**5. Advances in Brillouin based distributed optical fiber sensors**

#### **5.1. Concept of Brillouin dynamic grating**

It is obvious to know that the condition that the strain and temperature can be successfully

In fact, the Brillouin-based distributed sensing system always suffer a measurement uncer‐ tainty (∆y1 and ∆y2), which is in a linear proportional relation with the discrimination errors

A possible solution using one fiber is to monitor two acoustic resonance peaks at different orders of Brillouin gain spectrum (BGS) in a specially-designed optical fiber [13, 37, 76, 77]. So far, this method cannot ensure accurate discrimination because all the acoustic resonance frequencies exhibit similar behaviors in their dependences on strain and temperature (see Fig. 11) [49]. There is another kind of method reported for discrimination that relies on the possibility that the peak amplitude and BFS of the BGS could have quantitatively different dependences on strain and temperature [78-81]. Its accuracies is not sufficient (e.g., several degrees Celsius and hundreds of micro-strains), which is mainly due to the low signal-to-noise ratio in the BGS peak-amplitude measurement particularly for distributed sensing where

There are several system limitations in time-domain BOTDA/BOTDR and correlation-domain BOCDA/BOCDR, which comes from their individual sensing techniques. For example, BOTDA/BOTDR suffers a typical limitation of spatial resolution (~1 m) mainly determined by the linewidth of BGS or the lifetime (~10 ns) of acoustic phonons. Narrower pulse width corresponding to higher spatial resolution according to Eq. (33) weakens the acoustic phonons due to the lifetime of the acoustic phonons and leads to broader BGS as well as lower frequency accuracy due to the convolution between the intrinsic BGS and broader spectrum of the pulse [82, 83]. Moreover, although the time-of-the-flight feature of BOTDA/BOTDR is suitable for long distance sensing, the nature of pump depletion and fiber transmission loss confines the

On the other hand, BOCDA/BOCDR can provide extremely high spatial resolution of cm order or mm order with a cost of system complexity. However the correlation-domain sensing nature means that there intrinsically exist periodic correlation peaks in the fiber. Besides, the nominal definitions of spatial resolution and measurement range (see Eq. (34) and Eq. (35)) show that they both depend on the modulation frequency and thus they are in a tradeoff relation with each other [59]. The accumulation of the entire BGS along the FUT corresponding to the measured BGS at the sensing location should include a highmagnitude background of the BGS at the uncorrelated positions, which makes it difficult achieve large range of strain or temperature since higher strain or temperature change shifts the measured BGS closer to the background. As introduced in **Section 3.2**, the access ability of BOCDA/BOCDR is random and the sensing speed in one location is high. However, the

12 12 *AB BA* ¹ . (38)

distinguished is determined by

in strain (∆*ε*) and temperature (∆*T*), also given by Eq. (37).

24 Advances in Optical Fiber Technology: Fundamental Optical Phenomena and Applications

troublesome noise from non-sensing locations is accumulated.

**4.2. System limitation of time-domain or correlation-domain technique**

maximum of measurement range within several tens of kilometers [84].

Dynamic grating can be generated by use of gain saturation effect in rare-earth-metal-doped optical fibers [85-87] or stimulated Brillouin scattering (SBS) process in optical fibers [88-93] and even in a photonic chip [94]. Dynamic grating is more advantageous for certain applica‐ tions than fiber Bragg grating (FBG) [95] because it can be dynamically constructed using two coherent pump waves while FBG is static after fabrication. In comparison, the SBS-generated dynamic grating, also called Brillouin dynamic grating (BDG), is superior to the saturation gain grating due to its elasto-optic nature and lack of quantum noise [1]. In addition, the BDG is much easier to experimentally characterize [88, 90-93] while the saturation gain grating needs sophisticated double lock-in detection [86].

Up to date, there are various methods to generate BDG in optical fibers, which are schemati‐ cally compared in Fig. 13 [93]. The basic principle of BDG in optical fibers is quite similar, which is shown in Fig. 13(a). Two coherent optical waves, i.e. the pump and probe (or Stokes) waves in the SBS process, are launched from the two opposite ends of optical fibers. When their optical frequency offset (ν1= f <sup>1</sup> f 1 ' ) is equal to the BFSv B as well as the resonance frequency of the fundamental acoustic mode (νac (1) ) defined by Eq. (8):

$$\nu\_1 \equiv f\_1 - f\_1 \text{"= } \nu\_{\text{B}} = \nu\_{\text{ac}}\text{"}\tag{39}$$

where *f*1 and *f*1' are the optical frequencies of the pump and probe waves, a strong acoustic wave of the fundamental acoustic mode (the so-called BDG) is optically generated. As long as the third optical wave (i.e. the readout wave) is injected from the same end as the pump wave, there is a diffracted/reflected optical wave originating from the BDG. The diffraction or reflection efficiency (also called BDG reflectivity) is determined by the phase-matching condition, under which the pump/probe and readout wave can efficiently couple their energy via the BDG.

