1. Introduction

Brillouin dynamic grating (BDG) is a refractive index grating that moves at the speed of sound generated through stimulated Brillouin scattering. BDG has a feature that is reconfigurable with light and provides a promising new technology for optical sensing and signal-processing applications [1,2]. In distributed fiber sensing [3,4], BDG technologies have enabled birefringence measurement [5,6], strain/temperature discrimination [7,8], high spatial resolution sensing [9], surrounding media sensing [10], and so on [2,11].

The technique called Brillouin optical correlation domain analysis (BOCDA) [12,13] can be applied to create localized BDG [14,15]. The BOCDA technique itself was developed to measure the distribution of the Brillouin gain spectrum (BGS) by controlling the mutual coherence of the pump and probe light counter-propagating through a fiber. The measurement mechanism of the BOCDA enables high spatial-resolution measurement of temperature or strain that is not limited to the excitation lifetime of acoustic waves, unlike the time-domain techniques [16]. Our group has demonstrated the discriminative and distributed measurements of temperature and strain by using both BGS and BDG reflection spectrum measured using the BOCDA technique [8]. This is termed as the BDG-BOCDA method. A distinctive feature of the BDG-BOCDA system is that a continuous-wave light source is used for both reading and writing of the BDG, and can therefore be implemented with a single continuous-wave laser [17], not requiring high-speed devices for time-resolved measurement. Although the BDG-BOCDA method achieves a relatively high spatial resolution with high discrimination accuracy, the spatial resolution of the BDG reflection spectrum is empirically known to be about 10 times worse than that of the BGS measured using the BOCDA technique. Therefore, the lower spatial resolution of the BDG spectrum is a limiting factor in the discriminative measurement [8,18].

To address this problem, we recently proposed the intensity-modulation (IM) technique synchronized to the frequency-modulation (FM) of the light source, which enhances BDG localization at the expense of brightness, and confirmed the validity of the proposed technique by simulations [19]. In this paper, we experimentally confirm the effectiveness of the proposed method and demonstrate the improvement in the spatial resolution of the BDG refection spectrum to almost the BOCDA resolution. We also demonstrate a distributed measurement of BDG spectrum by using the proposed method and show the successful detection of an 8-cm cooled section with a 100-m-long polarization-maintaining fiber (PMF). The length we detected is shorter than the shortest detection length reported so far in the BDG-BOCDA system (12-cm section in an 8-m-long fiber [8]) along with a much longer measurement range. Finally, we describe the fundamental problem of the spectrum broadening that prevents further improvement.

2. Principle

Figure 1 shows the schematic illustration of the BDG-BOCDA system for measuring a local BDG reflection spectrum. The pump and probe light, which are linearly polarized to the slow-axis direction of the PMF, propagate in opposite direction through the fiber. Sinusoidal FM applied to the light source develops a correlation peak (CP) along the PMF, where the acoustic waves are strongly excited through stimulated Brillouin scattering [12]. The center frequency of the probe light is downshifted by the Brillouin frequency shift, $\Omega _B$, from pump center frequency $\omega _0$ to create an intense BDG. As the wavenumber of the BDG at the CP position oscillates due to the FM of the light source, the reading light polarized to the fast-axis direction also needs an FM synchronized to the pump FM to obtain a single-peak reflection spectrum [14]. The peak of the BDG reflection spectrum is detuned from the pump frequency by an amount proportional to the fiber birefringence. The birefringence-induced shift, $\nu _{yx}$, is about 50 times more sensitive to temperature changes than the Brillouin frequency shift in a standard PMF, enabling discriminative measurement of temperature and strain with high accuracy [7,20].

 

Fig. 1. Schematic illustration of the BDG-BOCDA system.

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In the BOCDA system, effective methods to improve the spectrum shape of a light source through IM is developed, which is called apodization methods [13,21] (Fig. 2). The phonon power distribution can be controlled by the apodization because the phonon distribution is closely related to the optical coherence function, which is a Fourier transform of the light source spectrum. The conventional apodization method applies a sinusoidal IM at twice the FM frequency to eliminate the intensity of the instantaneous frequency that creates the sharp edges of the light source spectrum, which means the suppression of side lobes of the coherence function. Although this conventional apodization method has been shown to have an improvement effect on the spatial resolution of the BDG reflection spectrum [22,23], we recently proposed a more effective IM waveform (term half-apodization) [19,24]. In the half-apodization method, the amount of light for half the FM period is eliminated so as not to change the apodized spectrum of the light source. As shown in the lower part of Fig. 2, the generated phonon distribution in the half-apodization method is well localized to the position of $z = 0$ corresponding to the CP position. However, in the conventional apodization method, the phonon power is suppressed around the CP but restored far away from it, constituting measurement noise. This observation suggests that the half-apodization method could further improve the spatial resolution.

 

Fig. 2. Modulation waveform of the light source (FM and IM) and resulting phonon power distribution along the fiber in each method.

