Remote Speckle-Based Measurements of Backward Brillouin Acoustic Vibrations in Optical Fibers

: We propose a novel technique for measurements of Brillouin acoustic vibrations based on temporal tracking of back-reﬂected speckle patterns. The proposed method holds the potential to enhance some of the limiting factors in Brillouin frequency measurements while yielding increased spatial resolution and shorter scanning times of the inspected ﬁber. Experimental results show the capabilities of the proposed method are presented, using a two pump-waves conﬁguration.


Introduction
Stimulated Brillouin scattering (SBS) is a nonlinear effect that was first observed in 1964 [1] and has been studied extensively [2][3][4][5][6][7]. This effect has been observed in a wide range of liquids [2], gases, and solids [5]. The Brillouin effect was also observed and analyzed in optical fibers, first for the case of stimulated Brillouin scattering [4] and later for the case of spontaneous scattering [8,9]. The Brillouin effect in optical fibers is very useful for several applications like optical filtering [10], amplification of signals [11], and sensing [12].
Brillouin scattering can be described entirely as a coupled three-wave interaction: Two counter-propagating optical waves called pump and Stoke and an acoustic wave. In the case of stimulated Brillouin, both the pump and the Stokes waves are applied externally from both sides of the fiber. The interference between those two generates an acoustic wave within the fiber through a process called electrostriction. The refractive index grating caused by the acoustic wave scatters the pump wave, while the backscattered light is downshifted in its frequency resulting in optical power transfer from the pump wave to the Stokes wave [6,7]. In the case of spontaneous Brillouin, only the pump wave is applied externally. In this case, the acoustic wave which exists within the fiber naturally as a result of thermally generated phonons scatters the pump wave. The back-reflected signal is downshifted in frequency due to the Doppler effect [6]. This shift in frequency called Brillouin frequency and its magnitude depends on the velocity of the acoustic wave, which is proportional to the density of the material in the fiber. Since the density of the material is temperature and strain-dependent, measurement of the Brillouin frequency of the fiber can be used for development of temperature or strain sensors [12].
Currently, the Brillouin frequency measurements are indirectly performed by finding the frequency shift between the injected pump wave and the back-reflected Stokes signal. Several approaches for distributed fiber sensors were suggested in recent years to find the Brillouin frequency in every Appl. Sci. 2020, 10, 664 2 of 9 point along an optical fiber. In the basic method, called Brillouin optical time domain reflectometry (BOTDR), a short pump pulse is inserted into an optical fiber. By measuring the frequency shift of the backscattered light as a function of time, it is possible to find the Brillouin frequency at any point along the fiber [13]. For Brillouin optical time domain analysis (BOTDA), one laser pulse acts as a pump and a second counter-propagated continues wave laser acts as a probe. By measuring the probe amplitude as function of time, and by scanning the frequency difference between the pump and the probe it is possible to find the Brillouin frequency for each point along the fiber [14]. For both mentioned modalities, the spatial resolution is limited to about 1 m by the damping time of the acoustic wave [15]. Several methods were proposed to overcome this spatial resolution limitation like methods that are based on pre-existence of an acoustic wave [16], frequency-domain methods [17,18], Brillouin dynamic grating [19], or correlation-based methods which reach a very high spatial resolution [10][11][12][13][14][15][16][17][18][19][20][21][22].
Recently, we proposed a new detection modality based on speckle-sensing for phonon detection in optical fibers [23]. In this method, the acoustic vibrations resulting from the Brillouin effect are directly measured by temporal tracking of the back-reflected secondary speckle patterns, generated while illuminating the tested fiber. This approach holds the potential to improve the spatial resolution for Brillouin scattering detection since it is determined by the size of the illuminated part of the fiber, which can be very small in size (i.e., a few millimeters). Our method also enables us to detect only a specific section of the fiber, without scanning the whole inspected fiber. This property may be significant when we work with long fibers. Moreover, if the field of view of the camera that is capturing the speckle patterns matches to the length of the inspected fiber, then the mapping of the Brillouin frequency along the fiber can be obtained at once without the need to apply time-dependent scanning process. In previous work, we introduced primality results of the detection of Brillouin radial acoustic modes by using this method [23].
In this paper we show for the first time, remote detection of acoustic vibrations in optical fiber resulting from the backward Brillouin effect. Those measurements were performed by using a two pump waves configuration to decrease the frequency of the acoustic vibrations. First, this principle of measurement will be explained in detail. Then we introduce the experimental setup and the received results that show the ability to sense the Brillouin vibrations in an optical fiber by speckles analysis, and finally, we will discuss the meaning of the obtained results.