The method of BDG generation and detection can be classified into two different cases, which depends on the used optical fibers. In the first case of polarization maintaining fiber (PMF) [88-90] or few-mode fiber (FMF) [91] (see Fig. 13(b)), the BDG generation is separated from the BDG detection by use of orthogonal polarization states or different optical modes, respectively. The phase-matching condition means that the BFS of the BDG generation and detection should be unique as Eq. (39), which results in a frequency difference determined by the PMF's

**Figure 13.** Principle of BDG in an optical fiber. (a): Orientation of optical injection. (b) and (c): Two different cases of the optical frequency relation among the pump, probe (Stokes), readout, and BDG reflection. (After Ref. [93]; © 2013 OSA.)

birefringence (*B*) or the FMF's modal refractive index difference (neff-neff' with neff' the higherorder modal refractive index):

$$
\Delta f \equiv f\_2 - f\_1 = \frac{B}{n\_{\text{eff}}} \cdot f\_1,\tag{40}
$$

$$
\Delta f \equiv f\_2 - f\_1 = \frac{n\_{\rm eff} - n\_{\rm eff}}{n\_{\rm eff}} \cdot f\_1,\tag{41}
$$

where f<sup>2</sup> is the optical frequency of the readout wave.

As shown in Fig. 13 (c), the BDG in a SMF [92] or dispersion shifted fiber (DSF) [93] can be generalized into the second case. If the readout wave with the optical frequency of f<sup>2</sup> is launched for BDG detection, multiple-peak Stokes wave is intrinsically backscattered via SpBS. The *i*th-peak Stokes wave is downshifted in frequency from the readout wave by

$$\mathcal{V}\_2^{(0)} = \frac{2\mathbf{n}\_{eff}}{c} \cdot V\_a^{(0)} \cdot f\_2,\tag{42}$$

where V a (i) is the acoustic velocity of the *i*th-order acoustic wave. The phase-matching condition of the BDG generation and detection turns to be determined by the frequency difference between the pump and readout wave:

$$
\Delta f \equiv f\_2 - f\_1 = \frac{\nu\_1^{(\rm i)} - \nu\_1^{(\rm i)}}{1 - 2n \cdot V\_a^{(\rm i)} / \mathcal{c}} \approx \nu\_1^{(\rm i)} - \nu\_1^{(\rm i)},\tag{43}
$$

where ν1 (i) is the *i*th-order resonance frequency of the BGS measured by the pump-probe SBS process, also given by Eq. (42) except that f <sup>2</sup> is replaced by f <sup>1</sup>. The approximation in Eq. (43) is reasonable since the acoustic velocity (V a (i) =~5300-5900 m/s) in silica-based fibers is far smaller than the optical velocity (*c=*3.0× 108 m/s) [11]. Note that the BDG observed in a SMF [92] can be regarded as one special example of the generalized second case withΔ f =0 or f 2= f 1 in Eq. (43) because the BDG generation and detection share the same fundamental acoustic mode.

In comparison, the method based on a PMF is more attractive because the BDG generation and readout are oriented and separated in two orthogonal polarization states [88-90]. The frequen‐ cy-deviation property provides an additional degree of freedom to precisely characterize the birefringence according to Eq. (28). Figure 14 depicts the optical spectra of the BDG reflection measured by an optical spectrum analyzer (OSA), including four components (leaked pump and probe waves, BDG reflected wave, and Rayleigh scattered wave from left to right). The BDG property is qualitatively confirmed by the great enhancement of the third component (BDG reflected wave), since it is transferred from weak SpBS to strong SBS process under the assistance of the BDG generated by pump and probe waves. The frequency deviation can be roughly estimated to be 44.0 GHz by a wavelength meter, which gives the birefringence value of 3.28\*10-4. However, the resolution is limited to about 1\*10-6 due to 0.1 GHz-level resolution of the wavelength meter.

birefringence (*B*) or the FMF's modal refractive index difference (neff-neff' with neff' the higher-

n**2**

**Figure 13.** Principle of BDG in an optical fiber. (a): Orientation of optical injection. (b) and (c): Two different cases of the optical frequency relation among the pump, probe (Stokes), readout, and BDG reflection. (After Ref. [93]; © 2013

**(Stokes),** *f***1' Read,** *f***<sup>2</sup>**

**Brillouin dynamic grating (BDG)**

**BDG,** *f***<sup>2</sup> An optical fiber '**

**Pump** 

**Read** 

*f***1**

**Pump** 

**Read** 

*f***2**

*f***1**

D*f*

*f***2**

D*f*

*eff*

*eff*

As shown in Fig. 13 (c), the BDG in a SMF [92] or dispersion shifted fiber (DSF) [93] can be generalized into the second case. If the readout wave with the optical frequency of

'

*<sup>B</sup> ff f f <sup>n</sup>* (40)

*n n ff f f <sup>n</sup>* (41)

f<sup>2</sup> is

**Pump,** *f***<sup>1</sup>**

**Optical frequency,** n

**Optical frequency,** n

21 1 Dº - = × ,

2 1 1, - Dº - = × *eff eff*

<sup>2</sup> is the optical frequency of the readout wave.

order modal refractive index):

**Probe** 

Optical power [log scale]

Optical power [log scale]

**BDG reflection**

*f***1'**

**<sup>1</sup>** *f* **' <sup>2</sup>'**

**Case 1: PMF or FMF** 

**BDG reflection**

**Case 2: SMF or DSF**

**SBS amplified probe**

*f***1'**

**(***f***2')**

**Probe**

**Probe**

n**1** n**2**

n**1**

**SBS amplified probe**

26 Advances in Optical Fiber Technology: Fundamental Optical Phenomena and Applications

**(a)**

**(b)**

**(c)**

OSA.)

where f Most recently, a heterodyne detection was demonstrated to straightforwardly characterize the physical BDG property in a high-delta PMF [96]. Figure 15(a) summarizes a 3D distribution of the heterodyne-detected electronic spectra between the BDG reflection and the readout wave while scanning the pump–probe frequency offset (ν1 or *f*1-*f*1') around the BFS of 10.510 GHz. The peak frequency and power dependence of the on *f*1-*f*1' are shown in Fig. 15(b) and Fig. 15(c), respectively. The frequency dependence is a linear relation because the acoustic reso‐ nance frequency of the BDG is determined by *f*1-*f*1' so that the diffraction wave suffers the identical frequency downshift from the readout wave. The Brillouin gain determined by the

**Figure 14.** Qualitative characterization (optical spectra) of BDG reflection in a PMF with *B*=3.3\*10-4. Black-solid, all pump, probe and readout waves are launched; blue-dash-dotted, only readout wave; red-dashed, only probe wave; green-dotted, only pump wave.

