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Abstract
We demonstrated the distributed measurement of Brillouin dynamic grating spectra along a polarization-maintaining optical fiber without moving the correlation peak position, which is a measurement position scanned in the conventional correlation-domain methods. Our results present new possibilities for developing spatially resolved measurement methods using the correlation-domain technique.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Distributed fiber sensors enable spatially resolved measurements of environmental changes such as temperature and strain along with a sensing fiber over a long distance [1,2]. Brillouin backscattered light is often used for probing local changes because of its strain sensitivity, narrow linewidth, and high signal intensity. Various distributed measurement methods for Brillouin fiber sensing have been demonstrated so far, such as time- [3,4], frequency- [5,6], and correlation-domain methods [7,8], and each has different characteristics.
Among them, the correlation-domain method (BOCDA [7–12] and BOCDR [8,13,14]) is characterized by high spatial resolution [10,15] and random accessibility [8,16]. To realize position selective measurement, the light source optical frequency is modulated periodically in standard BOCDA and BOCDR [7,8,13,14]. The output spectrum of the methods is obtained by integrating the convolution at each fiber position of the "beat power spectrum" and the "intrinsic Brillouin gain spectrum (BGS)" along the test fiber [7,17]. Here, the beat power spectrum represents the distribution of the modulated frequency difference between the pump and probe lights propagating oppositely through the fiber. The probe’s peak frequency in the BGS is shifted by about ten gigahertz from the pump frequency in silica fibers. This peak frequency shift is called Brillouin frequency shift (BFS), which changes almost linearly with temperature and strain. Therefore, using the correlation-domain method, we aimed to estimate the unknown intrinsic BGS (or BFS) using the known beat power spectrum. Almost all the conventional correlation-domain methods enable measuring the local BGS by forming the beat power spectrum into a two-dimensional delta-like function and scanning its peak position, called the correlation peak (CP) position. By setting the CP at the desired measurement location, we can determine the BGS change at that position. However, the method scanning the pointed CP is clearly not the only one to determine local BGS changes using the correlation-domain technique.
In addition, moving the CP to other positions is sometimes problematic. Usually, a long delay fiber that gives an optical path difference is inserted between the pump and probe paths. The CP on the test fiber can be moved by changing the modulation frequency of the light source frequency in a system with a delay path. However, the delay fiber may cause unwanted nonlinear effects and hinder downsizing of the measurement system. Furthermore, changes in the modulation frequency may affect system performance parameters, such as spatial resolution and modulation waveform compensation for laser nonlinearity. When using external modulation rather than direct laser modulation [9,18,19], a delay path can be eliminated by applying a different modulation in each path. The method using an incoherent light source needs a variable delay to move the CP position, which may impose limitations on system performance [10,11].
In this research, we developed a method to measure the distributed spectrum of Brillouin dynamic grating (BDG) without scanning the CP position. A BDG is an acoustic grating that accompanies stimulated Brillouin scattering [20]. Because a BDG has similar reflection characteristics to conventional fiber Bragg gratings and can be rewritten at high speed using light, it attracts considerable attention for sensing and signal processing applications [21–29]. Here, we have experimentally demonstrated distributed temperature measurements through birefringence changes on a polarization-maintaining fiber, using BDG spectra localized by the correlation-domain technique without moving the CP position. The measurement results obtained using the proposed method agree well with those obtained using the conventional method of scanning the CP position. The idea of our approach is to move the beat spectrum in the frequency domain instead of the spatial one, considering that the position of a beat spectrum corresponds one-to-one to the frequency in the half-apodization method proposed recently [30,31]. We expect these results to facilitate the development of new distributed measurement methods with various beat spectrum designs.
