Non-Abelian gauge field in optics

Non-Abelian optics has emerged as a promising research field with the potential to revolutionize our understanding of light–matter interactions and enable new applications in areas including topological photonic devices, quantum computing, optical sensing, and communications. This review provides an overall framework for the rapidly developing field of non-Abelian properties in optics, including the basic concepts of non-Abelian optics, the physical mechanism of non-Abelian statistics, the non-Abelian gauge field in optics, non-Abelian braiding in optics as a special phenomenon of the non-Abelian gauge field, and current challenges and opportunities. This review is intended to provide a new perspective on non-Abelian optics, summarize the current status and advanced progress in non-Abelian gauge fields and braiding in optics, and stimulate dialog about future perspectives.