**3. Brillouin–based distributed sensors**

#### **3.1. Sensing of measurands**

( ) = g

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

/ . *P L k GL <sup>p</sup>* (28)

(c) (d)

**Figure 8.** (a) Simulated BGS at different positions in the fiber. (b) Critical position *xc*, determined by the normalized gain *k* and injected power ratio γ. The critical positions divide the fiber into two parts with and without the spectral hole burning phenomenon. Measured BGS in the middle (c) or at the end (d) of a 50-m-long fiber. (after Ref. [42]; ©

Figure 8(c) and 8(d) illustrates the measured BGS under different pump power for two different positions (in the middle and at the far end, respectively) of a 50-m-long dispersion compen‐ sated fiber (DCF). The probe power is fixed at 9.8 dBm. At the far end, the BGS [see Fig. 8(d)] rises with the power increased but always preserves the Lorentz shape. While in the middle, the experimental result [see Fig. 8(c)] is in a qualitative accordance with the numerical analysis [see Fig. 8(a)]. The Brillouin gain keeps rising with the increase of optical power, while the peak at the local Brillouin frequency shift seems to be saturated gradually and a hollow starts appearing when it reaches ~20 dBm, which is just the spectral hole burning phenomenon. The hollow in the BGS may introduce great errors to pump-probe-based Brillouin distributed

The pump power leading to the BGS saturation is approximately characterized as the critical pump power (for instance, 21.3 dBm at z=30 m). The measured critical powers for two positions (*z=*20 m or 30 m) of 50-m-long DCF are depicted in Fig. 9, where the simulated critical powers are compared. It illustrates that the critical pump powers approximately measured for several

sensors since it disables the peak-searching of the Brillouin frequency shift.

2014 JJAP.)

The first report of Brillouin based distributed optical fiber sensors [43] was based on the same principle as that of optical time domain reflectometry (OTDR) or Raman based OTDR (ROTDR) technique as a non-destructive attenuation measurement technique for optical fibers. In that proposal [33], SBS process was performed by injecting an optical pulse source and a continuous-wave (CW) light into two ends of FUT. When the frequency difference of the pulse pump and CW probe is tuned offset around ν<sup>B</sup> of the FUT, the CW probe power experiences Brillouin gain from the pulse light through SBS process. Similarly like the case of OTDR, the SBS distributed measurement could measure attenuation distribution along the fiber having no break from an interrogated optical power as a function of time, but it has much higher signal-to-noise ratio (more than ~10 dB) than OTDR due to SBS high gain. Later, Horiguchi and co-researchers found that this non-destructive can be extended into **a frequency-resolved technique** because νB of optical fibers has linear dependence on measurands of strain and temperature as follows [44, 45]:

$$
\Delta \nu\_B - \nu\_{B0} = A \cdot \delta \varepsilon + B \cdot \delta T,\tag{29}
$$

where ν*B0* is measured at room temperature (25o C) and in the "loose state" as a reference point, ∆*ε* the applied strain and ∆*T* the temperature change. The "loose state" means that the FUT is laid freely in order to avoid any artificial disturbances. *A (or C*ν*ε*) is the strain coefficient in a unit of MHz/μ*ε* and *B (or CΤε*) is the temperature coefficient in a unit of MHz/ <sup>o</sup> C. Figure 10 illustrates the characterized strain or temperature dependence in a standard SMF under the experimental setup of Fig. 7(a), where the BGS always moves towards higher ν*<sup>B</sup>* and its gain reduces or increases when ∆*ε* or ∆*T* is increased, respectively. At 1550 nm, *A*=0.04~0.05 MHz/ μ*ε* and *B*=1.0~1.2 MHz/ oC, which depends on the fiber's structure and jackets**. Note that Eq. (29) is the basic sensing mechanism of Brillouin-based distributed sensors.**