Stimulated Brillouin Scattering
As we mentioned in the introduction, the Brillouin acoustic wave scatters the pump wave while the scattered light will be downshifted in frequency [6,7]. Since the pump wave at frequency ω p is scattered from a retreating sound wave, the scattered radiation will be shifted downward in frequency to: where ω s is the backscattered frequency and Ω B is the acoustic wave frequency, called the Brillouin frequency. Since the Brillouin frequency is related to the acoustic wave vector, and since this wave is driven by the beating of the two counter-propagate pump and Stokes, it is possible to show that the Brillouin frequency is given by [7]: where ν a represents the velocity of sound, c is the velocity of light and n is the refractive index of the fiber. Since the acoustic velocity in optical fiber is about 5800 m/s [15], the typical value for Brillouin frequency for pump wave with a wavelength of 1550 nm is about 10 GHz.

Speckles Analysis
The random self-interference pattern known as speckle, allows us to track changes in the phase of the light being scattered from a rough surface while being illuminated and vibrated [24,25]. By tracking the position of the time-varying correlation peak, it is possible to extract the movement trajectory. In this way, very small temporal shifts and movements of an object can be measured [16]. The shift of the speckle pattern is related to the changes in the physical properties of the tissue being tested [25]. By recording the temporal speckle pattern, and by using correlation analysis of the video, we can calculate the relative shift between the frames which stands for the temporal oscillation profile. By calculating the Fourier transform of the shifts' vector, the oscillation frequencies of the captured speckle pattern can be computed [26]. The speckles analysis has already been tested successfully for several kinds of measurements such as extraction of multiple speech sources and heartbeats [27], breathing, heart rate, pulse pressure, blood Coagulation, blood oxygenation [28], alcohol concentration [29], detection of pigmented lesions, and human skin hydration [30].

The Method of Measurements
The maximal vibration frequency that can be detected by the technique presented above depends on the frame rate of the camera that is used for recording the speckles pattern as a function of time. As we mentioned above, the typical value for Brillouin frequency is about 10 GHz, which is much higher compared to the maximal camera's frame rate. Thus, to detect the backward Brillouin effect by using speckles analysis, we need to find a way to reduce the frequency of the acoustic vibrations. This can be achieved by performing amplitude modulation to the Pump wave. If we modulate the pump with frequency modulation of ω m we will get two sidebands to the main laser frequency ω p,0 [31]: According to Equation (2), for each pump we will get the corresponding acoustic wave, where the frequencies of those waves are given by: where i = 0, 1, 2. For those pump waves we also get the corresponding back-reflected Stokes waves, with frequencies of: B, we also have the cross interaction between each pump wave and the generated Stokes waves of the other pump waves [32]. For example, the cross interaction between pump number 1 with frequency ω p,1 to Stokes number 2 ω s,2 will generate the next acoustic frequency: And by using the Equation (3) we get: And similarly, it can be shown that the cross interaction between Pump number 2 to Stokes number 1 will generate the next acoustic frequency: It can be seen from Equation (8) that if we choose the modulation frequency to be very close to the Brillouin frequency Ω B,2 we can get acoustic vibrations with a frequency that may be detected by using our relatively fast (but not 10 GHz fast) camera.

Experimental Setup
The experimental setup can be seen in Figure 1.
It can be seen from Equation (8)  we can get acoustic vibrations with a frequency that may be detected by using our relatively fast (but not 10 GHz fast) camera.

Experimental Setup
The experimental setup can be seen in Figure 1. A CW-laser with a wavelength of 1550 nm was used as a pump source. To achieve the desired frequency difference, an intensity electro-optic modulator was used, which created two sidebands to the spectrum of the laser source. The modulation frequency was chosen according to the principle that was presented in the previous section according to the camera's frame rate which, in our experiment, was 900 kHz. The Brillouin frequency was approximately found by measuring the frequency shift between the inserted pump wave and the back-reflected Stokes wave. This measurement was performed by using a Fabry Perot scanner with a spectral resolution of about 67 MHz. Since the accepted value was about 10.6 GHz, modulation frequencies around 5.3 GHz were scanned in small steps of 200 khz, to ensure that the generated acoustic frequency will be able to detect by our camera.
The pump waves were amplified by an erbium-doped fiber amplifier (EDFA). The output power of the EDFA was 26 dBm, and it was connected to 12 km single-mode silica fiber via an optical circulator. The core diameter of the fiber was 8 μm and its cladding diameter was 125 μm. The fiber was fixed on a metallic reflector and was illuminated by CW-laser at a wavelength of 532 nm. This illumination passes the fiber cladding and core and due to the reflection at the metallic mirror, a speckle pattern was generated. The illuminated fixed part of the fiber was coiled to many rounds on the reflected surface to increase the interaction between the light and the fiber, and so to enhance the influence of the acoustic vibration on the recorded speckle pattern. The speckle pattern was captured with a high-speed camera (with 128 by 16 pixels) using a 75 mm lens. As we noted above, the camera's frame rate was 900 frames per second.

