilon\_{\text{g}} \cdot \upsilon\_{B}}{2\pi f\_{m} \cdot \Delta f} \tag{8}
$$

where vg is the group velocity, ν<sup>B</sup> is the Brillouin gain linewidth, f <sup>m</sup> and Δf are the modulation frequency and amplitude of the FM. By sweeping the frequency difference between the pump and probe wave, the BGS of the measured fiber position is scanned.

It is difficult to determine the contribution of the Brillouin interaction from multiple points of the fiber simultaneously. Therefore, the modulation frequency of both waves and the delay from one side should be carefully set, so that only a single correlation peak along the fiber is measured at a time. Thus, the sensing range of a BOCDA system is usually short and limited by the distance between adjacent correlation peaks dm ¼ vg= 2f <sup>m</sup> . The location of the measured correlation peak can be shifted by changing the modulation frequency.

In comparison with other Brillouin sensing techniques, BOCDA has an excellent performance in achieving high spatial resolution, which depends on the FM modulation amplitude and the natural Brillouin linewidth. Besides, since the acoustic wave is excited by CW waves, the BGS linewidth will not be broadened. However, since each point along the fiber must be measured individually, the total measurement time will be linearly proportional to the amount of resolved points, which makes the measurement time also longer, compared to the other Brillouin sensing techniques.

#### 3.2.4 BOFDA

The principle of the Brillouin optical frequency domain analyzer (BOFDA) [49] is based on the measurement of the complex transfer function that relates the amplitudes of the CW counterpropagating pump and probe wave with the FUT. The probe wave is frequency downshifted to the pump by the BFS and amplitude modulated with a sinusoidal function at a variable frequency. The modulated pump and probe wave intensities are measured at the end of the FUT with two separate photodiodes (PD) that fed to a network analyzer (NWA). By sweeping the modulation frequency, the NWA measures the baseband transfer function of the FUT,

whose inverse fast Fourier transformation approximates the pulse response of the FUT and represents the temperature and strain distribution. The high spatial resolution that BOFDA could achieve depends on the frequency sweep range, though, at the cost of the measurement time.

σVð Þ¼ z σð Þz

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 3 � δ � Δν<sup>B</sup>

The State-of-the-Art of Brillouin Distributed Fiber Sensing

3=2

!η¼0:5 σð Þz ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 3 4 δ � Δν<sup>B</sup>

<sup>¼</sup> <sup>1</sup> SNR zð Þ

NAV <sup>p</sup> , the frequency error will also

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 3 4 δ � Δν<sup>B</sup>

(9)

r

r

As expected, a denser frequency sampling and a higher SNR value lead to a more accurate BFS estimation. Taking the relation of the SNR and number of averaging

decrease significantly after thousands of averages due to an enhanced SNR. Owing to the linear dependence of the Brillouin phase response in the vicinity of the BFS, the sensor performance can also be evaluated by the linear fitting of the BPS [53] with a narrow frequency scanning and reduced measurement time (see black curve

As discussed in Section 2.3, the Brillouin gain is highly dependent on the SOP of the pump and probe wave. Due to the weak birefringence of SMF, the SOP change of pump and probe leads to a highly nonuniform Brillouin gain along the fiber and consequently to a poor SNR for almost every fiber section, which is called polarization fading [50]. There are several solutions for polarization fading in a BOTDA system. The first proposed idea was to sequentially launch two orthogonal SOPs of the pump (or probe) wave and average the two measured results [4]. Another option is polarization scrambling, where the SOP of the pump and probe is varied rapidly so that the SOP is effectively randomized over time. It can be used in various scientific setups to cancel the errors caused by polarization-dependent effects. With a polarization scrambler and a digitizer, the traces can be averaged over thousands of pump pulses until a required high enough SNR is reached,

According to the round-trip relation, the Brillouin interaction in a conventional BOTDA system takes place in a fiber section with a length of cT=ð Þ 2n , which can be seen as the spatial resolution [54], where c is the light speed in vacuum, n is the fiber refractive index and, T is the pulse duration. In principle, the spatial resolution could be enhanced by using shorter pulses. However, two main factors limit the

First of all, decreasing the pulse duration will shorten the Brillouin interaction length and hence lower the SBS gain and consequently the SNR. Furthermore, the pump power spectrum for a shorter pulse will be severely broadened. Therefore, the resulting effective BGS should be modified as the convolution of the pump

where Ipð Þν is the pump pulse power spectrum, which is significantly broadened to 1=T for pulses shorter than 20 ns [55]. The inherent broadening of the BGS leads to a decrease of the peak gain, which makes the estimation of the BGS peak more sensitive to the noise level. Moreover, it also indicates that the probe wave will be amplified only after the acoustic field is excited by the pump-probe interaction, which takes 10–30 ns. Due to the abovementioned reasons, the spatial resolution of

<sup>B</sup> ð Þ¼ ν gBð Þν ⊗Ipð Þν (10)

spectrum density and the natural Brillouin linewidth [21], that is,

g eff

8 ffiffi 2 <sup>p</sup> ð Þ <sup>1</sup> � <sup>η</sup>

NAV into consideration, that is, SNR zð Þ<sup>∝</sup> ffiffiffiffiffiffiffiffiffi

3.5 Major issues and limitations of BOTDA

though, at the cost of the BGS acquisition time.

3.5.2 Limitations on pump pulse width

spatial resolution to only 1 m.

67

s

DOI: http://dx.doi.org/10.5772/intechopen.84684

and yellow line in Figure 6(b)).

3.5.1 Polarization fading