The nowadays telecom optical fibers (ITU-T G.651, G.652, G.653, and G.655) mostly have GeO2-doped fiber cores [46] and pure-silica (or other-doped-silica) cladding. Naturally, the GeO2 doping induces the reduction of the longitudinal acoustic velocity in GeO2-doped core *Vl*1 with respect to that in pure-silica cladding *Vl*2 (i.e. *Vl*1 < *Vl*2) [24, 47]. It provides a waveguide of longitudinal acoustic modes in the core region as schematically depicted in Fig. 3(b). A recent study further proves that the acoustic modes sense better confinement than the optical modes in a GeO2-doped optical fiber [13]. The enhanced confinement results in the existence of multiple *L*0*<sup>l</sup>* acoustic modes in a single-mode optical fiber (SMF) [8], and also leads to that the first-order *L*<sup>01</sup> acoustic mode among all *L*0*<sup>l</sup>* modes is best confined in the core and even better confined than the fundamental *LP*01 optical mode [13]. Furthermore, the enhanced confinement shows that the effective acoustic velocity of *L*<sup>01</sup> mode (*Va*) is close to *Vl*1 (i.e. *Va* ≈ *Vl*1), the longitudinal acoustic velocity in the core. Therefore, the change of the *L*01 mode's effective acoustic velocity *Va* is dominantly due to the change of the core's acoustic velocity *Vl*<sup>1</sup> but negligibly (less than 1%) due to that of the cladding's acoustic velocity *Vl*2, even though the core's acoustic velocity *Vl*1 and the cladding's acoustic velocity *Vl*2 vary equally [12].

The longitudinal acoustic velocity *Vl*1 in the GeO2-doped core (approximately, the *L*01 mode's effective acoustic velocity *Va*) is determined by the Young's modulus (*E*1) and the density (*ρ*1) [48]:

$$V\_a \approx V\_{l1} = \sqrt{E\_1 \wedge \rho\_1},\tag{30}$$

For convenience, we introduce a normalized strain coefficient (*A*'=*A*/ν*B0*, in a unit of 10-6/μ*ε*) and a normalized temperature coefficient (*B*'=*B*/ν*B0*, in a unit of 10-6/ <sup>o</sup> C). The normalized strain coefficients include three respective factors[49]:

$$A' \equiv \frac{A}{\nu\_{B0}} = A'\_{\
u \mathcal{H}} + A'\_{\
\rho} + A'\_{\
u},\tag{31}$$

$$B' \equiv \frac{B}{\nu\_{B0}} = B'\_{\
u \circ \mathcal{V}} + B'\_{\
\rho} + B'\_{\
u}.\tag{32}$$

Each three parts in the right sides of Eq. (31) and Eq. (32) are determined by relative change rates in *n*eff, *E*1, and ρ1 due to the applied strain ∆*ε* or the temperature change ∆*Τ. A'neff* and *B'neff* are determined by the elasto-optic and thermo-optic effects; *A'ρ* and *B'ρ* are subject to the straininduced distortion and the thermal expansion; *A'E* and *B'E* are decided by the strain-induced second-order nonlinearity of Young's modulus and the thermal-induced second-order nonlinearity of Young's modulus.

where ν*B0* is measured at room temperature (25o

[48]:

∆*ε* the applied strain and ∆*T* the temperature change. The "loose state" means that the FUT is laid freely in order to avoid any artificial disturbances. *A (or C*ν*ε*) is the strain coefficient in a

illustrates the characterized strain or temperature dependence in a standard SMF under the experimental setup of Fig. 7(a), where the BGS always moves towards higher ν*<sup>B</sup>* and its gain reduces or increases when ∆*ε* or ∆*T* is increased, respectively. At 1550 nm, *A*=0.04~0.05 MHz/ μ*ε* and *B*=1.0~1.2 MHz/ oC, which depends on the fiber's structure and jackets**. Note that Eq.**

