## 1 Introduction  
Light-sensitive liquid crystalline elastomers (LS-LCEs) are soft materials that combine an orientational order of liquid crystals and the rubber elasticity of elastomers with the photoresponsivity of photoisomerizable compounds [1; 2; 3]. As optical holographic materials, they show many intriguing properties. For instance, they exhibit recording sensitivity that is several orders of magnitude larger than conventional (non-liquid crystalline) elastomers containing similar photoisomerizable moieties [4; 5; 6; 7; 8; 9]. The recording process takes place in a very nonlinear manner that allows an intricate control over the spatial structuring of the refractive index modulation. The associated diffraction effects are particularly interesting in the temperature region close to the nematic-paranematic phase transition, in which phenomena such as the recording of \"hidden holograms\" and \"hologram dark enhancement effect\" can be observed [10]. Light-sensitive LCEs are also very efficient for recording polarization gratings generated by the superposition of orthogonally polarized writing beams. In the vicinity of the Bragg angle, those gratings exhibit an unusual splitting of the diffraction peak, which is a consequence of the strong absorption anisotropy for the actinic optical radiation [11]. All of the above-mentioned properties are predominantly associated with the liquid crystalline character of the LCEs. However, their elastomeric character can also yield several interesting features. The most evident one is the possibility of regulating the spatial periodicity of optical patterns by mechanical straining, which was demonstrated in our recent study, and which makes LCE films very promising for applications in mechanically tunable diffractive optical elements, such as adjustable optical filters or stretchable diffractive lenses [12]. However, in designing practical devices, it is very important to know not only how mechanical manipulation affects the diffracted patterns, but also how it affects the efficiency of the related diffractive phenomena. Consequently, in this work, the emphasis is on the effects of stress and strain on the diffraction efficiency of some selected holographic grating structures. The stress-strain relationship \(\sigma(\varepsilon)\) of an orientationally aligned (monodomain) LCE film strongly depends on the straining direction. For straining along the preferential orientation of the liquid crystalline (mesogenic) molecular units, known as the nematic director \(\mathbf{n_{0}}\), stress increases proportionally to strain, similar to conventional elastomers. For straining in the direction perpendicular to \(\mathbf{n_{0}}\), a nonlinear behavior known as (semi)soft elasticity is observed, which is characterized by a plateau region in which stress remains nearly constant during the increasing strain [1; 13]. This phenomenon is associated with a continuous reorientation of the mesogenic molecular units in the embedding polymer network. The exact dependence of \(\sigma(\varepsilon)\) is affected also by the sample preparation procedure and by the temperature. For LCE materials with a smooth (continuous) phase transition from the nematic to the isotropic phase (also called paranematic phase) [14; 15], as the one used in our study, the behavior of \(\sigma(\varepsilon)\) is also smooth at all temperatures. The anisotropy of the stress-strain relationship decreases with the increasing temperature, and more or less vanishes at the transition temperature \(T_{0}\)[16; 17]. In LS-LCEs, illumination with ultraviolet (UV) light affects the stress-strain relationship in a similar manner as heating, i.e., it causes a decrease of the liquid crystalline order that is governed by the illumination intensity [2; 18; 19; 20].