**Figure 15.** Characterization of the BDG reflection based on heterodyne detection. (a) 3D plot of electronic spectra of heterodyne detection when the pump-probe frequency offset (*f*1-*f*1') is scanned. Dependence of peak frequency (b) and power (c) of each spectrum on *f*1-*f*1'. The dashed inset denotes Lorentz fitting (solid curve) to the linear vertical scaled symbols in (c). (After Ref. [96]; © 2013 JJAP.)

pump-probe-based SBS process is well known to be changed when *f*1-*f*1' is swept [12], which is herein reflected by the measured power dependence [see Fig. 15(c)] since the diffraction/ reflection wave sees the same change of the induced Brillouin gain. As shown in the inset of Fig. 15(c), Lorentz fitting provides the central frequency of ~10.510 GHz (just equal to the BFS), and Brillouin intrinsic linewidth of ~18 MHz. All experimental observation matches well the theoretical analysis of the BDG [97].

#### **5.2. Complete discrimination of strain and temperature**

193.54 193.55 193.56 193.57 193.58 193.59 193.60 193.61 193.62

AllOn ProbeOnly PumpOnly Readonly

All waves on Only probe wave Only pump wave Only readout wave

*BDG enhanced*

*y*-pol. Rayleigh

10.46 10.48 10.50 10.52 10.54 10.56

10.48 10.52 10.56 <sup>0</sup>

[GHz]

3-dB width: ~18 MHz

SSBM1 RF frequency n<sup>1</sup>

2 4 6

Optical frequency (THz)

ESA freq. [GHz]




Peak power [dBm]

**Figure 15.** Characterization of the BDG reflection based on heterodyne detection. (a) 3D plot of electronic spectra of heterodyne detection when the pump-probe frequency offset (*f*1-*f*1') is scanned. Dependence of peak frequency (b) and power (c) of each spectrum on *f*1-*f*1'. The dashed inset denotes Lorentz fitting (solid curve) to the linear vertical scaled



**Figure 14.** Qualitative characterization (optical spectra) of BDG reflection in a PMF with *B*=3.3\*10-4. Black-solid, all pump, probe and readout waves are launched; blue-dash-dotted, only readout wave; red-dashed, only probe wave;


(a)

*x*-pol. probe

28 Advances in Optical Fiber Technology: Fundamental Optical Phenomena and Applications

*x*-pol. pump ~44 GHz

Optical power (dBm)

green-dotted, only pump wave.

10.46

10.48

10.50

10.52

Peak frequency [GHz]

10.54

10.56

Power [dBm]

10.46 10.48 10.50 10.52 10.54 10.56

[GHz]

(b) (c)

SSBM1's RF frequency, n<sup>1</sup>

symbols in (c). (After Ref. [96]; © 2013 JJAP.)

As mentioned in **Section 5.1**, the BDG in a PMF can be generated by two coherent pump and probe waves in one principal polarization while readout by another wave deviated in fre‐ quency and separated spatially in the other principal polarization. This feature enables the BDG in a PMF working as a dynamic reflector for any optical wavelength of the readout wave by simply tuning the wavelengths of the pump and probe waves. The location of the BDG generation can be also dynamically assigned by changing the fiber's longitudinal structure [98] or programing the interaction position of the pump and probe waves [90, 99-103]. Up to date, the BDG in a PMF has been used for many applications in microwave photonics, all-optical signal processing, and Brillouin-based distributed sensors. For example, the BDG programmed in position or spectrum is very useful in microwave photonics of tunable optical delays [98, 104-106] or programmable microwave photonic filter [107]. Besides, it can also find significant applications in all-optical signal processing such as storing and compressing light [108], ultrawideband communications [109], and all-optical digital signal processing [110].

The first, but most successful, application of the BDG in a Panda-type PMF was demonstrated for complete discrimination of strain and temperature responses for Brillouin based distrib‐ uted optical fiber sensing applications [89]. Figure 16 shows the basic experimental configu‐ ration of the high-precision BDG characterization, which can be used to precisely measure the birefringence of a PMF and to completely discriminate strain and temperature. The BDG generation is based on the pump-probe scheme, which is also the high-accuracy BGS charac‐ terization shown in Fig. 7(a). The BDG measurement is realized by the lock-in detection of the BDG reflection since the BDG is periodically chopped due to the chopping of the pump wave. The birefringence-determined frequency deviation defined in Eq. (40) is characterized within a standard error of ∆*fyx*=4 MHz, corresponding to a high-accuracy birefringence of ∆*B*=3 × 10-8.

