Objective The solid-state slab laser has become one of the most reliable, promising and potential lasers among current high-power lasers due to its small size, lightweight and high conversion efficiency. It is commonly used in various fields, including scientific research, industry and medical treatment. High output power and good beam quality are two constant goals in the development of high-power solid-state slab lasers. As laser output power increased, the edge effects became more severe and distorted the wavefront of the solid-state slab laser output beam, resulting in a non-linear drop in laser beam quality. Several methods are present to compensate for the distortions, including the use of static compensation components, non-linear optical compensation methods, and adaptive optics. Adaptive optics is a promising method to compensate for wavefront distortion in the laser output beam. The direct slope reconstruction method is commonly used in the research of solid-state slab laser beam clean-up, and the least-squares algorithm is used to solve the system’s optimal solution.

Although adaptive optics can considerably improve the beam quality of laser output beams, some issues still need to be addressed. The least-squares reconstruction method’s criteria are to minimise the sum of slope residual squares. The adaptive optics system’s correction capability is limited by factors such as materials and cost. When the adaptive optics system can completely compensate for wavefront distortion, the least-squares reconstruction method can be used to obtain the system’s optimal solution. However, if a portion of the distortions is beyond the capability of adaptive optics system, the wavefront distortions of the laser beam cannot be fully compensated and a considerable amount of wavefront residual is still present after compensation; the minimum sum of slope residuals squares is not equivalent to the best beam quality at this time. When the solid-state slab laser operates at high gain, the wavefront distortions are very likely to exceed the adaptive optics system’s correction capability. Under these conditions, the least-squares reconstruction method cannot produce the optimal system solution.

Methods To solve the abovementioned problems, the most straightforward and effective method is to increase the number of actuators or even cascade multiple deformable mirrors with compatible wavefront sensors to improve an adaptive optics system’s inherent correction capability. However, as the number of actuators in deformable mirrors increases, their size, weight and cost also increase. Another approach is to optimise the adaptive optics system’s correction method, and a weighted least-squares reconstruction method has been proposed to improve the beam quality by assigning low weights to the uncorrectable wavefront components in the least-squares method. Unfortunately, determining the weights in a practical adaptive optics system is difficult. The edge effect remains a challenge, particularly when the number of actuators is limited because of the beam size or cost.

We proposed a novel adaptive optics correction method to further improve beam quality when wavefront distortions exceed the adaptive optics system’s correction capability. In this method, we used the idea of optimal correction in the wavefront sensor-less adaptive optics system and combined it with the traditional adaptive optics system, with the improvement of beam quality as the optimisation goal, and the optimisation algorithm is used to optimise the calibration position of the wavefront sensor according to wavefront distortions and the correction capability of the deformable mirror, and it then uses the traditional adaptive optics system for aberration compensation.

Results and Discussions We used simulation to validate the proposed method. First, we combined the two-dimensional Legendre polynomials based on the characteristics of the solid-state slab laser’s output wavefront to obtain a wavefront with severe edge distortion, and the corresponding beam quality is β=5.1 (Fig. 6). Then, the optimisation algorithm is used to find the best solution; the best beam quality that can be obtained after correction is β=1.8 (Fig. 7). Finally, the proposed method and the traditional correct method are used to compensate for the distortions (Fig. 8). After correction using the traditional method, the beam quality improves to β=3.7, whereas correction with the proposed method improves the beam quality to β=2.0, which is closer to the optimal solution. Analysing the wavefront slope distribution using a different method reveals that after processing using the proposed method, the effect of uncorrectable large distortions on adaptive optics systems is reduced (Fig. 9).

Conclusions When the correction capability of the deformable mirror is limited, the correction results obtained using different methods show that, when compared with the traditional adaptive optics system without calibration optimization the method proposed in this paper can effectively improve the correction effect of the adaptive optics system.