## 4 Results and Discussion
### Temperature-Dependent Measurements
The analytical form of Equation (15) with the fitting parameters determined from a fit to the data is used to determine \(d\sigma/dT\) for each fiber for a range of temperatures. Using an analytical fit function provides a cleaner determination of the derivative than would the raw data. The derivative \(d\sigma/dT\) is related to the thermal expansion coefficient. As the fiber is slightly stretched when mounted to prevent buckling when its length increases, an expanding fiber will result in a decrease of the stress; so, \(d\sigma/dT<0\). This can be understood from the fact that the fiber's resting length is less than its stretched length at the start of the experiment. If the fiber's resting length increases due to light actuation, the force read by the sensor decreases as the resting length grows closer to the stretched length, which is fixed by the distance between the clamps. Figure 7 shows that all dye-doped fibers have a positive thermal expansion coefficient. For temperatures above 308.15 K, the temperature-induced stress change is larger for unannealed DR1/PMMA fibers than for annealed ones. Similarly, the stress derivative \(d\sigma/dT\) in annealed plain PMMA fiber is lower than in the unannealed ones. So, annealing is observed to decrease the thermal expansion coefficient. Finally, dye-doped fibers show greater thermal expansion than plain fiber, an effect that is most pronounced at the highest temperatures. Figure 6: Change in stress of a stretched fiber as a function of temperature for PMMA and DR1/PMMA fibers. Note that the fiber is slightly stretched between the clamps to prevent buckling; thus, when the fiber expands, the stress decreases as the stretching strain decreases. \(\sigma_{0}\) is an arbitrary offset due to the nonzero reading of the sensor when no stress is applied. To understand the results, we consider two processes that lead to thermal expansion. First, the polymer expands as the temperature increases due to the polymer chains getting excited with thermal energy. Secondly, a change in temperature affects the relative populations of the two isomers of the dopant molecules [16; 23]. The competition between these two processes determines the net response. Figure 7 shows that the thermal expansion coefficient of the dye-doped fibers grows relative to the undoped fibers with temperature. The dye dopant appears to enhance the thermal expansion coefficient. The cis isomer population increases at higher temperatures and, given its larger volume, adds to thermal expansion in the DR1/PMMA fibers. The glass transition temperature \(T_{g}\) is lower in DR1-doped fibers than in plain ones. Since the thermal expansion coefficient increases as the temperature is increased, the larger stress change in DR1/PMMA relative to plain PMMA at a fixed temperature might be explained by this depression in the glass transition in doped polymers. Moreover, annealing the samples increased their \(T_{g}\) by decreasing their free volume; so, the rearrangement of molecules in the annealed samples is smaller than the unannealed ones, leading to a smaller thermal expansion coefficient in the annealed samples. Intensity-Dependent Measurements  
Here, we characterize the mechanical properties of fibers that are exposed to 488 nm-wavelength light produced by a krypton/argon laser as a function of intensity and polarization. Young's modulus is measured before, during, and after irradiation to determine the immediate and persistent effects of the light. Figures 8 and 9 show typical stress-strain curve data for unannealed PMMA and DR1/PMMA fibers illuminated with vertical and horizontal pump light polarizations. The flat part in Figures 8 and 9 is due to mechanical backlash in the mounts and is excluded when determining Young's modulus. The stress is observed to decrease during irradiation and persists to varying degrees in both PMMA and DR1/PMMA fibers after irradiation at the maximum intensity. In plain PMMA, the horizontally polarized pump has a larger influence on the stress change than the vertically polarized pump.