The principle of the complete discrimination is based on the dependence of the BFS on strain and temperature as introduced in Eq. (29) and the orthogonal dependence of the birefringence (*B*) or its determined frequency deviation on strain and temperature. This is because the residual tensile stress (σ*xy*) determining the Panda-type PMF's birefringence scales with the ambient temperature (*Ti* ):

$$B \ll \ \sigma\_{xy} = k \cdot (\alpha\_3 \text{ - } \alpha\_2) \cdot (T\_{\beta c} \text{ - } T\_l), \tag{44}$$

where *Tfic* denotes the fictive temperature (e.g., 850 o C) of silica glass, α<sup>3</sup> (α2) the thermal coefficient of B2O3-doped-silica stress-applying parts (pure-silica cladding), and *k* a constant determined by the geometrical location of stress-applying parts in the fiber [111]. When temperature increases (∆*T=Ti* -25 > 0), the residual stress is released and thus the birefringence decreases as

$$
\Delta B^T = -B\_0 \cdot \frac{\Delta T}{T\_{\rho c} - 2S},
\tag{45}
$$

where *B*0 is the intrinsic birefringence at room temperature (*Ti* =25 o C).

**Figure 16.** Configuration of the BDG characterization and strain-temperature discrimination. Part A, Pump-probe scheme to measure the BFS along *x*-axis and generate the BDG. Part B, Detection of the BDG diffraction spectrum to *y*polarized readout wave. (After Ref. [89]; © 2009 OSA.)

In contrast, when an axial strain ∆*ε* is applied upon the fiber, additional stress is generated because the stress-applying parts and the cladding contract in the lateral direction differently due to their different Poisson's ratios (γ3>γ2) [111], the birefringence is enlarged with applied strain as

$$
\Delta B^{\varepsilon} = +B\_0 \cdot \frac{(\chi\_{\ddagger} - \chi\_{\ddagger})}{(a\_{\sharp} - a\_{\sharp})(T\_{\ddagger\varepsilon} - 2\Im)} \cdot \Delta \varepsilon. \tag{46}
$$

Consequently, the birefringence-determined frequency deviation (∆*f*) varies linearly with respect to temperature increase and to applied strain. Suppose that *Cf ε* and *Cf <sup>Τ</sup>* are the strain Brillouin Scattering in Optical Fibers and Its Application to Distributed Sensors http://dx.doi.org/10.5772/59145 31

determined by the geometrical location of stress-applying parts in the fiber [111]. When

<sup>0</sup> , <sup>25</sup>

*fic*

<sup>D</sup> D =- × -

*<sup>T</sup> B B*

chopping

LIA1 PD1

LIA2 PD2

**Figure 16.** Configuration of the BDG characterization and strain-temperature discrimination. Part A, Pump-probe scheme to measure the BFS along *x*-axis and generate the BDG. Part B, Detection of the BDG diffraction spectrum to *y*-

In contrast, when an axial strain ∆*ε* is applied upon the fiber, additional stress is generated because the stress-applying parts and the cladding contract in the lateral direction differently due to their different Poisson's ratios (γ3>γ2) [111], the birefringence is enlarged with applied

3 2

Consequently, the birefringence-determined frequency deviation (∆*f*) varies linearly with

( ) . ( )( 25)

e

3 2


a a

g g

0

respect to temperature increase and to applied strain. Suppose that *Cf*

e

*B B*

EOM

EDFA1

PC1

SSBM EDFA3

EDFA2 polarizer

**PM-CIR1**

PC2

**VOA**

*T*

30 Advances in Optical Fiber Technology: Fundamental Optical Phenomena and Applications

where *B*0 is the intrinsic birefringence at room temperature (*Ti*

microwave,n<sup>B</sup>


*<sup>T</sup>* (45)

[ probe]

[ pump]

n

x-pol.

n

x-pol. PBS

**P**

*<sup>T</sup>* (46)

*ε* and *Cf*

*<sup>Τ</sup>* are the strain

**M-CIR2**

y-pol.

**TBF**

Part B: BDG Measurement

PC3

**F**

**U**

**T**

DFB-LD2

ramp-swept

=25 o C).

PM-ISO

temperature increases (∆*T=Ti*

isolator

Part A: Pump-Probe BDG Generation

50% 50%

DAQ

polarized readout wave. (After Ref. [89]; © 2009 OSA.)

decreases as

DFB-LD1

computer

strain as

**Figure 17.** BGS (a, b) and BDG reflection (c, d) measured at various strain (a, c) and temperature (b, d). (After Ref. [89]; © 2009 OSA.)

**Figure 18.** Brillouin frequency shift and birefringence-determined frequency deviation measured as functions of strain (a) and temperature (b). (After Ref. [89]; © 2009 OSA.)

coefficient and the temperature coefficient of the birefringence-determined frequency devia‐ tion, which can be deduced from Eqs. (40), (44), (45) and (46) as follows:

$$\begin{aligned} C\_f^c &= +\Delta f\_0 \cdot \frac{(\mathcal{Y}\_3 - \mathcal{Y}\_2)}{(\alpha\_3 - \alpha\_2)(T\_{fc} - 2\mathcal{S})} \\ C\_f^r &= -\Delta f\_0 \cdot \frac{1}{(T\_{fc} - 2\mathcal{S})}, \end{aligned} \tag{47}$$

where ∆*f*0 is the frequency deviation at 25o C and in loose condition.

