# Non-Local Effects in Brillouin Optical Time-Domain Analysis Sensors
## 2 Non-Local Effects Induced by Pump Pulse Depletion
When the detailed interaction is taken into account, it is found than in a dual-probe BOTDA there is still pump depletion, although it is greatly diminished. This is due to the fact that the pulse is interacting with two probe waves with a power slightly unbalanced by the interaction itself [9]. In this case, it is found that the pump depletion is no longer independent of the pulse peak power nor of its temporal duration. In particular, the greater the power and/or the longer the duration, the higher the depletion factor of the pulse. In a long-range dual-probe BOTDA sensor, deploying 10-ns pump pulses with peak power set just below the typical MI threshold of 20 dBm, pump depletion imposes a theoretical upper limit for the probe wave injected in the fiber of approx. 7 dBm in order to have a BFS systematic measurement error of less than 1 MHz. Note that for a longer pulse duration, the limit of probe power is more stringent. Therefore, the dual-probe BOTDA sensor configuration could be seen as greatly ameliorating non-local effects due to pump pulse depletion. However, later work showed that the probe power limitation in this setup was actually more restrictive due to the onset of so-called second-order non-local effects. These non-local effects are related to the appearance of linear distortion of the pump pulse spectrum due to its interaction with the two probe waves [13]. As is shown in Figure 2a, when the frequency detuning between pump and probe waves equals the BFS of the fiber, the loss and gain spectra generated upon the pulse perfectly compensate each other and non-local effects are largely avoided. However, in order to retrieve the full Brillouin gain spectra, it is mandatory to scan the frequency detuning between pump and probe. In this way, as is portrayed in Figure 2b,c, when the frequency difference does not match the BFS of the fiber, the Brillouin gain and loss spectra generated by both probe waves over the pump pulse do not overlap perfectly, leading to linear distortion of the pump pulse spectrum. Figure 1: Effect of pump pulse depletion frequency dependence on a Brillouin gain spectrum, when scanning a fiber section displaced \(\delta v\) MHz from the Brillouin frequency shift (BFS) of the fiber. As is depicted in Figure 3, the distortion of the pulse spectrum leads to a distortion of the measured gain spectra and BFS measurement error [14]. It is found that this limits the maximum probe wave power to around \(-3\) dBm for typical standard single-mode fiber parameters. This is well below the theoretical limit imposed by the Brillouin threshold of the fiber, which is around 7 dBm for typical single-mode fiber. Therefore, at least 10 dB of SNR is being wasted in long-range dual-probe BOTDA sensors. Therefore, the development of techniques to overcome this limit is of paramount importance to improve the performance of the sensor. Figure 3: Pulses at the output of the fiber and measured Brillouin spectra for a conventional dual-probe BOTDA in two cases for probe wave powers of \(-6\) dBm (**a,b**) and 5 dBm (**c,d**). (From [PERSON], [PERSON], [PERSON], [PERSON], [PERSON] and [PERSON], “Overcoming Nonlocal Effects and Brillouin Threshold Limitations in Brillouin Optical Time-Domain Sensors,” in _IEEE Photonics J._**2015**, 7, 1–9. With permission. Copyright 2015 IEEE). Figure 2: Stimulated Brillouin scattering (SBS) interaction process over the pump pulse in dual-probe wave Brillouin optical time-domain analysis (BOTDA) configurations and its consequences on the pulsed wave for different frequency spacing of the conventional scan process (**a**) when the frequency detuning equals the BFS of the fiber (**b**) when it is higher than the BFS and (**c**) for a smaller frequency shift.