The nowadays telecom optical fibers (ITU-T G.651, G.652, G.653, and G.655) mostly have GeO2-doped fiber cores [46] and pure-silica (or other-doped-silica) cladding. Naturally, the GeO2 doping induces the reduction of the longitudinal acoustic velocity in GeO2-doped core *Vl*1 with respect to that in pure-silica cladding *Vl*2 (i.e. *Vl*1 < *Vl*2) [24, 47]. It provides a waveguide of longitudinal acoustic modes in the core region as schematically depicted in Fig. 3(b). A recent study further proves that the acoustic modes sense better confinement than the optical modes in a GeO2-doped optical fiber [13]. The enhanced confinement results in the existence of multiple *L*0*<sup>l</sup>* acoustic modes in a single-mode optical fiber (SMF) [8], and also leads to that the first-order *L*<sup>01</sup> acoustic mode among all *L*0*<sup>l</sup>* modes is best confined in the core and even better confined than the fundamental *LP*01 optical mode [13]. Furthermore, the enhanced confinement shows that the effective acoustic velocity of *L*<sup>01</sup> mode (*Va*) is close to *Vl*1 (i.e. *Va* ≈ *Vl*1), the longitudinal acoustic velocity in the core. Therefore, the change of the *L*01 mode's effective acoustic velocity *Va* is dominantly due to the change of the core's acoustic velocity *Vl*<sup>1</sup> but negligibly (less than 1%) due to that of the cladding's acoustic velocity *Vl*2, even though the

unit of MHz/μ*ε* and *B (or CΤε*) is the temperature coefficient in a unit of MHz/ <sup>o</sup>

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

**(29) is the basic sensing mechanism of Brillouin-based distributed sensors.**

core's acoustic velocity *Vl*1 and the cladding's acoustic velocity *Vl*2 vary equally [12].

1 11 *VV E a l* » = / ,

' ' ' ',

' ' ' '.

º = ++ *neff <sup>E</sup>*

º = ++ *neff <sup>E</sup>*

and a normalized temperature coefficient (*B*'=*B*/ν*B0*, in a unit of 10-6/ <sup>o</sup>

0

0

*B*

n

*B*

n

coefficients include three respective factors[49]:

The longitudinal acoustic velocity *Vl*1 in the GeO2-doped core (approximately, the *L*01 mode's effective acoustic velocity *Va*) is determined by the Young's modulus (*E*1) and the density (*ρ*1)

r

r

r

*<sup>A</sup> A A AA* (31)

*<sup>B</sup> B B BB* (32)

For convenience, we introduce a normalized strain coefficient (*A*'=*A*/ν*B0*, in a unit of 10-6/μ*ε*)

C) and in the "loose state" as a reference point,

(30)

C). The normalized strain

C. Figure 10

**Figure 10.** (a) Stain and (b) temperature dependences of BGS in SMF; (c) Strain and (d) temperature dependences of Brillouin frequency shift νB in SMF.

Strict experimental characterization on a series of optical fibers with different GeO2 concen‐ tration is depicted in Fig. 11 [49]. The BFS has linear dependence on the GeO2 concentration in the fiber's core (i.e.-87.3 MHz/mol%), which corresponds to ν*B0* change of-87.3 MHz regarding 1-mol% increase of GeO2 concentration in the core (i.e. an incremental ∆ of 0.1 %). It specifies the previously reported values [25, 50, 51]. Besides, the frequency spacing between neigh‐ bouring acoustic modes increases by orders when the GeO2 concentration is enhanced, for example, ~50-60 MHz for Fiber-A (SMF, 3.65 mol%) versus ~700-720 MHz for Fiber-C (HNF, 17.0 mol%).

**Figure 11.** (a) BGS, (b) BFS, (c) normalized strain coefficient, and (d) normalized temperature coefficients in silica opti‐ cal fibers with different GeO2 concentration. (After Ref. [49]. © 2008 OSA/IEEE.)

The normalized strain and temperature coefficients defined in Eq. (31) and Eq. (32) were characterized by repeating the BGS measurement under different applied strain and temper‐ ature change. It shows a linear dependence of *A*' or *B*' on GeO2 concentration with slope of-1.48 %/mol% or-1.61 %/mol%, which denote that *A'* and *B'* are relatively decreased by-1.48 % and-1.61 % for an incremental ∆ of 0.1 %. The theoretical study further indicates that both the strain and temperature dependences in Eq. (29) are dominantly (~92%) responsible from the strain-induced and thermal-induced second-order nonlinearities of Young's modulus, that is, Eq. (31) and Eq. (32) [49].

