## 3 Results  
The dominant origin of holographic recording in LS-LCEs is UV illumination-induced _trans_-to-_cis_ isomerization of azomesogenic side groups [5; 28; 29]. The rate of this process is proportional to the intensity of the UV irradiation; therefore, it predominantly takes place in the regions of high intensity, while in the regions of low intensity, it is nearly absent. Consequently, a spatially modulated concentration of the _cis_ isomers \(N_{\mathrm{C}}(\mathbf{r})\) is established. _Cis_ isomers act as impurities in the liquid crystalline phase [18], so they cause a local decrease of the scalar nematic order parameter \(S\) (\(S=<(3\mathrm{cos}^{2}\theta-1)/2>\)), where \(\theta\) is the angle between the long axis of the mesogenic molecules and the direction \(\mathbf{n_{0}}\), and brackets denote averaging), which can be described as:  
\[S(\mathbf{r},T)=S_{0}(T)+\Delta S(N_{\mathrm{C}}(\mathbf{r}),T), \tag{3}\]  
where \(S_{0}\) corresponds to the order parameter in the dark (when all of the azomesogens are in the _trans_ state), \(\Delta S<0\) is the isomerization-induced modification of \(S\), \(N_{\mathrm{C}}(\mathbf{r})\) the concentration of _cis_ azomesogens at a selected position \(\mathbf{r}\), and \(T\) is the temperature. Local modifications of \(S\) result in modifications of optical birefringence of the material \(n_{b}=(n_{e}\)\(-\)\(n_{o})\)\(\propto\)\(S\), where \(e\) and \(o\) denote the extraordinary and the ordinary ray, respectively. Therefore, after illumination with the periodic UV interference pattern, \(n_{o}\) as well as \(n_{e}\) become periodically modulated, i.e., an anisotropic optical grating structure is formed [9]. This structure decays with time due to spontaneous _cis_-to-_trans_ back isomerization of the azomesogens. The decay process is exponential, and the corresponding decay time \(\tau\), as a function of the temperature, exhibits the Arrhenius behavior [30]. For the investigated LCE material, the value of \(\tau\) at room temperature (23 \({}^{\circ}\)C) is around 250 min, while at transition temperature \(T_{0}=\) 81.6 \({}^{\circ}\)C, it decreases to about 5 min. The spontaneous decay of the grating structure is of course not suitable for practical applications, but it is very convenient for research purposes, because the one and same sample can be used to perform different experiments. The decay of recorded patterns can be prevented by using photosensitive mesogens with very long lifetimes of the _cis_ isomer, or by using the light-induced covalent attachment of mesogenic groups to the polymer backbone [31; 32]. In the experiments performed at room temperature, we first recorded the grating, and then analyzed its diffraction properties as a function of strain. The length of the sample was increased or decreased in steps of few micrometers, corresponding to strain in the interval from 0 to a maximum of 15%. The time interval between subsequent measurements was 1 min, which provided enough time for the equilibration of the structure. Figure 2a shows the observed dependence of a relative elongation of the lattice period of a one-dimensional grating (line grating) with \(\Lambda=\) 2.3 \(\upmu\)m as a function of the tensile strain \(\varepsilon_{\parallel}\) applied in the direction parallel to \(\mathbf{n_{0}}\). For modulation along \(\mathbf{n_{0}}\), the value of \(\Delta\Lambda/\Lambda\) increases with increasing strain, while for modulation perpendicular to \(\mathbf{n_{0}}\), it decreases with increasing strain. The decrease observed in the latter case is about two times smaller than the increase observed in the former case, which is in agreement with the volume conservation of the material [1]. The values of \(\Delta\Lambda/\Lambda\) obtained during increasing (solid symbols) and decreasing strain (open symbols) are very similar, i.e., the behavior is reversible.