By jointly considering the BFS (νB) and the frequency deviation (∆*f*), one can deduce the strain (∆*ε*) and temperature (∆*Τ*) referred to Eq. (37):

$$
\begin{pmatrix} \Delta \varepsilon \\ \Delta T \end{pmatrix} = \frac{1}{C\_{\nu}^{\varepsilon} \cdot C\_{f}^{T} - C\_{\nu}^{T} \cdot C\_{f}^{\varepsilon}} \begin{pmatrix} C\_{f}^{\mathrm{T}} & -C\_{\nu}^{\mathrm{T}} \\ -C\_{f}^{\varepsilon} & C\_{\nu}^{\varepsilon} \end{pmatrix} \begin{pmatrix} \nu\_{g} \cdot \nu\_{B0} \\ \Delta f \cdot \Delta f\_{0} \end{pmatrix},\tag{48}
$$

where ∆*f*0 and νB0 are the frequency deviation and the BFS at room temperature and in loose state.

In physics, the two phenomena/quantities, i.e. the νB and ∆*f* of the fiber, are inherently independent. In mathematics, *Cf <sup>Τ</sup>* has a sign opposite to those of other three coefficients, so that the denominator (*C*ν*ε Cf <sup>Τ</sup>*-*C*ν*<sup>Τ</sup> Cf ε*) of Eq. (48) has a significant value. The experimental results are depicted in Fig. 17 and Fig. 18, which give the two groups of coefficients (*C*ν*ε*=+0.03938 MHz/μ*ε* and *C*ν*<sup>Τ</sup>*=+1.0580 MHz/o C; and *Cf ε*=+0.8995 MHz/μ*ε* and *Cf <sup>Τ</sup>*=-55.8134 MHz/ <sup>o</sup> C). Putting above strain/temperature coefficients into Eq. (48), and taking the standard errors of the measurement system (∆ν*Β=*0.1 MHz and ∆*fyx*=4 MHz, respectively) into account, the accuracy of the discrimination is given as high as ∆*ε*=± 3.1 μ*ε* and ∆*Τ*=± 0.078 o C. Therefore, a complete discrimination of strain and temperature based on simultaneous measurement of the two quantities is ensured.

For distributed discrimination of strain and temperature, the localized BDG generation and readout in the PMF should be firstly proved to be effective. A correlation-based continuouswave technique based on the BOCDA system [99] is used for random access and a pulse-based time-domain technique based on the BOTDA system [100] is employed for continuous access. It was found that the generation and readout waves based on the BOCDA system should be synchronously frequency-modulated because of the dispersion properties of all four waves (see Fig. 19) [112], including pump and probe waves, readout wave and acoustic wave (BDG as well).

The preliminary success of distributed discrimination of strain and temperature was realized by use of several lasers based on the BOCDA system [113] or the BOTDA system [114]. In [113], all pump, probe, and readout waves are synchronously modulated in frequency by sinusoidal functions to the two laser diodes. The measurement range of the distributed BGS and BDG is

coefficient and the temperature coefficient of the birefringence-determined frequency devia‐

3 2

*fic*

C and in loose condition.

0 0

*<sup>Τ</sup>* has a sign opposite to those of other three coefficients, so that

*ε*) of Eq. (48) has a significant value. The experimental results

*<sup>Τ</sup>*=-55.8134 MHz/ <sup>o</sup>

C. Therefore, a

C).

*ε*=+0.8995 MHz/μ*ε* and *Cf*

(47)

( ) ( )( 25)

3 2

a a


*fic*

 e

*f f f*

C; and *Cf*

accuracy of the discrimination is given as high as ∆*ε*=± 3.1 μ*ε* and ∆*Τ*=± 0.078 o

ç ÷ <sup>=</sup> ç ÷ç ÷ è ø <sup>D</sup> ×-× - è ø D D è ø

æ ö - æ ö

 n

*T T*

g g

<sup>1</sup> , ( 25)

By jointly considering the BFS (νB) and the frequency deviation (∆*f*), one can deduce the strain

<sup>1</sup> - , n

*C C*

*T T f B B*

> e

n n

*<sup>T</sup> CC CC C C f f* (48)

n

e

where ∆*f*0 and νB0 are the frequency deviation and the BFS at room temperature and in loose

In physics, the two phenomena/quantities, i.e. the νB and ∆*f* of the fiber, are inherently

are depicted in Fig. 17 and Fig. 18, which give the two groups of coefficients (*C*ν*ε*=+0.03938

Putting above strain/temperature coefficients into Eq. (48), and taking the standard errors of the measurement system (∆ν*Β=*0.1 MHz and ∆*fyx*=4 MHz, respectively) into account, the

complete discrimination of strain and temperature based on simultaneous measurement of the

For distributed discrimination of strain and temperature, the localized BDG generation and readout in the PMF should be firstly proved to be effective. A correlation-based continuouswave technique based on the BOCDA system [99] is used for random access and a pulse-based time-domain technique based on the BOTDA system [100] is employed for continuous access. It was found that the generation and readout waves based on the BOCDA system should be synchronously frequency-modulated because of the dispersion properties of all four waves (see Fig. 19) [112], including pump and probe waves, readout wave and acoustic wave (BDG

The preliminary success of distributed discrimination of strain and temperature was realized by use of several lasers based on the BOCDA system [113] or the BOTDA system [114]. In [113], all pump, probe, and readout waves are synchronously modulated in frequency by sinusoidal functions to the two laser diodes. The measurement range of the distributed BGS and BDG is

tion, which can be deduced from Eqs. (40), (44), (45) and (46) as follows:

32 Advances in Optical Fiber Technology: Fundamental Optical Phenomena and Applications

e

*f*

*T f*

e

n

*<sup>Τ</sup>*-*C*ν*<sup>Τ</sup> Cf*

where ∆*f*0 is the frequency deviation at 25o

(∆*ε*) and temperature (∆*Τ*) referred to Eq. (37):

æ ö De

independent. In mathematics, *Cf*

MHz/μ*ε* and *C*ν*<sup>Τ</sup>*=+1.0580 MHz/o

the denominator (*C*ν*ε Cf*

two quantities is ensured.

state.

as well).

