A state-of-the-art review on computational techniques in laser beam shaping across additive manufacturing

Laser beam shaping technology has become a revolutionary means to improve the quality, stability, and efficiency of many laser manufacturing processes, including laser welding (LW), laser powder bed fusion (LPBF), directed energy deposition (DED), and ultrafast laser processing. Although there have been remarkable experimental developments, the application of computational methods such as finite element analysis (FEA), molecular dynamics (MD) simulations, phase-field modeling, and machine learning (ML) to predict and optimize beam shaping procedures, as well as even to guide procedures, has been little reported in the literature. This review provides a comprehensive, systematic examination of computational methods used in laser beam-shaping research. The paper provides a theoretical background by reviewing the state-of-the-art beam-shaping technologies: static beam shaper technologies (diffractive optical elements (DOEs), aspheric lens groups and microlens arrays), dynamic beam shaper technologies (spatial light modulators (SLMs), deformable mirrors (DMs), acousto-optic deflectors (AODs), multi-plane light conversion (MPLC)), coherent beam combining (CBC) and dynamic beam laser (DBL). In the following sections, we discuss the current status of computational simulations for shaped-beam processing, classify simulation methodologies by manufacturing domain, and analyze the potential of artificial intelligence (AI) for beam-shaping optimization. The review also identifies opportunities, limitations, and challenges, and highlights promising research areas where computational modeling and beam-shaping technology converge. This review aims to structure this interdisciplinary research field and offer researchers and practitioners a framework for adopting computational tools to continue pursuing beam-shaping-enabled manufacturing processes. The review summarizes the field's evolution from descriptive modeling to inverse modeling of optimal beam shapes; the evolution of predictive capability from atomistic to part scale using multi-fidelity frameworks; and the emergence of new capabilities through the use of AI, including real-time closed-loop beam control, and identifies physics-informed neural networks (PINNs), digital-twin integration, and multi-objective inverse design as key areas for future development.