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• Abstract

SECTION I

## INTRODUCTION

Brillouin optical time domain analysis (BOTDA) has gain much attention over the past two decades, owing to its superiority of distributed monitoring of temperature or strain along the optical fiber over a distance of several tens of km with sub-meter resolution [1], [2]. This technology is commonly based on Brillouin gain spectrum (BGS) measurement, in which the amplitude of Brillouin gain or loss is analyzed to determine the Brillouin frequency shift (BFS). Meanwhile, the Brillouin interaction not only amplifies or depletes the probe, but also changes its phase [3]. This phase change is called Brillouin phase-shift in Ref. [4].

Recently, the concept of vector measurement is adopted from the vector network analyzer (VNA) and applied to BOTDA, giving rise to vector Brillouin optical time domain analysis (VBOTDA) [5], which exhibits the capacity of measuring both the amplitude and phase-shift of Brillouin gain or loss. The first vector Brillouin measurement is attributed to A. Loayssa, et al. [6], where the measurement is implemented in a continuous operating mode. The VBOTDA [5] employed a heterodyne scheme based on a double-frequency phase modulation, and measured both the intensity and phase spectrograms of the Brillouin interaction in the distributed sense. The phase spectrogram vividly featured the high-order acoustic resonances, which were not clear on the intensity spectrogram. The Brillouin phase-shift has a linear shape near the BFS, and has been applied to dynamic strain measurement [7]. Besides, the phase of the heterodyne signal is independent of Brillouin gain, and thus is immune to non-local effects, showing huge potential of enhanced long-haul distributed sensors [8]. With Raman assistance, VBOTDA shows considerable potential in long-range distributed measurements [9]. A similar structure with phase modulated probe is reported in [10], also shows the feature of vector measurement. All those VBOTDAs commonly employ the phase modulation to generate the probe wave. However, the high-order modulated sidebands would beat to generate heterodyne signals as well, and degrade the VBOTDA performance. Moreover, the involved demodulations, RF demodulation [4], [7], [8] for instance, are not easy to access or implement.

In this paper, we demonstrate a VBOTDA with heterodyne scheme, and use IQ demodulation algorithm to demodulate the heterodyne signals. The operation principle of the heterodyne-based VBOTDA and the IQ demodulation algorithm are explained in Sections 2 and 3, respectively. In the experiment, we employ an acousto-optic frequency shifter (AOFS) to generate a single-frequency reference, avoiding the high-order sidebands in the phase modulation and directly featuring the Brillouin gain and phase-shift. Distributed Brillouin gain and phase-shift spectrograms measurement is successfully performed in an $\sim$1.6-km standard single-mode fiber (SMF) consisting of two different kind of fibers, with an $\sim$2-m spatial resolution. The temperature dependences of the Brillouin gain and phase-shift spectra are measured on a 12-m fiber section. The temperature dependences of the BFSs show excellent linearity larger than 0.999 and these two temperature coefficients are almost identical, with the value of 1.166 and 1.159 MHz/°C.

SECTION II

## PRINCIPLE

In a conventional BOTDA system, two light waves, most often a pulsed Brillouin pump wave and a CW probe wave, countpropagate along an optical fiber with a frequency difference near the BFS, usually 10–11 GHz for standard SMFs. In a gain-based scheme (which will be discussed afterward), the pump wave generates a local Brillouin gain for the probe wave, as shown in Fig. 1(a) transfers its energy to the probe wave. The probe wave is amplified by the pump wave where they encounter. The amplification depends on the pump power, but more importantly on the frequency difference of the two waves. This relationship is regarded as BGS, which has a Lorentzian shape of the form [See the blue solid line in the Fig. 1(b).]TeX Source$$g(\nu_{S}, z) = g_{0}{\Delta\nu^{2}_{B} \over 4\Delta \nu^{2} + \Delta\nu^{2}_{B}}\eqno{\hbox{(1)}}$$ where $g_{0}$ is the peak gain, $\Delta\nu_{B}$ is the Brillouin linewidth, $\Delta\nu = \nu_{P} - \nu_{S} - \nu_{B}(z)$ is the detuning of the probe frequency from the center of the BGS, $\nu_{P}$ and $\nu_{S}$ are the frequencies of the pump and probe waves respectively, $\nu_{B}(z)$ is the BFS at position $z$. The BFS is linear with the circumstance temperature and the applied strain, which is the fundamental of BOTDA sensors.

Fig. 1. (a) Principle of the VBOTDA. A reference wave (Ref.) is introduced for heterodyne detection of Brillouin signal. (b) Brillouin gain and phase-shift spectra.

