# Remote Speckle-Based Measurements of Backward Brillouin Acoustic Vibrations in Optical Fibers
## 1 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 everypoint 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.