0

*C f <sup>T</sup>*

0

*C f <sup>T</sup>*

= -D × -

**Figure 19.** Dispersion properties of all optical (pump, probe and readout) and acoustic wave (Brillouin dynamic gra‐ ting). (After Ref. [112]; © 2011 OSA.)

commonly given by the neighboring correlation peaks of the BOCDA system as defined in Eq. (35). Although the spatial resolution of the BGS measurement is still given by Eq. (34), that of the BDG reflection was thought to be determined by the BDG bandwidth (∆fyx) as follows:

$$
\Delta Z\_{\rm nDG} = \frac{\mathcal{L}}{2\eta f\_m} \cdot \frac{\Delta f\_{yx}}{\pi \Delta f} \,. \tag{49}
$$

The feasibility of distributed discrimination of strain and temperature was experimentally demonstrated with 10-cm spatial resolution. The *fm*=12.429 MHz determines the nominal measurement range as *dm*=8.35 m according to Eq. (35). For local BGS and BDG measurement, the ∆*fB*=1.5 GHz and ∆*fD*=10 GHz correspond to a nominal spatial resolution ∆*zB*=5 cm and ∆*zD*=8 cm [see Eq. (34) and Eq. (49)], respectively. As shown in Fig. 20(a), a ~8-m PMF sample is prepared, which consists of nine (A-I) cascaded fiber portions of 10-16 cm in length. The A, C, G and I portions were loosely laid at 25.1 o C for reference, while the B, D, F, and H portions were loosely inserted into a temperature-controlled water bath with 0.1-o C accuracy. The E portion was also inserted into the water bath and glued to a set of translation stages to load strain. The measured distribution of the changes of ∆*v*B and ∆*f*yx are summarized in Figs. 20(b) and 20(c), respectively. Referred to the characterized coefficients in Fig. 18 and the crosssensitivity matrix in Eq. (48), the deducted distribution of temperature and strain along the fiber is depicted in Figs. 20(d) and 20(e), which clearly shows the feasibility of distributed discrimination of strain and temperature. In [114], all pump, probe, and readout waves are pulsed in time domain; in turn, the BDG generation and readout as well as the BGS and BDG reflection are continuously localized by control of their relative delay towards the FUT and thus the local νB and ∆*f* are detected for distributed discrimination of the strain and temperature responses.

**Figure 20.** Preliminary experiment of distributed discrimination of strain and temperature based on two lasers modu‐ lated in frequency. (a) FUT configuration. Measured distribution of Brillouin frequency shift (b) and the birefringencedetermined frequency deviation (c). Deduced distribution of temperature (d) and strain (e). (After Ref. [113]; © 2010 IEEE.)

One-laser-based Brillouin correlation-domain distributed discrimination system [112] by use of the sideband-generation technique was recently demonstrated to overcome the frequency fluctuation among the free-running lasers for pump, probe, and readout waves, and thus improve the accuracy of distributed discrimination of strain and temperature. Figure 21 represents the experimental setup. A 40-GHz intensity modulator (IM2) laid after the laser diode is driven by a radio frequency synthesizer (RF2 at νRF2) with a proper dc bias so as to generate double sidebands with suppressed carrier (DSB-SC). The optical filtering (FBG and tunable band-pass filter) is used to separate the two sidebands for the BDG generation and readout. By control of the RF1 (similar to Fig. 16), the BFS can be precisely measured and then fixed; by tuning of the RF2, the BDG reflection can be also precisely characterized; by simply change of the modulation frequency of the one laser diode, the location of the BGS and BDG can be swept for distributed measurement.

pulsed in time domain; in turn, the BDG generation and readout as well as the BGS and BDG reflection are continuously localized by control of their relative delay towards the FUT and thus the local νB and ∆*f* are detected for distributed discrimination of the strain and temperature

A B C D E F G H I

E

2.3 2.5 2.7 2.9 3.1 3.3 3.5 3.7 3.9

2.3 2.5 2.7 2.9 3.1 3.3 3.5 3.7 3.9

A B C D F G H I

E

Position [m]

 Case 1: No strain applied on E portion Case 2: Strain applied on E portion

2.3 2.5 2.7 2.9 3.1 3.3 3.5 3.7 3.9

2.3 2.5 2.7 2.9 3.1 3.3 3.5 3.7 3.9

A B C D F G H I

**Figure 20.** Preliminary experiment of distributed discrimination of strain and temperature based on two lasers modu‐ lated in frequency. (a) FUT configuration. Measured distribution of Brillouin frequency shift (b) and the birefringencedetermined frequency deviation (c). Deduced distribution of temperature (d) and strain (e). (After Ref. [113]; © 2010

E

Position [m]

<sup>D</sup> <sup>F</sup> <sup>H</sup> <sup>E</sup>

F H

<sup>A</sup> <sup>B</sup> <sup>C</sup> <sup>G</sup> <sup>I</sup>

D

 Case 1: No strain applied on E portion Case 2: Strain applied on E portion)

Probe

4.3 m

**(d)**

**(e)**

G I

responses.

2.3 m

A

B

C

**(a)** Readout

34 Advances in Optical Fiber Technology: Fundamental Optical Phenomena and Applications

**(b)**

**(c)**

Pump

Change of n

Change of

D

De [e]

IEEE.)

