## 4 Results and Discussion
### Temperature-Dependent Measurements
To measure the contribution of photothermal heating to the photomechanical stress response, the PMMA fibers are painted with black markers that absorb all of the light, converting all of the energy to heat. These fibers are irradiated with 488 nm-wavelength light and the stress response as a function of time is measured for vertically and horizontally polarized pump light. Figure 15 shows typical data for the stress versus time for one full cycle of painted fiber. The black points are the smoothed data and the solid curve is a fit to a single exponential. The fit is based on the model developed previously [16; 23], given by  
Table 2.4  
and  
Table 2.5  
Table 2.6 Young’s Modulus of unannealed and annealed PMMA and DR1/PMMA fibers as a function of vertically polarized absorbed pump intensity. The lines are fits to the non-zero-intensity data points. where \(\sigma^{(n)}\), \(t_{1}\), and \(t_{2}\) are the amplitudes, turn-on time constant when the pump is on, and turn-off time constant when the pump is off, respectively. \(t_{0}=30\) s is the time duration of the beam being on and off. Table 2.7 Young’s Modulus for unannealed and annealed PMMA and DR1/PMMA fibers as a function of maximum vertically polarized absorbed pump intensity. Table 2.8 Young’s Modulus for unannealed and annealed PMMA and DR1/PMMA fibers as a function of maximum horizontally polarized absorbed pump intensity. \(\sigma^{(1)}\) represents the strength of the photomechanical stress response of the material. This stress, when divided by the intensity of the light \(I\) that induces this stress, is the definition of the photomechanical constant. Details of this definition can be found in the literature [16; 22]. If the sole mechanism is photothermal heating, as it should be in such painted fibers, then \(t_{1}\) and \(t_{2}\) should be the same as the Newton heating and cooling time constants [23]. Figures 16 and 17 show the turn-on and turn-off time constants \(t_{1}\) and \(t_{2}\) as a function of intensity that are derived using the fitting functions in Equations (16) and (17). We will assume that these are the Newton heating/cooling time constants to determine the photothermal heating contribution. The photothermal heating contribution to the photomechanical response can be determined from Equation (7). \(\Delta T/I_{0}\) is determined using Equation (5). Table 4 lists the independently determined values of \(\rho\) and \(c\) for PMMA and \(w\) is measured with a caliper for the fiber used in our measurements. \(d\sigma/dT\) is calculated from the values in Table 5, which are determined from fits to the temperature-dependent stress as described above. The heating contribution to the photomechanical response are shown in Table 2.9 \"\(|\)\" and \"--\" denote the response along and perpendicular to the long axis of the fibers, which are mounted vertically [23]. The photomechanical response for PMMA fibers marked with black ink and DR1/PMMA fibers as a function of temperature cluster at about \(\kappa_{\sigma}^{(1)}=400\) s/m for both polarizations as well as for the painted and unpainted fibers. The response in painted PMMA fibers is only due to heating. The fact that this is the same as the response in unpainted DR1/PMMA fibers strongly suggests that the contribution of photoisomerization and/or molecular reorientation in DR1/PMMA fibers to the photomechanical response is negligible. Furthermore, the fact that the time constants of the response for both painted and unpainted fibers are the same also suggests that the heating mechanism dominates. \[T_{c}^{\text{Unannealed PMMA}}=T_{c}^{\text{Unannealed DR1}}\]0 Typical smoothed stress versus time data and a fit to Equations (16) and (17) for one full On/OFF cycle. \[T_{c}^{\text{Unannealed PMMA}}=T_{c}^{\text{Unannealed DR1}}\]1 Time constant \(t_{1}\)—light on—as a function of absorbed intensity for unannealed and annealed PMMA and DR1/PMMA fibers for vertical and horizontal pump polarization. The insets show the average time constants over all intensities as a function of the fiber’s composition.