## 3 Results and Discussion
### The Grating Slant \(\Phi\)
#### 3.2.1 Impact of the Recording Intensity: \(\Phi(I)\)  
Once again, the behaviour \(\Phi(I)\) strongly depends on the duration of the exposure. The three emerging cases are shown in Figure 3. The respective schemes to the right illustrate corresponding consequences with regard to the lattice plane orientation.  
In the evaluation of these results, it must be considered that the lateral scans are performed horizontally from the left to the right side of the grating (from the top-view perspective, _i.e._, polymer on top of the substrate). As a consequence, a positive slant \(\Phi>0\) corresponds to a tilt of the lattice planes to the left (again from top view perspective), while a negative value \(\Phi<0\) means a slant to the right.  
In the case of short exposure, it was found that \(\Phi\) is positive on the left side of the grating and negative on the right side. As a consequence, the grating period decreases from the surface towards the substrate (see lowermost right-hand scheme in Figure 3). In the case of long exposure duration, the situation is _vice versa_, _i.e._, \(\Phi<0\) on the left side and \(\Phi>0\) on the right side. In addition, an intermediate case is observed in between (see middle row in Figure 3).  
Figure 3: Lateral progressions of the grating slant \(\Phi(I)\), derived from lateral scans from the left to the right (**left side**), numbers indicate the individual, sequentially performed rotation scans; plus corresponding schemes with respect to the orientation of the lattice planes (**right side**). In the case of short exposure duration (lowermost, blue curve) the slant angle changes from positive to negative values, with the result of decreasing grating pitch towards the substrate. Conversely, in the case of long exposure duration (uppermost, orange curve) the slant angle changes from minus to plus, with the result of increasing grating pitch towards the substrate. In between an intermediate behavior arises (central, green curve).  
Interpretation of the findings with respect to the grating slant appears more complicated than in case of the grating constant. This is due to the fact that the information, provided with regard to \(\Lambda\), is assigned to the lateral plane, while in the case of \(\Phi\) the depth of the layer is involved. Accordingly, local variations of optical shrinkage in the lateral plane can be assigned to recording-intensity-distribution-related effects, whereas several potential causes must be considered for the explanation of modifications trough the depth of the layer. On the one hand, adhesion between polymer layer and glass substrate appears reasonable in view of specific epoxy characteristics [30]. On the other hand, the thick, uncovered surface of the polymer layer may tend to the formation of a superficial film. Additionally, non-uniform chemical composition may be obtained as a consequence of sample dark storage. Finally, a possible decrease of the recording intensity might result from absorption of the recording beams.  
Depending on the respective interpretation, the results suggest more expansion at the substrate or rather more shrinkage at the surface in case of long exposure (uppermost case in Figure 3), while in the case of short exposure, the situation is _vice versa_ (lowermost case in Figure 3). In the intersection, forces cancel each other out (central case in Figure 3). This is also illustrated in view of the strength of the tilting effects, _i.e._, the value of \(\Delta\Phi\) in Figure 3.  
In view of results presented in Section 3.1.2 as well as in [13, 28], namely the decrease of optical shrinkage or rather the refractive index increase, observed with increasing exposure duration, interpretation of the results in terms of a superficial film formation is suggested. However, starting from the assumption of recording beam absorption would be preferable as well, inasmuch as it is in compliance with results from Section 3.1.1, where a decrease of \(\Lambda\)(\(I\)) was found.