During the Brillouin amplification, the probe wave would experience a phase-shift process according to the Kramers-Kronig relations [3]. The Brillouin phase-shift is dependent on the pump power and the frequency difference of the two waves as well, and is illustrated as the red dash line in Fig. 1(b). This dependence has an expression as follows, TeX Source$$\varphi_{B}(\nu_{S}, z) = g_{0}{2\Delta\nu_{B}\Delta\nu \over 4 \Delta\nu^{2} + \Delta\nu^{2}_{B}}.\eqno{\hbox{(2)}}$$ Eq. (2) suggests that, measuring Brillouin phase-shift can also determine BFS along the fiber, thus determine the circumstance temperature and the applied strain. It is clear from Fig. 1(b) that the Brillouin phase-shift has a good linearity approximation near the BFS, which has been applied to dynamic strain measurement [7].

In the VBOTDA scheme with heterodyne detection, a coherent CW reference is introduced to propagate with the probe along the fiber in the same direction, as depicted in Fig. 1(a). But its frequency is away from the probe and outside BGS of the pump. Therefore, it does not interact with the pump via Stimulated Brillouin Scattering (SBS). Then, the optical field at the detector, coming from the amplified probe and the reference at a particular position in the fiber, $z$, is given byTeX Source\eqalignno{E = &\, E_{S} \exp\left(g(\nu_{S}, z)\right) \exp\left(j2\pi\nu_{S} t + j\varphi_{B}(\nu_{S}, z)\right) + E_{R} \exp\left(j2\pi(\nu_{S} + f_{0})t\right)\cr \approx &\, E_{S} \left(1 + g(\nu_{S}, z)\right)\exp\left(j2\pi\nu_{S} t + j\varphi_{B}(\nu_{S}, z)\right) + E_{R} \exp\left(j2\pi(\nu_{S} + f_{0})t\right)&\hbox{(3)}} where $E_{S}$ and $E_{R}$ are the amplitudes of the optical fields of the probe and reference, $f_{0}$ is the frequency difference between the probe and reference. The approximation in (3) is obtained assuming a small gain in the general cases of BOTDA sensors. It is notable that $f_{0}$ is just several hundred MHz, so the chromatic dispersion of the two waves is ignored here.

The detected optical intensity at the frequency $f_{0}$ can be expressed asTeX Source$$I(f_{0}) = 2E_{S}E_{R}\left(1 + g(\nu_{S}, z)\right) \cos\left(2\pi f_{0}t - \varphi_{B}(\nu_{S}, z)\right).\eqno{\hbox{(4)}}$$ The amplitude of the heterodyne signal contains Brillouin gain information, while the phase implies Brillouin phase-shift information. Obviously, the gain and phase of the heterodyne signal in (4) are exactly the Brillouin gain and phase-shift expressed by (1) and (2), not the modified expression as obtained by phase modulation in Ref. [7] and [8]. Thus more physical insight could be got into the Brillouin character of optical fibers, compared with phase modulation.

SECTION III

## IQ DEMODULATION ALGORITHM

IQ demodulation algorithm is very popular to measure the RF amplitude and phase in RF signal processing, and is widely employed to retrieve the phase information in the interferometric fiber optic sensors [11], [12]. This algorithm is quite easy to implement and requires a few calculations, which can reduce the measurement time of the VBOTDA systems and presents potentials for real-time demodulation.

The block diagram of the IQ demodulation algorithm is depicted in Fig. 2. The heterodyne signal is split and separately multiplied with two orthogonal references with the same frequency of heterodyne signal, $\cos(2\pi f_{0}t)$ and $\sin(2\pi f_{0}t)$. Thus the signals are down-shifted to the baseband, then they are low-pass filtered to remove the undesirable high frequency spectrum by two identical low-pass filters (LPF), generating the in-phase component, $I(t)$, and quadrature component, $Q(t)$. The cut-off frequency of the LPFs is critical, which should be less than the half of the heterodyne frequency, $f_{0}/2$. The amplitude of the heterodyne signal is given by calculating the square root of the quadratic sum of $I(t)$ and $Q(t)$, while the phase is deduced from the arctangent of $I(t)$ over $Q(t)$.

