## 2 Theory
### Tensor Response of Heating and Reorientation  
A common measurement configuration is a sample stretched between two clamps with a force sensor in series with one of the clamps [25]. This is the classical setup for tensile tests [46]. Then, the pump light illuminates the sample from the side, which can be polarized in the uniaxial stress direction or perpendicular to it. This configuration is ideal for detecting processes in which polarized light anisotropically changes the alignment or shape of the molecules because the stress measured is only along one axis (between the clamps)--call it \(z\)--for light polarized along \(x\) or \(z\). If light is polarized along \(z\), the measurement yields the stress response along \(z\), which is a measure of the \(zz\) tensor element, which we call \(\kappa_{//}^{(1)}\). If the light is polarized along \(x\), the tensor element \(zx\) is determined, which we call \(\kappa_{\perp}^{(1)}\). The anisotropy is related to the ratio between \(\kappa_{/}^{(1)}\) and \(\kappa_{\perp}^{(1)}\) as described in Section 2.2.1. Azo-dye chromophores, which change between two isomers upon light excitation, are an example of molecules that respond anisotropically to light. In DR1-doped PMMA, the lower-energy trans molecules that are aligned along the light's polarization will preferentially be excited to the cis state. This depletes the trans molecules that originally were oriented along the light's polarization. This process is called angular hole burning [47; 48; 49; 50; 51; 52],so named because of the depletion of trans molecules oriented along the light's polarization. Figure 1 shows a schematic diagram of the process. The trans molecules are depicted in the upper part of Figure 1 by straight lines with the isotropic distribution on the upper right. Below is a polar plot of the orientation distribution function \(G(\theta,\phi)\), which gives the probability density per unit solid angle of finding molecules oriented at angle \(\theta\). Due to uniaxial symmetry, \(G(\theta,\phi)\) is constant as a function of \(\phi\). The depleted trans molecules appear as the pinch in the orientational distribution function. Note that the cis isomers are not shown. The area inside the polar plot of the orientational distribution function is less when the trans chromophores are depleted, a distinguishing feature of angular hole burning. Since the cis isomer is shorter, we expect that the length of the material decreases along the light's polarization and remains the same in the direction perpendicular to it. In the clamped configuration, the decrease in length induces an increase of the measured stress. The cis isomer decays back to the trans state, but in no preferred direction. As a result, trans molecules aligned along the light's polarization vector get depleted and are subsequently isotropically redistributed. Both the excitation to the trans state and the reorientation that results when the cis molecule returns to its trans state leads to a depletion of molecules along the light's polarization and an increase of trans population perpendicular to it. This decay back to the trans state is called molecular reorientation. Figure 2 shows a schematic diagram. Note that the area of the orientational distribution function is unchanged from the original isotropic configuration. The net effect is that the stress exerted by the molecules on the polymer will decrease along the light's polarization and increase perpendicular to it as they transition to the trans state. Both angular hole burning and reorientation are at play, with angular hole burning dominating at early times and reorientation kicking in at later times. This behavior is commonly observed, with the time constants depending on the light's intensity [27; 53]. Figure 1: The lines in the upper plot represent an isotropic distribution of trans molecules, which are depleted along the pump light’s polarization (vertical) as they are converted to cis molecules. The bottom plots show the corresponding orientational distribution functions.