In a fiber array spectral beam combining (SBC) system, imperfections such as installation deviation of the fiber array, linewidth broadening, and thermal effects of the optical elements and internal optical channel coexist and interact with each other, leading to degradation of the combined beam quality. Specifically, the displacement deviation, rotation angle, linewidth broadening, and divergence angle of the fiber laser emitters independently affect the combined beam, leading to non-common-path phase perturbations in each sub-beam. In addition, thermal effects of the diffraction grating and internal optical path introduce aberrations, collectively referred to as common-path thermal aberrations. As the non-common-path phase perturbations and common-path thermal aberrations increase, the degradation of the combined beam quality inevitably becomes more severe. To date, an in-depth analysis of the comprehensive degradation effects and correction characteristics of the combined beam quality has been insufficient. Therefore, studying the integrated degradation and correction characteristics of the combined beam quality under these imperfections, particularly with adaptive optics (AO), is crucial for the effective management and control of beam quality in SBC systems.

This study presents a theoretical and numerical analysis aimed at improving the beam quality of spectrally combined fiber lasers using adaptive optics. First, a physical model is established for the fiber SBC system for the imperfect factors. It consists of four components: an AO-based SBC system, an optical transmission model, a physical model for the thermal deformation of the multilayer dielectric grating (MDG), and a multifield coupling interaction model that describes the light-fluid-solid interactions (LFS-MFCI) within the internal optical path. The AO-based SBC system is primarily composed of three elements: the SBC, expanding laser beam, and AO systems. Ray tracing and diffraction integral methods are employed to develop and solve the optical transmission model for the SBC system. Additionally, finite element models are constructed for the MDG and LFS-MFCI. This enables us to simulate and analyze the temperature distribution and thermal deformation in the MDG and the internal optical path after 60 s of irradiation at an initial temperature of 20 ℃ and a power density of 1000 kW/cm2. Subsequently, the degradation mechanisms and characteristics of the combined beam quality are investigated by categorizing the aberrations within the SBC system into two types: noncommon-path phase perturbations and common-path thermal aberrations. Finally, we discuss strategies for enhancing the spectrally combined beam quality using adaptive optics and simulations.

In the presence of imperfections such as displacement deviation, rotation angle, linewidth broadening, and divergence angle, the intensity distribution of the combined beam irradiating the multilayer dielectric grating displays a Gaussian-like profile that varies with the effect degree of these imperfections. Assuming an initial temperature of 20 ℃ and a power density of 1000 kW/cm2 for the incident laser, both the temperature and thermal deformation gradually decrease from the center toward the edge of the MDG after 60 s irradiation, approximating a Gaussian-like distribution. Moreover, the maximum temperature and thermal deformation of the MDG demonstrate a nearly linear increase with increasing incident laser power density (Fig. 5). In the axial cross section of the optical transmission, the temperature distribution and heat source distribution of the flow field within the internal optical path align with the Gaussian-like distribution of the laser irradiation. The peak values of the temperature and heat source are situated at the center of the optical path and reflector, respectively (Fig.7). The accumulated optical path difference induced by thermal effects in the gas is the primary contributor to the optical path differences, which significantly exceeds the thermal deformation on the surface of the reflector (Fig.8). Under the influence of non-common path phase perturbations and common path thermal aberrations, the far-field β factor of the combined beam increases, indicating deteriorating beam quality. After correction with the AO system, the far-field β factor decreases and approaches 1, demonstrating a significant improvement in the quality of the combined beam (Fig.10). Under the specific boundary conditions considered, the rotation angle of the fiber array is identified as the primary factor affecting output beam quality. When the variance of the rotation angle exceeds 1.5 mrad, the corrected far-field β factor remains higher than 1.5, indicating that the beam quality is still inadequate. Additionally, the degradation of the beam quality caused by the common-path thermal effects and optical path is comparatively less severe than that caused by non-common-path phase perturbations. The thermal effects are nearly uniform across each subbeam in the SBC system, making the correction through AO more manageable. The AO system exhibits superior correction capabilities for low-order common path aberrations resulting from thermal effects as opposed to high-order aberrations, thereby significantly enhancing the combined beam quality of the SBC system (Fig.12).

This study investigates the degradation and correction characteristics of the fiber array SBC system based on the established physical model of the fiber array with imperfect factors. The results indicate that both non-common-path phase perturbations and common-path thermal aberrations degrade the combined beam quality, which can be corrected by the AO system. Notably, AO demonstrates better correction capabilities for common-path thermal aberrations than for non-common-path phase perturbations. However, the combined beam quality after correction with the AO is still not sufficient for practical applications, particularly when the degradation of the combined beam quality is severe because of aberrations in the SBC system. Therefore, the control and management of the fiber array and other optical elements are crucial for reducing noncommon-path phase perturbations and alleviating the effects of common-path thermal aberrations within the SBC system.