2. Principle
Figure 1 shows a conceptual diagram of the method for measuring the local BDG reflection spectrum using the correlation-domain technique. The light source frequency is sinusoidally modulated, which periodically creates CP positions where the pump-probe frequency difference is constant. In the half-apodization method [30,31], intensity modulation (IM) is also applied to select only the ascending slope of the frequency modulation (FM), resulting in a sawtooth-like FM waveform. This intensity modulation includes cosine modulation to enhance the BDG localization. The pump and probe lights polarized along the slow axis of the polarization-maintaining fiber (PMF) propagate in opposite directions to form BDGs. BDGs are efficiently produced when the center frequency of the probe is lower than that of the pump by $\Omega _B$, the BFS. To read the reflection spectrum of the generated BDG, the “read” light polarized in the fast axis direction is incident from the fiber end with the pump light. The intensity of the BDG reflection becomes maximum when the read light frequency is separated from that of the pump light by an amount proportional to the birefringence of the PMF, $f_{yx}$. The birefringence-induced frequency shift tells us the environmental changes such as temperature and strain along the PMF [22].
Fig. 1. Schematic illustration of the BDG–BOCDA system. In this study, light source frequency and intensity are modulated with the half-apodization technique, where the FM and the IM waveform are synchronized with each other as shown in the figure, and only the half period of the lightwave is used and apodized by the IM. In the graphs showing frequency modulation waveforms (orange and green lines), the temporal intensity is expressed using color strength.
To discuss the principle more precisely, let us consider the equations of the light source modulation in the half-apodization, FM $f(t)$, and IM $I(t)$ [30]:
Here, $f_0$ is the center frequency of the light source, $\Delta f$ is the modulation amplitude, and $f_m$ is the modulation frequency. We also define the electric field amplitude of the pump as $E_1 (z,t)$ and the probe as $E_2 (z,t)$, and their beat power spectrum as $S_b(z,\omega )=|\mathcal {F}[E_1(z,t)E_2^*(z,t)]|^2$, where $\mathcal {F}[\cdot ]$ is a Fourier transform. The phonon power distribution generated by the pump and probe, $|\rho (z)|^2$, is determined by the overlap integral of beat power spectrum $S_b$ and the intrinsic BGS, $g_B(z,\omega )=g_{B0}/(\Gamma ^2-(\omega -\Omega _B)^2)$:
Here, $\Gamma$ is the Brillouin gain line width and $g_{B0}$ is the Brillouin gain coefficient. Although the BFS is generally a function of position, $\Omega _B(z)$, we considered it constant in our settings. This condition is valid in the following experiments of temperature measurement because the temperature coefficient of the BGS peak is much smaller than that of the BDG spectrum peak.
Now, we describe the proposed method for distributed measurement of BDG spectra and explain its mechanism. Figure 2 shows the simulation results of the beat power spectra of the pump and probe. In the drawings of Fig. 2, the ordinate and abscissa represent the position along the fiber and the pump-probe frequency difference, respectively. As shown in Fig. 2(a), the beat spectrum of the pump-probe light with a sinusoidal FM, which is for the ordinary BOCDA [8], has a delta-function-shaped peak at the CP position, and the peak spreads in an X shape from there. On the other hand, as shown by the white dashed line in Fig. 2(b), the beat spectrum of the half-apodized light source shows a one-to-one correspondence between position and frequency. Such a one-to-one correspondence is generally found in sawtooth-like (monotonically increasing) FM waveforms with a duty cycle $< 50\%$. In the conventional distributed measurement using correlation-domain technique, the measurement position where the acoustic phonons are intensely generated is shifted vertically by changing the FM frequency to the light source as shown in Fig. 2(c). In contrast, when the center frequency of the probe is shifted by $\Delta \omega$ instead of the change in the FM frequency, the beat spectrum moves horizontally on the frequency axis as shown in Fig. 2(d). As the BDG is efficiently generated when the beat frequency is in the region of $\Omega _B$ having a width of approximately 30 MHz (in short $g_B$, areas painted white in Fig. 2(c) and 2(d)), the probe frequency shift, $\Delta \omega$, corresponds to movement of the BDG measurement position by $\Delta z_c$, as shown in Fig. 2(d). This observation indicates that the local BDG spectra at different positions can be measured by shifting the center frequency of the probe light instead of moving the CP position. In the vicinity of the CP position, we can calculate the displacement ($\Delta z_c$) induced by the frequency shift ($\Delta \omega$) through linear approximation of the beat power spectrum:
Fig. 2. Beat power spectrum $S_b(z,\omega )$ of pump and probe in the no-apodization method (a), and in the half-apodization method (b). The ordinate shows the range equivalent to the CP interval, $d=c/2nf_m$, centered on the CP at $z=0$. When the pump-probe center frequency difference is equal to BFS, $\Omega _B$, $S_b$ shows the sharp-pointed peak at $z=0$. The beat spectrum intensity is normalized so that the maximum value at the CP is 1, but the upper limit of the color scale is set to less than 1 for visibility. The $S_b$ has a shape of cross in no-apodization but has a shape of a tilted line in the half-apodization. (c) Three cases of the $S_b(z,\omega )$ in the half-apodization where the CP position is moved by changing the FM frequency for the light source. (d) Three cases of the $S_b(z,\omega )$ in the half-apodization where the probe center frequency is detuned from $\Omega _B$ by $\pm \Delta \omega$, 0, without moving the CP position. The frequency detuning shifts phonon increasing position by $\Delta z_c$.