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First, we introduce theoretical spatial resolution $\Delta z$ and measurable range $d$ of the BOCDA method [12,13]: $\Delta z=v_g \Delta \nu _B/2\pi f_m \Delta f$, $d=v_g/2f_m$. Here, we denote the BGS linewidth as $\Delta \nu _B$, light speed in the fiber as $v_g$, FM amplitude as $\Delta f$, and FM frequency as $f_m$. The measurable range $d$ corresponds to the CP interval. $\Delta z$ is a general index of spatial resolution and depends on the modulation parameters ($\Delta f$, $f_m$). The BOCDA method is known to detect strain or temperature change in a section of about $\Delta z$ length; however, the reflection spectrum of BDG cannot be detected unless the distorted section is about 10 times longer than this length. The ratio of the detectable length to $\Delta z$ is an appropriate index to evaluate the improvement effect that does not depend on device settings such as modulation parameters.

3. Experiment

The experimental setup is shown in Fig. 3. A distributed feedback laser diode with a narrow linewidth was used as the light source, the frequency of which was sinusoidally modulated by direct current injection. All fiber system consists of PANDA-type PMFs. The first intensity modulator (IM1) was used for apodization (later used for temporal gating also), and the second one (IM2) was used for double side-band modulation. The upper band extracted by an optical tunable filter was used for reading out the BDG reflection spectrum, and the lower band was used for the pump-probe light to create a BDG. A single side-band modulator (SSBM) was used to downshift the probe frequency by the Brillouin frequency shift. The pump and probe light was propagated in the test fiber (FUJIKURA, SM15-PS-U25D, 100-m long) in the opposite direction generating a BDG at the CP position. The reflection spectrum of BDG was measured by launching the "read" light through the polarization beam combiner (PBC). We used lock-in detection synchronized to the pump chopping frequency of about 100 kHz of the intensity modulator (IM3). The typical optical powers of the pump, probe, and read light were about 100, 20, and 40 mW, respectively. We adjusted the optical path difference between the pump and read light at the test fiber entrance to almost zero through the variable delay in free space.

 

Fig. 3. Experimental setup of the BDG-BOCDA system. 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, photo detector; FUT, fiber under test.

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To confirm the effects of the three techniques introduced in Section 2, we present four types of measurement results, as shown in Figs. 4(a)–4(d). Each method of no apodization, conventional apodization, and half-apodization is represented by the black, blue, and red lines, respectively. The optical spectra of the light source measured by a scanning Fabry-Perot cavity are shown in Fig. 4(a). The optical spectrum of the frequency-modulated light source with respect to the sinusoidal wave has intensity peaks at both ends, which are suppressed by the IM in the conventional apodization method. In the half-apodization method, the intensity is halved so as not to change the light-source spectrum. When the pump and probe light are counter-propagated on the fiber, an acoustic wave is locally generated near the CP position ($z = 0$), as shown in Fig. 4(b). In the measurement of the phonon power distribution, the FUT length ($\sim 1$ m) was set sufficiently shorter than the CP interval ($\sim 120$ m) to obtain the local phonon power, which is proportional to the local Brillouin gain [19]. Then, the probe gain at a frequency shift of 10.85 GHz is measured when the CP position was scanned by changing modulation frequency $f_m$ from 705 to 905 kHz (equivalent to the CP interval, $d$), which corresponds to the phonon power distribution measured at a resolution of the FUT length. In the apodization method, the acoustic wave was more localized around $z = 0$ than no apodization one, but unnecessary phonons are generated at a position farther away from the CP (see also Fig. 2). On the other hand, the half-apodization method successfully suppresses these phonons. Figure 4(c) shows the BOCDA output of each method. In the apodization method, the signal peak observed in the no apodization method due to the Brillouin gain around the CP position is suppressed to provide a round spectrum, which improves the system performance [21]. The output spectrum in the half-apodization method is the same as that of conventional apodization. Figure 4(d) shows a typical BDG reflection spectrum of each method. This measurement compares the spectra over a sufficiently long cooling section ($\sim 3$ m) in a 100-m fiber to avoid the effects on the birefringence non-uniformity of the fiber. The characteristic point is that, in the half apodization method, the spectrum is halved and asymmetric. Consequently, we conclude that the results shown in Fig. 4 are in good agreement with the prediction results obtained through the numerical calculation [19].

 

Fig. 4. Comparison of each method in various measurements. (a) Light source spectra, (b) Phonon power distributions, (c) BOCDA outputs, and (d) BDG reflection spectra. The modulation parameters are (a) $\Delta f=3.6$ GHz; $f_m=1$ MHz; (b) $\Delta f=0.7$ GHz; (c) $\Delta f=0.15$ GHz, $f_m=1$ MHz; and (d) $\Delta f=3.6$ GHz, $f_m=1$ MHz.

