# Wide-Aperture Bimorph Deformable Mirror for Beam Focusing in 4.2 PW Ti:Sa Laser
## 2 Materials and Methods (Design of a 320 mm Bimorph Deformable Mirror)  
Experiments in high-power laser systems have shown that the real WF aberrations are so-called large-scale [11, 12], and, therefore, WF correctors, including the deformable mirrors, should be effective in compensating for such aberrations. In some contemporary wide-aperture lasers, adaptive optical systems include DMs based on piezoelectric actuators and mechanical step motors [13, 14, 15]. Since such mirrors have local response functions, surface deformation occurs locally, just in the area of each actuator, and thus a large number of actuators is required to compensate for large-scale aberrations. This, naturally, affects the complexity of the wavefront correctors, as well as the quality and reliability of the entire adaptive system. Moreover, the pattern of the actuators might print through the mirror substrate (so-called \"print-through\" effect) [13], which leads to the appearance of undesirable small-scale aberrations (almost like grating), diffraction scattering and additional maxima of intensity in the focal plane. In the future, ultra-high-power lasers should provide multipetawatt pulses with a repetition rate of 10 Hz (ELI HALPS project) [14] or even 100 Hz (GEKKO-EXA project) [15] to initiate laser confinement fusion. It should be noted that mechanical DMs are very slow (the time of one control cycle is more than 0.1 s), which does not allow using them to dynamically correct for the aberrations of each pulse with such a repetition rate. Bimorph deformable mirrors differ from the other types of mirrors due to their possibility of precise correction for the large-scale aberrations using the rather small number of control electrodes [16]. Bimorph DMs of medium size (100-170 mm in diameter) installed in titanium-sapphire lasers with a peak power of 100-200 TW have already made it possible to achieve the intensities of \(10^{19}\)-\(10^{20}\) W/cm\({}^{2}\)[17, 18, 19], which confirms the efficiency of this type of mirrors. This paper presents a wide-aperture bimorph deformable mirror for WF correction and improving the focusing quality of the petawatt power level laser beam. Since the size of DM in petawatt lasers must be large, the amplitude of the surface aberrations increases rapidly. Therefore, the DM design should include the possibility of preliminary adjustment of the surface shape. A traditional bimorph DM consists of a firmly glued-together passive reflecting substrate and a thin piezoceramic plate with a grid of control electrodes [16, 20, 21]. The one-piece piezoceramic plate can be used for small-to-medium sized correctors. However, the mosaic of individual piezoplates should be arranged to cover the entire area of the substrate when constructing a large bimorph mirror (over 240 mm), as it is not possible to have a thin piezo ceramic disk with a diameter more than 240 mm. The disadvantage of such a mosaic configuration might be the fact that the mirror areas within each plate acts as an independent corrector. As a result, the mechanical stresses arise at the boundaries between the piezoelectric elements, and thus the \"print through\" is visualized on the mirror surface. However, the specific shape and the arrangement of the piezoceramic elements can significantly reduce the influence of this effect [22]. For wide-aperture DMs (300 mm and more), when the ratio of the substrate thickness to its diameter is about 1/50, the impact of the mirror's own aberrations increases. In addition, when the thin substrate is fixed in the housing, the additional surface distortion appears in the area of the contact between the substrate and the mount parts (mirror housing). The value of the surface curvature also depends on the gravity and the changes in ambient temperature.