#### **3.2. Sensing of location**

Besides the sensing of measurands (see Eq. (29)), the mapping of spontaneous or stimulated Brillouin scattering process (not just non-destructive attenuation measurement [43]) is another key issue to realize distributed optical fiber sensing [52-54]. Two different mapping ways, as schematically illustrated in Fig. 12, were proposed. One is to repeat the localized BGS in scanned positions along the FUT; the other is to repeat the Brillouin interaction under different frequency offset.

There are three different mapping or position-interrogation techniques, including time domain [33, 52-56], frequency domain [57, 58], and correlation domain [59-61]. Regarding the injection ways of optical fields, there are two opposite groups, i.e. analysis versus reflectometry. The analysis is two-end injection based on SBS; while the reflectometry is one-end injection based on SpBS. Comparably, the analysis has much higher SNR than the reflectometry. Note that there is an additional method between analysis and reflectometry, called one-end analysis [55, 62, 63]. Its only difference from the traditional (two-end) analysis is the one-end injection and its SBS process occurs between the forward pump and the backward probe wave that is reflected at the far end of FUT.

The basic principle of time-domain sensing technique is the "time-of-flight" phenomenon in FUT. For two-end or one-end analysis, named Brillouin optical time domain analysis (BOTDA) [33, 52, 54], one of pump and probe waves is pulsed in time and the other is continuous wave (CW). Subsequently, they are successively interacted along the FUT during the time-of-flight of the pulsed wave. In contrast, for one-end reflecometry, called Brillouin optical time domain reflectometry (BOTDR) [53, 56], the pump wave is pulsed in time and the SpBS Stokes wave is reflected along the FUT during the pump's time-of-flight. The basic experimental configu‐ ration of BOTDR or BOTDA can be simply carried out in Fig. 5 or Fig. 6, respectively. The required modification is to insert an optical pulse generator (for example, an electro-optic intensity modulator driven by an electric pulse generator). The spatial resolution (∆*Z*TD) of time-domain distributed sensing is physically determined by the pulse width (τ)[43]:

$$
\Delta Z\_{\rm TD} = \frac{\boldsymbol{\pi} \cdot \boldsymbol{c}}{2\boldsymbol{n}},
\tag{33}
$$

where *c* is the light speed in vacuum and *n* the group velocity of the pulse. The BGS mapping is realized by repeating the above measurement when the spectrum of the reflected Stokes in BOTDR is processed or the optical frequency offset between the pump and probe in BOTDA is tuned around the BFS νB.

The normalized strain and temperature coefficients defined in Eq. (31) and Eq. (32) were characterized by repeating the BGS measurement under different applied strain and temper‐ ature change. It shows a linear dependence of *A*' or *B*' on GeO2 concentration with slope of-1.48 %/mol% or-1.61 %/mol%, which denote that *A'* and *B'* are relatively decreased by-1.48 % and-1.61 % for an incremental ∆ of 0.1 %. The theoretical study further indicates that both the strain and temperature dependences in Eq. (29) are dominantly (~92%) responsible from the strain-induced and thermal-induced second-order nonlinearities of Young's modulus, that is,

**Figure 11.** (a) BGS, (b) BFS, (c) normalized strain coefficient, and (d) normalized temperature coefficients in silica opti‐

9600

60

(c) (d)

70

80

Normalized B (10


oC)

/

(a) (b)

90

Fiber-D

100

110

10000

BFS (MHz)

10400

10800

Fiber-D

11200

0 2 4 6 8 10 12 14 16 18 20 22 24

Fiber-B2

0 2 4 6 8 10 12 14 16 18 20 22 24

] (mol.%)

Fiber-C

[GeO2

] (mol.%)

[GeO2

(a) (b)

Fiber-A

Fiber-B2

Fiber-A

F-HDF

Fiber-C

Besides the sensing of measurands (see Eq. (29)), the mapping of spontaneous or stimulated Brillouin scattering process (not just non-destructive attenuation measurement [43]) is another

Eq. (31) and Eq. (32) [49].

