## 4 Results and Discussion
### Intensity-Dependent Photomechanical Measurements
Here we define the linear intensity-dependent photomechanical response, \(\kappa^{(1)}(I_{0})\), which quantifies the linear photomechanical response of a material that is bathed in light of intensity \(I_{0}\). This quantifies the change in stress for a small added intensity \(\delta I\) to the large background intensity \(I_{0}\). It can be determined from a measurement of the stress \(\sigma(I)\) as a function of \(I\), yielding  
\[\kappa_{\sigma}^{(1)}(I_{0})=\left.\frac{\partial\sigma(I)}{\partial I} \right|_{I_{0}}=\kappa_{\sigma}^{(1)}+2\kappa_{\sigma}^{(2)}I_{0}. \tag{36}\]  
We can view the normal linear response \(\kappa_{\sigma}^{(1)}\) as being the limiting case of \(\kappa_{\sigma}^{(1)}(I_{0})\) when \(I_{0}\to 0\). As such, \(I_{0}\) provides another parameter that can be varied to test hypotheses of what makes a large photomechanical response. The data for vertically and horizontally polarized pump beams are separately fit to Equations (33) and (34). Figure 11 shows a plot of the parameter \(\sigma=\sigma_{1}\), the steady state light-induced stress at infinite time, which is determined from such fits at each pump  
Figure 10: Typical time-dependent stress data (each point in the plot is smoothed over 100 points) and a fit to the theory given by Equations (33) and (34) (smooth curve) for a pump that turns on and off over a period of 60 s.  
polarization. Also shown is a fit to the first two terms of the Taylor series expansion given by Equation (35). This expansion is a good approximation to the intensity-dependent response with a small quadratic contribution. The results of the linear photomechanical and nonlinear stress response \(\kappa_{e^{\prime}}^{(1)}\) and \(\kappa_{e^{\prime}}^{(2)}\) for vertical and horizontal polarization of light and as a function of CTA volume fraction are displayed in Table 3. The linear photomechanical response is the same within experimental uncertainties for all CTA volume fractions, so is independent of the polymer chain length. Furthermore, the linear response is independent of the polarization within experimental uncertainties, but the smaller values for the vertically polarized pump relative to the horizonal polarization are consistent with a small contribution from molecular reorientation. The quadratic stress responses \(\kappa_{e^{\prime}}^{(2)}\) for the vertically polarized pump are all the same, within experimental uncertainty, as a function of CTA volume fraction, but the response for a perpendicular pump becomes more negative. This suggest a nonlinearity, due to a mechanism that is not isotropic, as is heating. This increase in the magnitude of the quadratic response correlates with the decrease in [PERSON]'s modulus and the decrease in  
Figure 11: Polarization-dependent steady-state stress response at long times as a function of pump intensity at a pump wavelength of 488 nmfor different CTA volume fractions. The pump light is polarized parallel to the fiber’s long axis (**top**) and perpendicular to the fiber axis (**bottom**). polymer chain length. The chain length and Young's modulus decreases result in greater chain mobility and, hence, greater mobility of the dopant molecules, allowing them to reorient. However, the negative sign is opposite to what we would expect; with increased molecular reorientation, a horizontal pump would induce an increased stress response along the uniaxial direction. Figure 12 shows the photomechanical response as a function of intensity calculated from Equation (36) at the measured intensities using the fit parameters \(\kappa_{\sigma}^{(1)}\) and \(\kappa_{\sigma}^{(2)}\) from Table 3. The intensity-dependent response for pump light polarization along the axis containing the force sensor (which we will call vertical) changes by less than or equal to approximately 10%. The heating model given by Equation (7) predicts that the change in stress induced by the photothermal heating mechanism is independent of the intensity.