# Remote Speckle-Based Measurements of Backward Brillouin Acoustic Vibrations in Optical Fibers
## 4 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.  
Figure 1: Schematic diagram of the experimental setup. PC: polarization controller; EDFA: Erbium doped fiber amplifier and OSA: optical spectrum analyzer.  
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.  
\begin{table}
\begin{tabular}{c c} \hline
**Wave** & **Peak (THz)** \\ \hline Pump 0 & 195.7106 \\ Pump 1 & 195.7051 \\ Pump 2 & 195.7156 \\ Stokes 0 & 195.6995 \\ Stokes 1 & 195.6944 \\ Stokes 2 & 195.7051 \\ \hline \end{tabular}
\end{table}
Table 1: The peak frequencies of the different optical waves in the system.  
Figure 2: The spectrum of the input (pump waves) and the back-reflected (Stokes waves) signals, measured by optical spectrum analyzer (OSA).  
Figure 4: Experimental Results: The oscillation frequencies of the speckle pattern in horizontal (X direction) and vertical (Y direction) axes with pump, with different frequencies of modulation: (**a**) modulation frequency of 5.3001 GHz; (**b**) modulation frequency of 5.3003 GHz; (**c**) Modulation frequency of 5.3005 GHz; and (**d**) modulation frequency of 5.3007 GHz.  
Figure 3: Experimental Results: The oscillation frequencies of the speckle pattern in horizontal (X direction) and vertical (Y direction) axes; (**a**) without pumps and (**b**) with two pump waves.