## 3 The Material
These response values are typical of those found in the literature for optical fiber with conventional coatings [105]. Deviation from them depends on the absolute fiber configuration, coating, and glass composition. For instance, it has been shown [106; 107] that one can enhance the thermal sensitivity with a coating of high coefficient of thermal expansion (CTE). Going in the other direction, a reversal of the sign of the thermal response was demonstrated by using a high-CTE core cladded in low-CTE silica [34]. As discussed below, these possibilities stem from silica's anomalous behavior of decreasing acoustic velocity with increasing applied pressure (compression) [108; 109; 110] (this is the leading reason why \(\mathrm{v}_{\mathrm{B}}\) increases with applied strain). The glass composition also plays a primary role in the magnitude and sign of the response coefficients. [PERSON] et al. [57] showed that the addition of GeO\({}_{2}\) to silica decreases the magnitude of the thermal coefficient. Interestingly, the addition of Al\({}_{2}\)O\({}_{3}\)[52], SrO [70], BaO [71], La\({}_{2}\)O\({}_{3}\)[73], and Lu\({}_{2}\)O\({}_{3}\)[74] were all found to reduce the magnitudes of both the thermal and strain coefficients. This is interesting from the perspective of designing a fiber whose response to temperature changes or strain is zero. [PERSON] et al. [57] also showed that the Brillouin spectral width decreases with increasing temperature in germanosilicate optical fiber. This was attributed to acoustic absorption in the tails of the thermo-absorption curve. Since the acoustic attenuation (damping, or also \(\Delta\
u_{B}\)) has a peak at cryogenic temperatures (just over 100 K at 27.5 GHz hypersonic frequency using 633 nm optical illumination, see Figure 6) [111], the Brillouin spectral width must then be decreasing in value moving away from this peak (increasing temperature). Interestingly, being far from the peak also gives rise to the frequency- (or inverse-wavelength-) squared dependence of \(\Delta\
u_{B}\). More specifically, the Brillouin spectral width can be expressed as [112] \begin{table}
\begin{tabular}{c c} \hline
**Parameter** & **Value** \\ \hline \(\mathrm{d}n/\mathrm{d}T\) (\(10^{-6}\) K\({}^{-1}\)) & +10.42 [94] \\ \(\mathrm{d}V_{a}/\mathrm{d}T\) (\(\mathrm{m}/\mathrm{s}/\mathrm{K}\)) & +0.555 [94] \\ \(\mathrm{d}n/\mathrm{d}\epsilon\) (\(1/\epsilon\)) & \(-(n_{o}{}^{3}/2)\times 0.174\)[52] \\ \(\mathrm{d}V_{a}/\mathrm{d}\epsilon\) (\(\mathrm{m}/\mathrm{s}/\epsilon\)) & +29,240 [97] \\ \hline \end{tabular}
\end{table} 
Table 4: Material response to changes in T and \(\epsilon\) for pure glass SiO\({}_{2}\). \[\Delta v_{B}=\left(\frac{2n}{\lambda_{o}}\right)^{2}\frac{\eta^{\prime}(v)}{\rho} \tag{19}\]  
where \(\eta^{\prime}(v)\) is a dynamic viscosity. Through an analysis utilizing the theory in [112], [PERSON] et al. [102] showed that when the temperature is far from the peak of the thermo-absorption curve, \(\eta^{\prime}(v)\) becomes independent of frequency. However, in some materials, they suggested, where the fiber fictive temperature is near such a peak, \(\Delta v_{B}\) acquires a sub-quadratic dependence on frequency, resulting from the frequency dependence of \(\eta^{\prime}(v)\). As also is apparent, the relative shape (magnitude and peak temperature) of these thermo-absorption curves must give rise to the relative contribution to \(\Delta v_{B}\) by dopants [57], as would seem to be confirmed with the case of GeO\({}_{2}\)[113]. For completeness, a simulation of \(\Delta v_{B}\) (after [111; 112]) as a function of temperature is shown in Figure 6.  
Each of the parameters presented above has some dependence upon the temperature of the optical fiber. From the perspective of the waveguide, as the refractive index or acoustic velocity changes with \(T\), so can guiding characteristics that influence \(\Gamma_{m}\) (though likely in an insignificant way). From a material perspective, as the fiber heats, the acoustic velocity changes, thereby resulting in a change in \(v_{B}\).