*T* [

oC]

*fyx*[MHz]

B[MHz]

**Figure 21.** Experimental setup of the one-laser-based Brillouin correlation-domain distributed discrimination system. (After Ref. [112]; © 2011 OSA.)

Figure 22 shows the higher stability and accuracy (several MHz) of the one-laser scheme when compared to the two-laser scheme (several hundreds of MHz) both under no averaging process. Note that the one-laser scheme can also provide higher speed in the measurement of BGS and BDG and simpler measurement without sophisticated synchronization. Its distrib‐ uted discrimination of strain and temperature was confirmed with the spatial resolution of ~10 cm and measurement range of ~5 m, which is depicted in Fig. 23 when the fiber was heated from 25 o C to 30 o C or/and the strain (*ε*=2000 μ*ε*) was applied both at the location of 3.1 m. The measured results match well with the setting situation.

In order to overcome the tradeoff between the spatial resolution and measurement range always existing in the BOCDA system, a temporal gating [115] or a dual frequency modulation scheme [116] with a simple modification in Fig. 21 was used to elongate the measurement range of distributed discrimination of strain and temperature. For temporal gating scheme, the pulse modulation of RF2 makes the frequency-modulated pump, probe and readout waves optically pulsed in time and only one of the multiple correlation peaks are effectively generated in the

**Figure 22.** Comparison of the stability and accuracy of one-laser (solid dots) and two-laser (dashed squares) schemes of the BDG reflection. (After Ref. [112]; © 2011 OSA.)

FUT. For dual frequency modulation scheme, two sinusoidal functions are combined together to simultaneously modulate the optical frequencies of the pump, probe and readout waves. The greater modulation frequency ensures the higher spatial resolution while the lower modulation frequency realizes the longer measurement range. A 20 times [115] or 7 times [116] enlargement of the ratio between the measurement range and the spatial resolution was successfully demonstrated. It is expectable to achieve Brillouin optical correlation-domain distributed discrimination of strain and temperature having both a higher spatial resolution (better than 10 cm) and a longer measurement range (better than 1,000 m) by combining the dual frequency modulation scheme with the temporal gating scheme, which is now under study. Most recently, an apodization method under the assistance of intensity modulation was proposed to suppress the sidelobe of SOCF and enhance the spatial resolution of the straintemperature discrimination by 4.5 times [117].

#### **5.3. System improvement of sensing techniques**

Many works have been involved in improving the system performance of BOTDA/BOTDR and BOCDA/BOCDR in terms of spatial resolution, measurement range, sensing speed and accuracy. In 1995, Bao *et al.* developed a Brillouin-loss-based BOTDA [118] by reversing the functions of the pulse laser and CW light. In other words, a strong CW light acts as a Brillouin pump wave and a pulse light with a scanned down-shifted frequency from that of the CW light works as a probe wave [119]. After monitoring the optical loss profile of the pump wave due to Brillouin interaction between the two light waves as a function of time or position along the fiber, a numerical signal processing of the poor SNR was used to achieve ~25 cm spatial resolution with a strain resolution of ~40 μ*ε* [120]. A pulse-pre-pump BOTDA (called PPP-BOTDA) was proposed to realize cm-order spatial resolution by using a wide pulse (larger than 10 ns) followed by a narrow pulse (smaller than 1 ns) [121], which is in principle similar to the BOTDA with a pulse generated by a finite extinction ratio [122]. A dark-pulse-based BOTDA was later presented to hopefully obtain 2-cm spatial resolution [123, 124], which

Brillouin Scattering in Optical Fibers and Its Application to Distributed Sensors http://dx.doi.org/10.5772/59145 37

FUT. For dual frequency modulation scheme, two sinusoidal functions are combined together to simultaneously modulate the optical frequencies of the pump, probe and readout waves. The greater modulation frequency ensures the higher spatial resolution while the lower modulation frequency realizes the longer measurement range. A 20 times [115] or 7 times [116] enlargement of the ratio between the measurement range and the spatial resolution was successfully demonstrated. It is expectable to achieve Brillouin optical correlation-domain distributed discrimination of strain and temperature having both a higher spatial resolution (better than 10 cm) and a longer measurement range (better than 1,000 m) by combining the dual frequency modulation scheme with the temporal gating scheme, which is now under study. Most recently, an apodization method under the assistance of intensity modulation was proposed to suppress the sidelobe of SOCF and enhance the spatial resolution of the strain-

**Figure 22.** Comparison of the stability and accuracy of one-laser (solid dots) and two-laser (dashed squares) schemes of

0 5 10 15 20 25

 One-LD scheme Two-LD scheme

Measurement times

Many works have been involved in improving the system performance of BOTDA/BOTDR and BOCDA/BOCDR in terms of spatial resolution, measurement range, sensing speed and accuracy. In 1995, Bao *et al.* developed a Brillouin-loss-based BOTDA [118] by reversing the functions of the pulse laser and CW light. In other words, a strong CW light acts as a Brillouin pump wave and a pulse light with a scanned down-shifted frequency from that of the CW light works as a probe wave [119]. After monitoring the optical loss profile of the pump wave due to Brillouin interaction between the two light waves as a function of time or position along the fiber, a numerical signal processing of the poor SNR was used to achieve ~25 cm spatial resolution with a strain resolution of ~40 μ*ε* [120]. A pulse-pre-pump BOTDA (called PPP-BOTDA) was proposed to realize cm-order spatial resolution by using a wide pulse (larger than 10 ns) followed by a narrow pulse (smaller than 1 ns) [121], which is in principle similar to the BOTDA with a pulse generated by a finite extinction ratio [122]. A dark-pulse-based BOTDA was later presented to hopefully obtain 2-cm spatial resolution [123, 124], which

temperature discrimination by 4.5 times [117].

