## 4 Fiber Configurations
To conclude, these fiber configurations are enabled by the relatively wide range of materials and their respective influences on the Brillouin scattering characteristic (see Table 2 or [35]). As an interesting side note, the aforementioned methods to tailor the BGS require transverse (radial and possibly azimuthal) engineering of the optical and acoustic waveguide properties. However, an optical fiber also may be tailored in the axial direction. Indeed, this has been a known method to suppress SBS in optical fibers: by varying the composition or waveguide properties along the fiber length, the BGS becomes distributed across a wider range of frequencies [144; 145; 146], thereby decreasing the peak value of \(g_{B}\). Such a fiber enables the possibility of having a unique one-to-one mapping of some position along the length of fiber to a frequency on the BGS. It was suggested [147] that such a fiber can be used for simple distributed sensing in that a modest continuous-wave (CW) measurement of the BGS of the entire fiber can give thermal or strain distributions along the axial direction of that fiber. Rather than obtaining full discriminative details about the fiber's environment, perhaps in some cases only a single parameter is wanted, such as a local \(\varepsilon\) or T alone. It may then be impactful to  
Figure 7: Example of a BGS tailored to have two acoustic mode interactions of similar strength. The responses of the modes to changes in \(T\) or \(\varepsilon\) differ. This illustration may represent a typical fiber whose temperature or applied strain has been increased in going from the blue to the red curve. devise a fiber that is immune to changes in \(T\) or \(\epsilon\), respectively. These are referred to as \"athermal\" and \"atensic\" (after [71]), respectively. As discussed in the previous section, it appears that the community has yet to observe an increase in \(C_{T}\) or \(C_{e}\) simply by adding dopants to silica. In other words, adding just about any oxide to the silica core will reduce the thermal or strain sensitivity. However, on the bright side, this represents a possible path to athermal or atensic fibers. One drawback to this approach, however, in many of the silicate systems studied (e.g., SrO [70], BaO [71], La\({}_{2}\)O\({}_{3}\)[73], and Lu\({}_{2}\)O\({}_{3}\)[74]), is that an athermal (or atensic) fiber composition usually is accompanied by a significant reduction in its sensitivity to strain (or temperature) and in \(g_{B}\). An exception was observed in [34] with the addition of Li\({}_{2}\)O to silica, wherein an athermal fiber composition (that also is optically single mode) could be achieved with a strain sensitivity similar to that of pure silica. As discussed in the previous section, this was attributed to a significant increase in the CTE of the core relative to the cladding with the addition of lithtia. A possible drawback to this structure was that it was acoustically anti-guiding with a wide \(\Delta\
u_{B}\). It was suggested that this could be avoided with the use of Na\({}_{2}\)O or K\({}_{2}\)O. Interestingly, the results in [34] were extrapolated to higher Li\({}_{2}\)O concentrations [148] and modeling results suggest a maximum (magnitude) thermal response in the range of \(-6.5\) MHz/K, roughly six times higher than silica (but negative), exists in the lithium silicate system; a value comparable to that in polymer fibers [149]. The effect of CTE mismatch between core and cladding also was studied in the aluminosilicate system in [150; 151] and the conclusion seems to be that in a fiber where the core CTE (once again, by adding just about anything to silica, etc.) is greater than that of the cladding (assumed to be pure silica), \(\epsilon\) also is a function of T. Note that a new model for the CTE using Equation (15) can be found in [152]. However, this dependence may be weak, depending on the absolute composition (which and in what quantity dopants are used).