3. Experiment
Figure 3 shows our experimental system. A distributed feedback laser diode (LD) with a narrow linewidth was used as the light source, the frequency of which was sinusoidally modulated as a function $f(t)$ of Eq. (1) through direct current modulation to the LD. All fibers used in the experiments were PANDA-type PMFs. The two intensity modulators (IM1 and IM2) were used for the half-apodization ($I(t)$ of Eq. (2)) and double side-band modulation to suppress the carrier, respectively. The upper band extracted using an optical tunable filter was used for the read light to interrogate the BDG reflection spectrum, and the lower band was used for the pump-probe light to create the BDG. For obtaining the BDG spectra, we scanned the frequency of the double side-band modulation, which corresponded to half the pump-read frequency difference. A single side-band modulator (SSBM) was used to downshift the probe frequency for sweeping the measurement point without moving the CP position. Although we inserted the delay fiber in the probe path for comparison measurements using the conventional method, it could be removed in the measurement using the proposed method. The pump and probe lights propagated in the fiber under test (FUJIKURA, SM15-PS-U25D, 100-m long) in the opposite direction, thus generating a BDG. We used lock-in detection with the time constant of 100 µs, synchronized to the pump chopping frequency of approximately 100 kHz of the intensity modulator (IM3). The optical path difference between the pump and read light at the test fiber entrance was set to almost zero through the linear stage.
Fig. 3. Experimental setup. LD, laser diode; FM, frequency modulation; IM, intensity modulator; SSBM, single side-band modulation; EDFA, erbium-doped fiber amplifier; PBC, polarization beam combiner; LIA, lock-in amplifier; PD, photodetector; FUT, fiber under test.
The phonon power distribution generated by the pump-probe lights, which were modulated both in the frequency and the intensity with the half-apodization technique, was measured for each probe frequency shift (10.47–11.27 GHz) without making the read light incident to the FUT, as shown in Fig. 4. We changed the FM frequency from 2.9 MHz to 3.3 MHz for a short test fiber (2 m) compared to the CP interval ($d=34$ m). This FM frequency change corresponds to moving the CP position by $2d$, as is schematically shown in Fig. 4(a). The probe Brillouin gain, which is proportional to the phonon power generated through Brillouin interaction, was measured while scanning the CP position through the FM frequency change. If the probe frequency shift matched the original BFS ($\Omega _B=$10.87 GHz), one of the CPs existed on the 2 m-long test fiber when the FM frequencies were 3.0 MHz and 3.2 MHz with amplitude $\Delta f=0.247$ GHz. In contrast, as the probe frequency shifted from the BFS, $\Omega _B$, the modulation frequency corresponding to the CP position moved, and the peak amplitudes decreased as shown in Fig. 4(b). This can be well explained using the simulation results shown in Fig. 4(c) [30]. As shown in Fig. 4(d), the simulated and experimental results agree in terms of the extent to which the phonon peak moves. Moreover, we can see the validity of $\Delta z_c=d\Delta \omega /2\pi \Delta f$ around the CP position. The broader peak width observed in the experimental results than those in the theoretical ones is owing to the low spatial resolution determined by the test fiber length.