Fig. 2. Block diagram of the IQ demodulation algorithm. LPF: low-pass filter; $I(t)$: in-phase component; $Q(t)$: quadrature component.
SECTION IV

## EXPERIMENTAL SETUP

The experimental setup of the proposed VBOTDA is schematically depicted in Fig. 3, which is very similar to the conventional BOTDA system, except the Mach-Zehnder (MZ) interferometer, in the red box, to generate the heterodyne signal. A distributed-feedback laser diode (DFB-LD), operating at $\sim$1550.1 nm with 5 dBm output power and $\sim$10 kHz linewidth, is used to generate Brillouin pump and probe signals and the reference. The CW-light is divided into two branches by a 3-dB coupler. The pulsed Brillouin pump light is generated by an acousto-optic modulator (AOM) with an extinction ratio larger than 30 dB, a high power erbium-doped fiber amplifier (EDFA) and a polarization scrambler (PS). The AOM is driven by an arbitrary waveform generator (AWG), with pulses of 20 ns width (corresponding to 2 m spatial resolution) and 10 kHz repetition rate. The PS is used to randomize the optical polarization and thus reduce the polarization-induced gain fluctuation. Note that the AOM used to chop CW-light has a side effect of frequency shift, which should be counted in the calculation of BFS.

Fig. 3. Experimental setup of the heterodyne based VBOTDA. DFB-LD: distributed-feedback laser diode; SSBM: single-sideband modulator; EDFA: erbium-doped fiber amplifier; AOFS: acousto-optic frequency shifter; PC: polarization controller; AOM: acousto-optic modulator; AWG: arbitrary waveform generator; PS: polarization scrambler; FUT: fiber under test. The insets show respectively, (a) the output optical spectrum of SSBM measured by an optical spectrum analyzer and (b) the FUT layout that consists of two different fibers.

On the upper branch, a single-sideband modulator (SSBM) and a microwave source are employed to generate the frequency-downshifted probe light whose optical spectrum is shown in the inset (a) of Fig. 3, where the carrier and unwanted sidebands have been suppressed with a suppression ratio of $\sim$26 dB through properly setting the DC biases of the SSBM. An EDFA is followed to compensate the loss of the SSBM and the following MZ interferometer. The upper arm of the interferometer, with 90% of the power, is used to generate the reference through a 200 MHz AOFS. A polarization controller (PC) is used to adjust the probes polarization on the lower arm of the MZ interferometer, to ensure the maximum visibility of the beat signal of the probe and reference. The reference and probe are recombined by a 3-dB coupler with balanced powers considering the insert loss of the AOFS.

After Brillouin interaction with the pump, the probe as well as the reference is amplified by an EDFA and then directed to a 400 MHz receiver via a circulator. Finally, the heterodyne signal is captured by a high-speed digital oscilloscope, and delivered to a computer for further signal processing. The fiber under test (FUT) consists of two sections of SMF with slightly different BFSs: Fiber-I with 33 m length and Fiber-II with 1541 m length, as shown in the inset (b) of Fig. 3. Such FUT layout is constructed for spatial resolution determination at the fused point of the two fiber sections.

SECTION V

## RESULTS AND DISCUSSIONS

An experiment is performed following the setup in Fig. 3 for a proof-of-concept validation of the proposed VBOTDA. The sampling rate of the oscilloscope is set to be 1 GSa/s. The sampled heterodyne signals are averaged 400 times to eliminate the Brillouin gain fluctuation and improve the signal to noise ratio, and then demodulated using the IQ demodulation algorithm. The Brillouin gain and phase-shift spectrograms are measured along the FUT through sweeping the microwave frequency. Compared with the traditional BOTDA system, the VBOTDA would increase the measurement time, which comes from the IQ demodulation algorithm. Fortunately, the algorithm execution time is less than one tenth of that spent in the frequency sweeping and data sampling. Besides, the demodulation can be implemented parallel with the frequency sweeping and data sampling. Therefore the measurement time is seldom increased.

Fig. 4(a) and (b) respectively show the 3-D plot of the measured Brillouin gain and phase-shift spectrograms along the $\sim$1.6-km long FUT. The corresponding BFSs versus position are calculated through fitting their respective raw data to Eq. (1) and (2), and shown in Fig. 4(c) and (d). It is clearly shown that the two fiber sections are fully distinguished both spatially and spectrally. Their BFSs are about 10.61 and 10.56 GHz, respectively. The uncertainties of the BFSs along the whole fiber are about 0.3 MHz for the Brillouin gain spectrograms and less than 0.9 MHz for the Brillouin phase-shift spectrograms. The two BFS distributions are almost identical, with a correlation of $\sim$0.998, which indicates the Brillouin phase-shift can also be applied to distributed sensors with the comparable performance of conventional Brillouin gain based distributed sensors. Notice that, the BFS variance of Fiber-II from 1.2 km to the end of the FUT is mainly due to the loosed strain, possibly resulting from the slack winding of fiber on the outside layers of spool.

Fig. 4. Measured Brillouin gain (a) and phase-shift (b) spectrograms as functions of frequency detuning and position, and the corresponding BFSs (c) and (d) along the FUT calculated from the spectrograms.