Results
The Pump wave was modulated in amplitude with a frequency of 5.3001 GHz. The spectrum of the input and the back-reflected signals were measured by an optical spectrum analyzer (OSA). Those measurements can be seen in Figure 2. A CW-laser with a wavelength of 1550 nm was used as a pump source. To achieve the desired frequency difference, an intensity electro-optic modulator was used, which created two sidebands to the spectrum of the laser source. The modulation frequency was chosen according to the principle that was presented in the previous section according to the camera's frame rate which, in our experiment, was 900 kHz. The Brillouin frequency was approximately found by measuring the frequency shift between the inserted pump wave and the back-reflected Stokes wave. This measurement was performed by using a Fabry Perot scanner with a spectral resolution of about 67 MHz. Since the accepted value was about 10.6 GHz, modulation frequencies around 5.3 GHz were scanned in small steps of 200 khz, to ensure that the generated acoustic frequency will be able to detect by our camera.
The pump waves were amplified by an erbium-doped fiber amplifier (EDFA). The output power of the EDFA was 26 dBm, and it was connected to 12 km single-mode silica fiber via an optical circulator. The core diameter of the fiber was 8 µm and its cladding diameter was 125 µm. The fiber was fixed on a metallic reflector and was illuminated by CW-laser at a wavelength of 532 nm. This illumination passes the fiber cladding and core and due to the reflection at the metallic mirror, a speckle pattern was generated. The illuminated fixed part of the fiber was coiled to many rounds on the reflected surface to increase the interaction between the light and the fiber, and so to enhance the influence of the acoustic vibration on the recorded speckle pattern. The speckle pattern was captured with a high-speed camera (with 128 by 16 pixels) using a 75 mm lens. As we noted above, the camera's frame rate was 900 frames per second.

Results
The Pump wave was modulated in amplitude with a frequency of 5.3001 GHz. The spectrum of the input and the back-reflected signals were measured by an optical spectrum analyzer (OSA). Those measurements can be seen in Figure 2 As can be seen in Figure 2, the modulation of the pump created two sidebands to the main wavelength. Accordingly, shifted back-reflected signals were generated for each pump wavelength. Besides the three main peaks of the Stokes signal, some additional peaks at the same positions as those of the pump signal are observed. Those peaks may be caused by leakage of the pump wave via the circulator (from port number 1 to port number 3) or by the Rayleigh scattering of the pump wave. It can also be seen that the accepted shifts in frequencies are about 10.6 GHz, following the typical Brillouin shift value. For each pump wave, the Brillouin frequency shift is slightly different because of the difference in the pump wavelength. Figure 2 illustrates that the frequency of pump number 1 is very close to the frequency of Stoke number 2, which means that their cross interaction yields relatively low acoustic frequency. The main peaks of the pump and the Stokes waves as extracted from Figure 2 can be seen in Table 1. Then, the speckle pattern was recorded and analyzed for two cases, with and without the above-illustrated pump waves. The accepted results can be seen in Figure 3. Figure 3 shows the oscillation frequencies of the speckle pattern in the horizontal (X direction) and vertical (Y direction) axes. As can be seen, for the case of the pumped fiber measurement, a peak at frequency 215.2 kHz was obtained. Note that without using pump waves, no frequency peak was accepted, which means the detected peak in the second case was achieved thanks to the acoustic vibrations in the fiber. Then, more modulation frequencies were scanned around the frequency of 5.3 GHz. The results can be seen in Figure 4. Table 2 shows the frequencies of the received peaks that As can be seen in Figure 2, the modulation of the pump created two sidebands to the main wavelength. Accordingly, shifted back-reflected signals were generated for each pump wavelength. Besides the three main peaks of the Stokes signal, some additional peaks at the same positions as those of the pump signal are observed. Those peaks may be caused by leakage of the pump wave via the circulator (from port number 1 to port number 3) or by the Rayleigh scattering of the pump wave. It can also be seen that the accepted shifts in frequencies are about 10.6 GHz, following the typical Brillouin shift value. For each pump wave, the Brillouin frequency shift is slightly different because of the difference in the pump wavelength. Figure 2 illustrates that the frequency of pump number 1 is very close to the frequency of Stoke number 2, which means that their cross interaction yields relatively low acoustic frequency. The main peaks of the pump and the Stokes waves as extracted from Figure 2 can be seen in Table 1. Then, the speckle pattern was recorded and analyzed for two cases, with and without the above-illustrated pump waves. The accepted results can be seen in Figure 3. Figure 3 shows the oscillation frequencies of the speckle pattern in the horizontal (X direction) and vertical (Y direction) axes. As can be seen, for the case of the pumped fiber measurement, a peak at frequency 215.2 kHz was obtained. Note that without using pump waves, no frequency peak was accepted, which means the detected peak in the second case was achieved thanks to the acoustic vibrations in the fiber. Then, more modulation frequencies were scanned around the frequency of 5.3 GHz. The results can be seen in Figure 4. Table 2 shows the frequencies of the received peaks that were achieved for each modulation frequency. As can be seen, for each modulation frequency the measured peak was slightly different.
were achieved for each modulation frequency. As can be seen, for each modulation frequency the measured peak was slightly different.   were achieved for each modulation frequency. As can be seen, for each modulation frequency the measured peak was slightly different.