9.6 9.8 10.0 10.2 10.4 10.6 10.8 11.0 11.2 11.4

Frequency (GHz)

Fiber-B2

0 2 4 6 8 10 12 14 16 18 20 22 24

] (mol.%)

cal fibers with different GeO2 concentration. (After Ref. [49]. © 2008 OSA/IEEE.)

Fiber-C

[GeO2

<sup>10</sup> Fiber-D

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

Fiber-C Fiber-B2 Fiber-A

0

2.6 2.8 3.0 3.2 3.4 3.6 3.8 4.0

Fiber-D

Fiber-A

Normalized A (10


/e)

2

4

6

Gain (a.u.)

8

**3.2. Sensing of location**

There are two kinds of correlation-domain sensing techniques, nominated Brillouin optical correlation domain analysis (BOCDA) [59, 60] and Brillouion optical correlation domain reflectometry (BOCDR) [61, 64]. Both of them originate from the so-called synthesis of optical coherence function (SOCF) [65, 66]. Nevertheless, the SOCF in BOCDA or BOCDR is generated between the pump and probe waves or between the pump-scattered Stokes wave and the optical oscillator, respectively. In experiment, the BOCDR and BOCDA can be executed by substituting a distributed feedback laser diode (DFB-LD) driven by a function generator (such as in a sinusoidal function) for the light source in Fig. 5 and Fig. 6, respectively. Thanks to the current-frequency transferring effect of DFB-LD [67], the optical frequencies of the light

**Figure 12.** Schematic of sensing of location or mapping of BGS.

sources are simultaneously modulated also in a sinusoidal function. Subsequently, the optical frequency offset between pump and probe or between scattered Stokes and optical oscillator changes with time as well as position, deviating from the preset constant frequency offset around the BFS νB. Only at some particular locations (called correlation peaks), the frequency offset is maintained as the constant frequency offset because of the in-phase condition so that the local SBS interaction or the beating of the local Stokes and oscillator is **constructive**. At other locations rather than correlation peaks, the frequency offset is always vibrating with time, which leads to a broadened and **destructive** SBS or SpBS. The spatial resolution of BOCDA and BOCDR are both determined by[59]

$$
\Delta Z\_{\rm CD} = \frac{c}{2\eta f\_m} \cdot \frac{\Delta \nu\_B}{\pi \Delta f},
\tag{34}
$$

where *f*m is the modulation frequency of the sinusoidal function, ∆*f* the modulation depth, and ∆νB the Brillouin linewidth defined in Eq. (10). Since the SOCF is naturally realized by an integral or summation signal processing in photonics or electronics, all SBS or SpBS along the entire FUT should be accumulated together (as an example shown in Fig. 6(a), accumulated by a LIA). Consequently, the maximum measurement length (or sensing range, *L*CD) is decided by the distance between two neighboring correlation peaks [59]:

$$L\_{\rm CD} = \frac{c}{2\eta f\_m}.\tag{35}$$

Because of the difference of the physical pictures between time domain and correlation domain, their sensing performance is different. For example, the spatial resolution of BOTDA/ BOTDR was typically limited to be ~1 m by the lifetime of acoustic phonons (10 ns) and the nature of intrinsic Brillouin linewidth. However, BOCDA/BOCDR is of CW nature free from this limitation, and their spatial resolution can be ~cm-order [60, 68] or even ~mm-order [69]. Since BOTDA/BOTDR carries out the whole mapping of BGS along the FUT during the timeof-the-flight while BOCDA/BOCDR realizes the distributed sensing by sweeping the modu‐ lation frequency (or correlation peak), the sensing speed is different. The entire sensing speeds for both BOTDA/BOTDR and BOCDA/BOCDR are time-consuming due to the tuning of pump-probe frequency offset, averaging of mapping, and signal processing of data fitting. However, the sensing position of BOCDA/BOCDR can be random accessed [59, 61], and the dynamic sensing with high speed at the random accessed position is possible [70, 71]. The detailed difference of other performances will be described in **Section 4** and **Section 5**.
