## 4 Fiber Configurations  
The previous two sections, with references (and the theoretical and empirical findings found therein), provided summaries of the waveguide and material properties that are used in discussing several novel Brillouin-tailored fibers that can be found in the literature. As a sensing tool, one logically can conclude that both the thermo-mechanical response and scattering efficiency of the Brillouin process are of primary interest. For instance, a fiber with enhanced \(g_{B}\) may be desirable for short- to moderate-reach sensors with high SNR. However, as discussed above, this may prove to be challenging since fused silica, among oxide compounds, has a relatively high \(g_{B}\) due to a narrow \(\Delta v_{B}\) coupled with a relatively large p\({}_{12}\). Figure 6: Brillouin spectral width simulation for pure silica at wavelengths of 633 nm and 1534 nm. Far from the peak, the spectral width is proportional to \(\
u_{B}\)\({}^{2}\). The spectral width is proportional to the acoustic attenuation coefficient. In terms of the thermo-mechanical response, a deployed optical fiber will be subject to changes in both T and \(\varepsilon\). Obviously, then, if one could somehow devise a configuration whereby a system of two equations with two unknowns (\(T\) and \(\varepsilon\)) can be formulated, then simultaneous strain and temperature sensing could be achieved. For instance, consider the simultaneous use of two independent fibers [117]. Further, consider that each has a unique thermal and strain coefficient. In this case, the system can be characterized by the matrix equation  
\[\left[ \begin{array}{c}\Delta v_{B1}\\ \Delta v_{B2}\end{array} \right]=\left[ \begin{array}{cc}C_{T1}&C_{c1}\\ C_{T2}&C_{c2}\end{array} \right]\left[ \begin{array}{c}\Delta T\\ \Delta\varepsilon\end{array} \right] \tag{21}\]  
where the Cs represent the two thermal and strain coefficients in the obvious way. Equation (21) describes the change in the \(v_{B}\)'s with changes in \(T\) or \(\varepsilon\). Therefore, knowing the Cs a priori, distributed measurements of frequency on the two fibers gives \(T\) and \(\varepsilon\) from some starting, relaxed state (by solving the inverse-matrix problem). As an aside, Equation (21) need not be limited to a 2 \(\times\) 2 matrix and can include other (even non-Brillouin) parameters, such as Brillouin power (as discussed at the end of the previous section). Other examples include simultaneous use of Brillouin scattering and changes in birefringence in a polarization-maintaining fiber [118; 119; 120], and the use of Brillouin scattering coupled with thermally-induced changes to the emission spectrum of Er doped into the fiber [121]. The Cs should differ significantly enough to achieve any required system sensitivity. For example, [PERSON] et al. [117] utilized a second fiber that could be kept loose such that no strain was experienced by that fiber. In this case, \(C_{c2}\) = 0 GHz/\(\varepsilon\) and \(C_{c1}\) could remain similar in magnitude to that of silica. The two fibers (or rather their cores) need not be part of independent structures. For example, [PERSON] et al. proposed a dual-core fiber for discriminative sensing [122] and detailed experimental validation was recently provided [123]. In this case, the two cores have non-overlapping values of \(v_{B}\) and have differing thermal and strain coefficients. [PERSON] et al. [124] described the use of multi- (7-) core fiber for the distributed Brillouin sensing application, but only characterized two of the cores for said application. They found that the thermal and strain coefficients differed by \(<\)10% in the first and second cores, but with one parameter being larger and the other being smaller in the first core. They suggested that the change in coefficients largely can be attributed to practical differences in the core materials. [PERSON] et al. [125; 126] showed that the Brillouin scattering response of multi-core fibers is highly sensitive to bending, thus paving the way for three-dimensional shape sensors.