Since the advent of optical waveguide technology, it has been widely applied in frontier fields such as optical communication, biomedicine, flexible electronics, and AR displays. The advancements in micro-nano optics and the exploration of new materials have promoted the diverse development of high-performance optical waveguides, which have the characteristics of miniaturization, low loss, flexibility, and biocompatibility. We follow the latest academic research progress, highlighting the innovative achievements of fiber optical waveguides, with a focus on bio-based fibers and other emerging optical waveguide functional fiber materials, such as aggregation-induced emission (AIE). The basic properties of these fiber materials are introduced, and their optical properties are discussed. The applications and potential of optical waveguides made from these functional materials in fields such as fiber optic sensing, biomedical monitoring and clinical treatment, and photonic devices are also presented. Finally, the current issues and future development of these fiber optical waveguides are briefly summarized.

Non-Abelian band topology is a recently proposed topological theory used to describe the topological properties of multi-band systems with space-time inversion symmetry. By drawing an analogy to defects in liquid crystal molecules, it is discovered that the non-Abelian topological charge in multi-band systems can be described using quaternions and generalized quaternions. Since this topological description involves multiple band gaps, the corresponding edge state distribution becomes more complex. Currently, non-Abelian band topology theory is primarily used to explain and describe the violation of the Nielsen?Ninomiya theorem, allowed nodal line configurations, braiding of nodal lines, and path-dependent nodal point collisions. In addition, the Euler number used to characterize the topological properties of triple degenerate points is also related to the non-Abelian topological charge and has been widely applied in the study of nodal lines. In this paper, we begin with the fundamental theory of non-Abelian band topology, systematically review the unique physical phenomena predicted by this theory in photonic and other systems, introduce the latest experimental observations, and further explore the future development prospects of this field.