Fig. 4. Phonon power distribution, $|\rho (z)|^2$, with each pump–probe frequency difference when half-apodization is applied to the light source. (a) The experimental setup used to measure $|\rho (z)|^2$ with relatively short FUT. (b) Experimental results with pump–probe frequency differences ranging from 10.47 GHz to 11.27 GHz. (c) Simulation results of phonon distribution showing the deviation of each frequency from BFS. (d) Comparison of phonon peak positions observed in simulations and experiments with each probe frequency deviation from BFS.
Figure 5 shows the distributed measurements of the BDG spectra. The fiber section at 40 cm near the center of the 100-m-long test fiber was immersed in cold water (6.0 °C) in a constant-temperature water tank, and the BDG spectra in the range of 20 m were measured. Figures 5(a1) and 5(a2) present the results of the proposed method obtained using the probe frequency shift from 7.847 GHz to 13.913 GHz with steps of 12.132 MHz. Figs. 5(b1) and 5(b2) show the results obtained from the conventional method of moving the CP position for comparison by changing $f_m$ from 0.984 MHz to 1.022 MHz with steps of 133.3 Hz. For obtaining the results shown in Figs. 5(a1) and 5(a2), the FM frequency $f_m$ was fixed to 1.0025 MHz, and then the CP did not move during the measurements. In contrast, for the results in Figs. 5(b1) and 5(b2), the probe frequency shift was fixed to 10.88 GHz. The pump-read frequency difference is scanned from 45 GHz to 48 GHz in 50 ms. It takes several minutes to finish the measurements at the entire position. Both results show successful detection of the cold water section with $\Delta f= 4.5$ GHz, which corresponds to a theoretical spatial resolution of 22 cm. Note that to verify the principle, we set the modulation parameters and measurement speed moderately in this experiment. We estimate the temperature coefficient of a birefringence-induced shift at $\sim 55$ MHz/K and the birefringence of the FUT at $\sim 3.5\times 10^{-4}$. Larger temperature coefficients will be obtained by using higher birefringent fibers. Including the birefringence fluctuations of the PMF in the other regions at room temperature, we can observe the agreement between the results obtained using our proposed method and the conventional one, thus confirming the validity of the proposed method.
Fig. 5. Distributed measurement results. (a1), (b1) Image plot of BDG reflection spectra obtained using the proposed and conventional methods. (a2), (b2) Peak frequency plots of (a1) and (b1), respectively.
4. Discussion
The distributed measurement results shown in Fig. 5 exhibited good agreement in the range of 20 m in the situation where the conventional method had a measurement range of 100 m. According to the phonon power distribution in Fig. 4, the measurement range of the proposed method is limited to less than half that of the conventional method. Indeed, as the distance from the CP position increases, the signal strength decreases, and the spatial resolution also deteriorates. The deterioration in spatial resolution will be eliminated by using a straight FM waveform (that is, sawtooth) instead of a sinusoidal one. Further, using the sawtooth modulation, the correspondence between the probe frequency and position through linear approximation will be satisfied in the entire range, which will simplify the conversion of them. In this paper, we adopted the sinusoidal FM for a correct comparison with the conventional method, and for consideration of its application to the BDG-BOCDA, which is a discriminative measurement technique of temperature and strain [22,31].
The proposed method uses the spatial uniformity of the BFS. It assumes that the refractive index in the slow axis direction is almost constant, and only the birefringence between the slow and fast axes changes. Such a situation occurs when the temperature change in a relatively small range of approximately $\pm 20$ °C is measured with a distortion-free PMF, as shown in this study. The situations where our method can be used may also include various other ones, such as measuring load [25] and hydrostatic pressure [26,27].
5. Conclusion
We demonstrated a method of measuring the BDG spectrum distribution by adding a frequency shift to the probe light instead of moving the CP position. Using the proposed method, we successfully detected a 40-cm cooling section on a 100-m-long polarization-maintaining fiber and obtained results similar to those of the conventional method at least within the range of 20 m. This method does not require a long delay line and sweeping of the FM frequency of the light source. Our results present new possibilities for developing spatially resolved measurement methods using the correlation-domain technique with various beat spectrum designs.
Funding
Japan Society for the Promotion of Science (JP18H01455, JP19K14999).
Disclosures
The authors declare no conflicts of interest.
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