Discussion
The results that are presented in Table 2 show that the locations of the measured seem to be not consistent with the changes of the modulation frequencies. According to the relation that is shown in Equation (8), a change of 200 kHz in the modulation frequency should lead to a change of 400 kHz at the measured peak. In our experiment, however, the difference between two consecutive peak values is between 10-68 kHz. However, the accepted results could be well explained by the aliasing phenomena, which cause different signals to become indistinguishable when sampled. Since changes of 400 kHz at the acoustic frequency can take us out of the sampling range (i.e., 450 kHz), the measured frequency Ω meas will be given by the modulo operation in the following way: It can be easily seen that for this relation, a change of 400 kHz in the acoustic frequency Ω c,1 leads to a change of 50 kHz at the measured frequency. This is quite close to the accepted results presented in Table 1 in which the difference between two consecutive peak values is between 10-68 kHz. To clarify this claim, suppose the first frequency peak in the table was sampled without aliasing. According to Equation (8), we can extract the acoustic frequency Ω B,2 : Which yields: Ω B,2 = 2 × 5.3001 × 10 9 + 215.8 × 10 3 = 10.6004GHz (12) If we put this value in Equation (10) together with the different modulation frequencies, we could find the theoretical values that should be measured in our experiment. Those values compared to experimental values are presented in Table 3. The small differences between the theoretical values to the experimental results may be explained by small changes in temperature that occurred during the measurement. Equation (10) shows that the measured frequency depends not only on the modulation frequency but also depend on the acoustic frequency Ω B,2 . According to Equation (5), this frequency depends on the acoustic velocity, which is a temperature-depended parameter. From both Equation (5) and Equation (10) it is possible to show that a small change of 0.01 m/s in the acoustic velocity leas to change of about 40 kHz in the measured peak, which may explain the small inconsistent of the accepted results.
Note that in our experimental setup there are some additional acoustic frequencies, besides the frequency presented in Equation (7) that may also be detected by our system. Those frequencies include the whole possible combinations of frequencies presented in Equation (5) and the second cross interaction frequency presented in Equation (9), where some of them may be found within the sampling rates or may be detected by the aliasing phenomena. The existence of these additional acoustic frequencies in our system may also be the reason for the secondary peaks accepted in some measurements (see Figure 4c,d). More experimental work is required to find the exact significance of the vibrations which were measured in this setup.

Conclusions
In this paper we demonstrated the ability to sense acoustic vibrations in optical fibers resulting from the Brillouin effect by temporal tracking of back-reflected speckle patterns. By using two pump waves in the same fiber, acoustic vibrations that were generated by the cross interaction between the first pump and the Stokes wave of the second pump were apparently detected. In future works, this new detection modality could be used for a realization of improved Brillouin fiber sensors, with high spatial resolution and with shorter measurement time.

Conflicts of Interest:
The authors declare no conflict of interest.