## 3 The Material
With regard to Figure 4, it is apparent that variations in the fiber processing/fabrication history, those that lead to differences in glass density, will give rise to fibers with different material characteristics. The same can be said of the properties of the individual glass constituents, including the SiO\({}_{2}\) component in a multicomponent glass. However, as a simplification, the latter usually is assumed to have fixed properties in the additive model. It was shown [76] experimentally, in a binary aluminosilicate system, that a 25% increase in the density of the Al\({}_{2}\)O\({}_{3}\) component gave rise to a 9% increase in V\({}_{\rm L}\) and 5% increase in n (in both cases for the Al\({}_{2}\)O\({}_{3}\) component). Regardless of some randomness associated with fabrication, it is not unreasonable to expect that the glass, in fiber form, would have properties not too dissimilar to those in bulk form. This comes with the caveat that fibers are rapidly quenched, whereas in many instances bulk glass samples are annealed, which can lead to some changes to the Brillouin scattering characteristics [77]. This is important to note, as the literature  
Figure 4: Simulated refractive index of binary germanosilicate as a function of the GeO\({}_{2}\) concentration (in mol %) for a base density of 3650 km/m\({}^{3}\) (blue curve). The effect of raising or lowering the density in the model affects the curvature of the functions. is replete with the elastic characterization of bulk glass (e.g., lithium and sodium silicates, with and without Fe\({}_{2}\)O\({}_{3}\)[78; 79], barium alkali silicate glasses [80], strontium manganese borate glasses [81], titanium silicate [82], alkali and alkaline earth metal aluminiosilicates [83], and lead and zinc silicate glass [84] just to name a few). Given their very different thermal histories, this argument also can be extended to the case of preform versus drawn fiber. For example, alumina seems to act somewhat differently in going from preform [55] to fiber [76]. It already is well-known that variations in draw tension, temperature, etc. can also lead to frozen-in effects that may influence the refractive index [85] and acoustic velocity [75; 86]. Thus, each of the design coefficients and equations provided above should be applied with some caution and care. The modeling presented thus far allows one, in a straightforward way, to design a desired frequency distribution for the Brillouin scattering interaction. Another common computational approach is the finite element method (FEM). Several groups have used FEM for the design or analysis of the Brillouin scattering spectra in optical fiber [87; 88; 89; 90]. One advantage is that these methods may offer greater computational efficiency for more complicated fiber structures, especially with the use of commercial software [91]. A drawback, however, especially with commercial software, is that they generally do not take into consideration those additional parameters that make up Equation (10). This may not be important if a fiber should be lightly doped and be comprised mainly of silica; \(g_{B}\) will remain about the same. However, even a few mol % of some additives can have a significant impact on \(g_{B}\) (see, for example, the effect of B\({}_{2}\)O\({}_{3}\) on \(\Delta v_{B}\)[75]). Early on, [PERSON] et al. [57] observed a significantly broadening spectrum (and therefore decrease in \(g_{B}\)) with increasing GeO\({}_{2}\) content. Indeed, this is true of all silicate additives listed in [35]. Continuing the discussion more broadly, several simulations, whether of the boundary-value [45] or FEM type, assume that the cladding acts as the predominant waveguide in an acoustically anti-guiding fiber [91]. More specifically, the interacting modes are those defined by the cladding-to-buffer boundary. There is value in scrutinizing this assumption since the phonon lifetime is on the order of 10 ns [49].