## 4 Discussion
Also in this case, the vertical difference between the two (dashed) curves \(\Delta n_{e}(T,\varepsilon_{\parallel})=n_{e}(T,T_{0},\varepsilon_{ \parallel})\,-\,n_{e}(T,T_{0}\,^{\prime},\varepsilon_{\parallel})\) gives the refractive index modulation between the dark and the UV-illuminated regions of the strained sample. By comparing the vertical separation between the two solid and the two dashed lines, one can notice that at room temperature (23 \({}^{\circ}\)C), the modulation of \(n_{e}\) in the strained material is smaller than in the unstrained material, which is in agreement with the experimentally observed decrease of the diffraction efficiency shown in Figure 3. In contrast, at \(T=75\)\({}^{\circ}\)C, the modulation of \(n_{e}\) in the strained material is larger than in the unstrained material, which is in agreement with the results shown in Figure 6b. Therefore, the above described model can well explain the effect of \(\varepsilon_{\parallel}\) on the diffraction efficiency of the grating structures in LS-LCEs. Straining in the direction perpendicular to \(\mathbf{n_{0}}\) in its initial stage (before reaching the plateau region in the \(\sigma(\varepsilon_{\perp})\) curve) causes a decrease of the internal strain, and consequently also a decrease of the order parameter \(S\)[39]. This corresponds to the increase of the critical exponent \(\zeta\)= \(1/(\gamma-1)\) and the decrease of the parameter \(A\) in Equation (4). To illustrate the associated effects, the dependences of \(n_{e}(T,T_{0},\varepsilon_{\perp})\) and \(n_{e}(T,T_{0}\,^{\prime},\varepsilon_{\perp})\) corresponding to \(\gamma^{\prime}=\gamma/2=2.4\) and \(A^{\prime}=A/10=0.008\) for the unilluminated and for the UV-illuminated strained material are shown as dashed lines in Figure 8b. The vertical difference between the two (dashed) curves \(\Delta n_{e}(T,\varepsilon_{\perp})=n_{e}(T,T_{0},\varepsilon_{\perp})\,-\,n_ {e}(T,T_{0}\,^{\prime},\varepsilon_{\perp})\) is again expected to describe the refractive index modulation between the dark and the UV-illuminated regions of the strained sample. Consequently, it follows that at room temperature, the refractive index modulation and consequently also the diffraction efficiency in the strained sample should be larger than in the unstrained sample, while at \(T=75\)\({}^{\circ}\)C, it should be vice versa. However, the experimental results on the influence of \(\varepsilon_{\perp}\) (and of the corresponding stress \(\sigma_{\perp}\)) on the diffraction efficiency of the grating structures are quite different from the predictions described above. We attribute this discrepancy to the formation of shear-stripe domains [34; 41; 42], which is not at all included in the presented model. The domain structure causes an additional refractive index modulation that competes with the modulation induced by the holographic patterning. The shear-stripe domains are always oriented along the straining direction. The experimental results  
Figure 8: Calculated temperature dependences of extraordinary refractive index \(n_{e}\) of the LCE material based on Equation (4). (**a**) Unstrained and unilluminated (black solid line), unstrained and UV-illuminated (orange solid line), strained along \(\mathbf{n_{0}}\) and unilluminated (black dashed line), and strained along \(\mathbf{n_{0}}\) and UV-illuminated (dashed orange line); (**b**) Unstrained and unilluminated (black solid line), unstrained and UV-illuminated (green solid line), strained perpendicular to \(\mathbf{n_{0}}\) and unilluminated (black dashed line), and strained perpendicular to \(\mathbf{n_{0}}\) and UV-illuminated (dashed green line). Grey vertical lines denote the temperatures at which the experiments were performed. shown in Figure 5 suggest that when those domains are oriented perpendicular to the line patterning from the holographic structure, they cause a reduction of the diffraction efficiency from the holographic pattern.