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To evaluate the spatial-resolution performance of each method, we conducted an experiment to measure the reflection spectrum of BDG while changing the length of the section immersed in cold water in a constant temperature water tank at the CP position from 20 cm to 2 m (Fig. 5). The modulation parameters are $\Delta f=3.6$ GHz and $f_m=1$ MHz, with the corresponding $\Delta z$ of 27 cm. The peak for the room temperature portion is due to the acoustic waves remaining at positions other than the CP, and the spatial resolution performance can be evaluated based on the intensity ratio of the cold-water peak to room temperature peak (see Figs. 5(a1)–5(a3)). The length at which this ratio exceeds 1 corresponds to the length that can be detected in the simple maximum value search. According to this peak ratio shown in Fig. 5(b), the spatial resolution performance is significantly improved in the half-apodization method. Thus, the half-apodization enables us to detect a length almost equal to the theoretical spatial resolution, $\Delta z$.

 

Fig. 5. BDG reflection spectra of (a1) no apodization, (a2) conventional apodization method, and (a3) half-apodization method, while changing the length of the section immersed in cold water at the CP position from 20 cm to 2 m. (b) Peak power ratio of section immersed in $11^\circ$C cold water to room-temperature section. The black dashed line shows the BOCDA theoretical resolution, $\Delta z=27$ cm, and the orange dashed line shows the peak power ratio of one.

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Finally, we demonstrate a distributed measurement using the half-apodization method (Fig. 6). An 8-cm section at the center of the test fiber is immersed in ice water ($\sim 5^\circ$C). The position of the CP is swept by changing the modulation frequency from 6.0435 to 6.0485 MHz with the amplitude of $\Delta f = 3.7$ GHz. This modulation parameter corresponds to $\Delta z =4.4$ cm. In addition to the half-apodization, we used a temporal gating technique [25] and enlarged the measurement range by five times. The cooled section was successfully detected with almost the actual length of 8 cm, which cannot be detected by the other conventional methods with the same $\Delta z$.

 

Fig. 6. (a) Distributed measurement result of BDG reflection spectrum in the half-apodization method when an 8-cm section at the center of the 100-m PMF is immersed in ice water. (b) Distribution of the maximum peak frequency in (a).

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4. Discussion and conclusion

We demonstrated that the spatial resolution of the BDG reflection spectrum in the BDG-BOCDA system can be improved using the recently proposed half-apodization method. In previous demonstrations [8,18], the spatial resolution was about 10 times worse than the theoretical spatial resolution of $\Delta z$ in the BOCDA. However, it was improved to almost the theoretical spatial resolution by using the half-apodization method, as shown in Fig. 5. Specifically, in [8], a 12-cm section was detected with a theoretical spatial resolution of 7.5 mm; in contrast, we succeeded in detecting an 8-cm section even with a theoretical spatial resolution of 4.4 cm. Our results show the validity of our theoretical model and a significant improvement of the spatial resolution in the discriminative measurement of temperature and strain in the BDG-BOCDA method.

Note that the realization of a higher spatial resolution of the BDG reflection spectrum is not straightforward. That is, even if modulation amplitude $\Delta f$ (or $f_m$) is increased and theoretical spatial resolution is improved, it is difficult to achieve a millimeter spatial resolution, which is achieved in BOCDA [26]. This limitation is because of the broadening of the BDG reflection spectrum, which is caused by the inverse increase of the spectrum width to the BDG length [27]. As shown in Fig. 5(a3), even when the cooled section is shorter than the length corresponding to the peak-power ratio = 1 (see the case for cooled section of 20 cm), the total power integrated along the frequency axis corresponding to the cooled section is larger than that corresponding to the room-temperature section. However, the cooled section cannot be detected by the simple maximum search method. This is a fundamental limitation that is not encountered from the viewpoint of phonon distribution. In addition, this effect cannot be evaluated by a relative figure of merit based on the ratio of $d/\Delta z$ but rather depends on the absolute value of $\Delta z$. As discussed in [9], this is not the case when the reflection spectrum information of the BDG is discarded.

It may be useful to provide an intuitive understanding of why our approach is effective in localizing BDG (for more details, see [19]). In general, it follows that IMs with higher frequencies than FMs can make BDGs more localized (also IMs with lower frequencies than FMs can extend the measurement range). The conventional apodization method has succeeded in localizing the BDG near the CP by modulating at a frequency twice the FM frequency. Nevertheless, there is unwanted phonon power at a position away from the CP (see Fig. 2 and Fig. 4(b)). So the half-apodization method is designed to remove this noise power. More specifically, at the CP position, the modulation applied to the pump and probe is synchronized; however, at positions far from the CP, they are oscillated out of phases. Therefore, in the half-apodization method, the pump and probe do not exist simultaneously, and the stimulated Brillouin scattering becomes suppressed as the position reaches a middle point between the CPs. Finally, we note that the half-apodization method is equivalent to a method that uses a light source repeating only an uphill (or downhill) slope of the FM waveform with the cycle period doubled using the temporal gating [25]. The half-apodization removes the intensity of the frequency return period in the FM. From this perspective, it is the asymmetry of the FM waveform that facilitates BDG localization. Because the asymmetric FM has a moment of rapid frequency increase (or decrease), the dwell time at which the instantaneous frequency difference between the pump and probe matches the Brillouin frequency shift becomes shorter away from the CP.