## 4 Results and Discussion
### Intensity-Dependent Photomechanical Measurements  
The sample is pumped with 488-nm wavelength light with a square wave intensity profile and the photomechanical stress response is measured as a function of time for three CTA volume fractions in the apparatus described in Section 3.2. The DR1 concentration is fixed in all fibers at 0.5% by weight. The stress is measured as a function of the intensity amplitude of the square wave separately for vertical and horizontal polarization of the pump light to determine the photomechanical stress response tensor. The black points in Figure 10 show typical smoothed data for a 60-s period square wave and the solid curve is a fit to a single exponential given by Equations (33) and (34) as described below. We note that the stress in Figure 10 changes sign, so the material transitions form a stretched state to a compressed state relative to its equilibrium dimensions. As a result, buckling may take place beyond the transition at high stress. Figure 10 is representative of data for the highest pump intensities. However, most of the intensities reported here are at levels below the buckling point. Even those above the buckling point are observed to follow the trends, so buckling does not appear to be an issue for samples of this geometry. Higher pre-stress than those used is avoided to prevent sample damage or inducing anisotropies. The data in Figure 10 behave as a single saturated exponentials in both the pump on and off regions. We require that the response in the two regions join together continuously but the time constants are permitted to be different. Putting these criteria together leads to the model  
\[\sigma_{on}=\sigma_{0}+\sigma_{1}(1-e^{(-t/t_{1})}) \tag{33}\]  
and  
\[\sigma_{off}=\sigma_{0}+\sigma_{1}(1-e^{(-t_{0}/t_{1})})e^{-(t-t_{0})/t_{2}}, \tag{34}\] \begin{table}
\begin{tabular}{c c c c c} \hline
**CTA Volume Fraction** & \(\sigma_{0}\) **(MPa)** & \(\sigma_{1}\) **(MPa)** & \(T_{0}\) (\({}^{\circ}\)**K)** & **n** \\ \hline \(1.33\times 10^{-3}\) & \(-300\) (\(\pm 0\)) & 301.21 (\(\pm 0.02\)) & 451.9 (\(\pm 2.5\)) & 13.66 (\(\pm 0.22\)) \\ \hline \(2\times 10^{-3}\) & \(-488\) (\(\pm 0\)) & 488.98 (\(\pm 0.01\)) & 431.4 (\(\pm 1.6\)) & 17.49 (\(\pm 0.22\)) \\ \hline \(2.66\times 10^{-3}\) & \(-29.4\) (\(\pm 0\)) & 32.39 (\(\pm 0.04\)) & 374.99 (\(\pm 0.33\)) & 9.76 (\(\pm 0.09\)) \\ \hline \end{tabular}
\end{table} 
Table 2: The parameters determined by fitting the temperature-dependent stress data in Figure 9 to Equation (6) for fibers with three different CTA volume fractions. Figure 9: Measured stress as a function of temperature for clamped DR1-doped PMMA fibers at three different CTA volume fractions (points) and fits to the model given by Equation (6). where \(A_{n}\) and \(t_{n}\) are the amplitudes and time constants and \(t_{0}=30\)s--the time durations of the beam being on and the beam being off. These types of fits are commonly used [49]. Depending on the material, light can induce an expansion or contraction. Since an increase in the length of a sample leads to a decrease in the stress for a pre-stressed sample, we define the photomechanical stress response to be of the form,  
\[\sigma(I,t\rightarrow\infty)\equiv\sigma(I)=-\sum_{n=0}^{\infty}\kappa_{ \sigma}^{(n)}I^{n}\approx-(\kappa_{\sigma}^{(1)}I+\kappa_{\sigma}^{(2)}I^{2}), \tag{35}\]  
where \(\sigma\) is the stress, \(\kappa_{\sigma}^{(n)}\) the photomechanical stress response, and \(I\) the intensity absorbed by the sample. With this definition, \(\kappa_{\sigma}^{(1)}\) is positive when the length of the sample increases [49; 50]. Figure 10 shows typical stress data as a function of time and fits to the theory given by Equations (33) and (34). Equation (35) assumes that the stress function \(\sigma(I)\) can be expanded in a series and that the first two terms are sufficient to approximate its behavior.