## 4 Fiber Configurations
Equation (21) need not be limited to the use of two or more optical fibers/cores. Coefficients 1 and 2 instead may refer to two distinct optical modes in a fiber (if the fiber is multimode) [127]. Should the thermal and strain responses of Brillouin scattering involving two orthogonal optical modes differ, they also may be utilized for discriminative sensing. To remind the reader, the result, or consequence, of the thermo-mechanical response is carried by the scattered optical mode via an interaction with the guided (or possibly anti-guided) acoustic wave. Both the optical and acoustic properties of the fiber may be functions of the environment, though, as discussed above, the latter dominates in fibers comprised mainly of silica. [PERSON] et al. [128] showed that the acousto-optic interactions in such fibers involve optical and acoustic modes that have the most similar shape, and therefore, as would be expected, largest spatial overlap (see Equation (8)). Very nice theoretical analyses of such interactions can be found in [129; 130]. [PERSON] et al. [62; 131] provided an analysis involving modes possessing orbital angular momentum, while [PERSON] et al. [132] described a hybrid Raman-Brillouin system in a few-mode fiber. Another possibility for discriminative sensing is the use of multiple acoustic mode interactions (or \"peaks\" in the BGS) in an optically single mode fiber, as first suggested by [PERSON] et al. [133]. In this case, both the fiber's acoustic velocity and refractive index profiles are tailored to enhance the gain on one or more HOAMs. Differences in the sensitivity coefficients between the various modes arise from variations in their spatial overlaps with the compositional profile. Figure 7 provides such a BGS (though fictitious) modified utilizing these procedures. The fundamental (L\({}_{01}\)) and one HOAM (such as L\({}_{03}\)) now have similar strength, and their responses to a change in T or \(\varepsilon\) differ. In this case, the HOAM may have greater overlap with a region containing a dopant that lowers \(C_{T}\) or \(C_{\varepsilon}\), since, as described above, these coefficients can be strong functions of the material. A potential drawback to this approach is that it lowers the gain on the LP\({}_{01}\)-L\({}_{01}\) acousto-optic interaction. However, it has been suggested [134; 135] that this could be advantageous in long systems due to the elevated threshold for the onset of the stimulated form of Brillouin scattering (SBS). In Refs. [133; 134], Corning LEAF fiber was utilized for discriminative sensing due to the presence of multiple acoustic mode interactions of reasonably similar magnitude. Along the aforementioned design approach, [PERSON] et al. [136; 137] described a fiber with a GeO\({}_{2}\)-doped core and F-doped inner cladding whereby such differences in material properties led to different thermal and strain coefficients for each guided acoustic mode. They also demonstrated enhancement of the strength of the interaction with the highly oscillatory L\({}_{03}\) mode. In a theoretical study, [PERSON] [138] suggested decoupling the optical and acoustic boundaries to achieve gain equalization between the fundamental mode (L\({}_{01}\)) and a HOAM. A diagram of such a scheme is provided in Figure 8. [PERSON] et al. [94; 97] demonstrated a simple means of calculating the thermal and strain coefficients for the interactions with the HOAMs in a radially non-uniform P\({}_{2}\)O\({}_{5}\)-doped fiber with matched inner cladding, with excellent agreement between theory and experiment. Note that a revised d\(n\)/d\(T\) for P\({}_{2}\)O\({}_{5}\) in silica was recently suggested [139]. Additional papers on tailoring the acoustic mode distribution can be found in Refs. [44; 61; 87; 140; 141; 142]. Finally, [PERSON] et al. [143] used three acoustic modes in LEAF and the relative intensity of two resulting beat signals in the several hundred MHz range for discriminative sensing.