Fig. 5 illustrates two representative Brillouin gain and phase-shift spectra of the two fiber sections at positions $z = 20\ \hbox{m}$ and $z = 700\ \hbox{m}$. The Brillouin gain linewidth at those two positions are estimated to be about 34 and 37 MHz. The figures explicitly show the experimental results match well with the previous theory explained in Section 2, and confirm the feasibility of the IQ demodulation algorithm for the heterodyne-based VBOTDA.

Fig. 5. Brillouin gain and phase-shift spectra at positions (a) $z = 20\ \hbox{m}$ and (b) $z = 700\ \hbox{m}$ of the FUT. Symbolic points, experimental data. Solid lines denote the fitting curves.

The Brillouin gain and phase-shift spectra are measured on a 12 m test section centered at position $z = 54\ \hbox{m}$ of the FUT with setting different temperatures. The test fiber section is immersed in temperature-controlled water tank. The water temperature is increased from 20 °C to 60 °C with a step of 2 °C. Five Brillouin gain spectra and five Brillouin phase-shift spectra are provided in Fig. 6(a) and (b) with a temperature spacing of 8 °C. Both Brillouin gain and phase-shift spectra move towards higher frequency when the water temperature increases. The fluctuation of the peak Brillouin gain and phase-shift is mainly owing to the power variation of the pump pulse. Fig. 6(c) and (d) show the temperature dependences of the BFSs obtained by fitting the Brillouin gain and phase-shift spectra. These two dependences exhibit excellent linearity larger than 0.999 and through linear fitting, these two temperature coefficients are estimated to be 1.166 and 1.159 MHz/°C, with a difference of just about 6%, which again demonstrates the sensing potential of the Brillouin phase-shift.

Fig. 6. Dependences of Brillouin gain (a) and phase-shift (b) spectra on temperature. Both spectra move to high frequency with temperature increasing. (c) and (d) present the temperature dependences of BFS calculating from the Brillouin gain and phase-shift spectra, respectively. Symbolic points denote the experimental data, while solid lines correspond to the fitting curves.

The spatial resolution in this experiment is verified to be $\sim$2 m, as shown in Fig. 7, where the spatial intervals for the BFS signals decreased from 90% to 10% are estimated to be $\sim$2 m. The spatial resolution is still limited by the pulse width and the acoustic phonon lifetime, which is the same as common BOTDA sensors. Most of the techniques used to circumvent this resolution limit in BOTDA can be simply applied to the VBOTDA.

Fig. 7. Zoom-out view of Fig. 4(c) and (d) near the fused point of these two type of fibers for verification of spatial resolution.

It should be noted that the frequency shift of the AOFS is critical, and there is a trade-off between choosing a low or high frequency shift of the AOFS. On one hand, the frequency shift should be faster than the frequency response of the signal to guarantee the spatial resolution, and be much larger than Brillouin gain linewidth (typically 30 MHz) to avoid the adverse interaction between the reference and pump. So the frequency shift places a block for the frequency measurement range of the VBOTDA. On the other hand, higher frequency shift requires a higher-bandwidth detector, which would significantly increase the noise. The detected higher-frequency heterodyne signal would lead to higher-speed and higher-cost A/D sampling equipment, and the resultant mass data would challenge the post signal processing.

SECTION VI

## CONCLUSION

In summary, we have demonstrated a VBOTDA using heterodyne detection and IQ demodulation algorithm. The employed AOFS generates a single-frequency reference, simplifying the probe spectrum compared with phase modulation and thus directly measuring the Brillouin gain and phase-shift. The IQ demodulation algorithm is quite simple and easy to implement, and requires a few calculations, allowing fast and real-time demodulation and making it very suitable for fast and dynamic strain measurement. A proof-of-concept experiment has been implemented in an $\sim$1.6-km long SMF consisting of two different fibers, and successfully measured the Brillouin gain and phase-shift spectrograms with an $\sim$2-m spatial resolution. The temperature dependences of the Brillouin gain and phase-shift spectra are measured and the temperature dependences of the BFSs show excellent linearity with almost identical slope.

The sensing distance of the VBOTDA system, which demonstrated here is just 1.6 km, however, is not restricted by the proposed heterodyne detection and IQ demodulation, and can be easily extended to over 10 km with proper power manipulation of the pump and probe. More importantly, the VBOTDA scheme is compatible with the pulse coding [13] and Raman amplification [14]. If combined with these techniques, the sensing distance can be increased to over 100 km. We believe that the proposed VBOTDA would lead to performance-enhanced distributed sensors, and make it possible to integrate multi-functions in one system, such as conventional strain or temperature sensing and dynamic measurement.

## Footnotes

This work was supported by the National Natural Science Foundation of China under Grant 61177073. Corresponding author: Z. Meng (e-mail: zhoumeng6806@163.com).

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