44.2

the BDG reflection. (After Ref. [112]; © 2011 OSA.)

44.4

Birefringence,

*f*

[GHz]

*yx*

44.6

44.8

36 Advances in Optical Fiber Technology: Fundamental Optical Phenomena and Applications

**5.3. System improvement of sensing techniques**

**Figure 23.** Experimental results of high-accuracy distributed discrimination of strain and temperature based on onelaser scheme. Distribution of Brillouin frequency shift (a), the birefringence-determined frequency deviation (b), strain (c), and temperature (d). (After Ref. [112]; © 2011 OSA.)

suffers a neglectful influence of the acoustic lifetime (~10 ns) but an experimental difficulty of high-qualify dark pulse and a scarified measurement range due to the pump depletion of the dc base. A new scheme by combination of the PPP-BOTDA and dark-pulse-based BOTDA [125] was demonstrated to achieve higher spatial resolution as well as better frequency resolution. Taking the similar principle of the PPP-BOTDA technique, a BDG-based BOTDA was proposed to obtain cm-order or sub-cm-order spatial resolution [126-128]. The only difference lies on the fact that the Brillouin interaction in the BDG-based BOTDA is generated by a long pulse along one principal polarization state (the BDG generation process) and detected by a short pulse along the orthogonal polarization state (the BDG readout process). Another type of the modified BOTDA with higher spatial resolution of less than 1 meter is based on a group of pulses, called differential pulse-width pair BOTDA (DPP-BOTDA) [129-132] or Brillouin echo BOTDA [133, 134]. In DPP-BOTDA, a pair of pulses with a small difference of the pulse widths are successively launched into the FUT; the Brillouin interaction is recorded for twice and a subtraction is performed to achieve the sensing trace with the high spatial resolution determined by the small pulse-width difference. The spatial resolution of BOTDR has been also more or less improved by an experimental optimization or signal processing process [135-137].

Although BOTDA and BOTDR are excellent for long sensing range (such as kilometers or tens of km), they still suffer the physical limitation of maximum range due to the nature of fiber loss and/or the Brillouin depletion effect. There are two typical methods, i.e. Raman-assisted BOTDR[138-140] or Raman-assisted BOTDA[141-145] and coded BOTDR[146] or coded BOTDA[147-151], to improve the poor SNR and achieve a very long sensing range. The best performance of the sensing range (longer than 120 km) [152, 153] with an acceptable spatial resolution (1 m or 2 m) has been renovated by combination of Raman assistance and coding although the system becomes extremely complicated. Most recently, specially-designed EDFA repeaters were used to extend the sensing measurements of BOTDA to more than 300 km [154]. Some efforts were also made to study the influence of Brillouin depletion on the maximum range of BOTDA [41] and to avoid it to some extent by use of Stokes together with anti-Stokes wave as Brillouin probe [155, 156].

BOCDA and BOCDR systems have natural advantages of high spatial resolution without any dependence on the acoustic lifetime and random programmable accessibility of the sensing location. Except for the great innovation of Brillouin optical correlation-domain distributed discrimination of strain and temperature introduced in **Section 5.2**, advances in BOCDA and BOCDR systems have also boosted in the past decade. The polarization disturbance along the FUT has been effectively solved by use of the polarization diversity scheme to the BOCDA system [157]. A complicated double-lock-in detection was proposed to improve the SNR of the BOCDA system [69, 158] although a modified lock-in detection based on variable chopping frequency [159] or a simplified but equivalent BOCDA system based on combination of Brillouin gain and loss [34] was later proposed. The existence of a big noise floor originated from the uncorrelated locations strongly limits the maximum strain or temperature change to be detected, which has been eliminated by use of intensity modulation for SOCF apodization [160, 161] or differential measurement scheme based on external phase modulation [162]. The measurement range of BOCDA [116, 163, 164] or BOCDR [165, 166] was extended by use of temporal gating or double frequency modulation scheme, respectively. Besides, combination of time-domain and correlation domain techniques [167, 168] has been proposed to enlarge the measurement range of the BOCDA [169] based on external phase modulation. The distributed sensing speed with cm-order spatial resolution [170-172] has been substantially increased to several Hertz along the entire FUT by optimizing the position sweeping and the BGS mapping although the local sensing speed of the BOCDA [173-175] or BOCDR [176] was well-known to be high at the random-accessed sensing location.

## **6. Conclusions**

We have presented an essential overview of Brillouin scattering in optical fibers and Brillouin based distributed optical fiber sensors. Started from the basic principle of Brillouin scattering in optical fibers, the basic mechanism of Brillouin based distributed optical fiber sensors (linear dependence of Brillouin frequency shift on strain and temperature) and the two different groups of Brillouin based distributed optical fiber sensors (time domain: BOTDA/BOTDR; correlation domain: BOCDA/BOCDR) were described in detail. The difficulties and challenges of how to simultaneously sense strain and temperature were demonstrated and the physical limitation of the sensing abilities (spatial resolution, measurement range, accuracy etc.) were introduced, respectively. Finally, we summarized recent advances of this field towards the solutions to those difficulties and challenges.

It is valuable to address that Brillouin based distributed optical fiber sensors are nowadays in a high technical level, which have been attracting industrial companies to commercialize for structural health monitoring in civil structures, aerospace, energy (gas, oil) pipeline, and engineers (power supply).
