## 4 Discussion  
In the following, we present a qualitative explanation of the effects of \(\varepsilon_{\parallel}\) and \(\varepsilon_{\perp}\) on refractive index modulation in a monodomain nematic LCE film. As shown in our recent paper [10], the temperature dependence of the order parameter \(S(T)\) and consequently also of the extraordinary refractive index \(n_{e}(T,T_{0})\) of such a film can be described by the heuristic function that is in agreement with the [PERSON] theory of supercritical phase transitions [9; 36]:  
\[n_{e}(T)=\left[\overline{\varepsilon}_{0}+\frac{2}{3}\beta S(T)\right]^{1/2}= \left[\overline{\varepsilon}_{0}+A\big{\{}\big{[}\big{(}1+B|T-T_{0}|^{\gamma} \big{)}/B\big{]}^{1/\gamma}-(T-T_{0})\big{\}}^{1/(\gamma-1)}\right]^{1/2} \tag{4}\]  
where \(\overline{\varepsilon}_{0}\) is dielectric permittivity in the paranematic phase (\(T>>T_{0}\)), and \(\beta\) is determined by the molecular anisotropy. The values of material parameters \(\gamma\) and \(B\) for the investigated material were obtained from the experimental data on the spontaneous elongation of the sample during cooling from the paranematic to the nematic phase, and are \(\gamma\) = 4.8 and \(B\) = 29 [10]. The values of the parameters \(A\) and \(\overline{\varepsilon}_{0}\) can be deduced from the values of refractive indices of the material at room temperature and at \(T>>T_{0}\). For side-chain LCE materials of the type as the one used in our study, those values are \(n_{e}(T>>T_{0})\)\(\sim\)\(n_{o}(T>>T_{0})\) = 1.58, \(n_{e}(T_{0}-50\ ^{\circ}\mathrm{C})\) = 1.66, and \(n_{o}(T_{0}-50\ ^{\circ}\mathrm{C})\) = 1.54 [37; 38], which gives \(\overline{\varepsilon}_{0}\) = 2.5 and \(A\) = 0.077. The resulting dependence of \(n_{e}(T,T_{0})\) is shown as the black solid line in Figure 8a. The effect of UV illumination-induced _trans_-to-_cis_ isomerization on \(n_{e}(T)\) can be modeled as a decrease of the transition temperature \(T_{0}\)\({}^{\prime}\) = \(T_{0}-C_{c}N_{c}\), where \(C_{c}\) is a proportionality constant [18]. The corresponding dependence of \(n_{e}(T,T_{0})\) for \(T_{0}\)\({}^{\prime}\) = \(T_{0}-10\ ^{\circ}\mathrm{C}\), which is typically realized in the experiments, is shown as the orange solid line in Figure 8a. The vertical difference between the two curves, namely \(\Delta n_{e}(T)\) = \(n_{e}(T,T_{0})-n_{e}(T,T_{0})\), corresponds to the refractive index modulation between the dark and the UV-illuminated regions of the unstrained sample. The effect of \(\varepsilon_{\parallel}\) (and of the corresponding stress \(\sigma_{\parallel}\)), which adds up to the intrinsic strain imposed during the fabrication process, can be modeled as a decrease of the critical exponent \(\zeta\) = 1/(\(\gamma-1\)). In addition to this, the value of \(A\) needs to be modified due to the strain-induced increase of the order parameter that can be described as \(\Delta S=C_{c}\varepsilon_{\parallel}\), where \(C_{c}\) is the proportionality constant dependent on the properties of the polymer network [39]. This effect in general results in the increase of \(n_{e}\) with  
Figure 7: **(a)** Time dependences of \(I_{\mathrm{d}}\) and \(\Delta F/F_{0}\) measured during recording and relaxation processes for a recording time of 3 min. The sample was clamped in the direction perpendicular to \(\mathbf{n_{0}}\). The drawing illustrates the orientation of the sample with respect to the grating lines. The inset gives the value of the prestraining force \(F_{0}\). **(b)** Time dependences of \(I_{\mathrm{d}}\) and \(\Delta F/F_{0}\) during the recording and relaxation processes for 15 min of recording. increasing \(\varepsilon_{\parallel}\)[40]. To illustrate the resulting behavior, the dependences of \(n_{e}(T,T_{0},\varepsilon_{\parallel})\) and \(n_{e}(T,T_{0}\,^{\prime},\varepsilon_{\parallel})\) corresponding to \(\gamma^{\prime}=2\gamma=9.6\) and \(A^{\prime}=3A=0.23\) for the unilluminated and for the UV-illuminated strained material are shown as dashed lines in Figure 8a.