Topological Evolution and Nonconservation of Fractional Vector Optical Fields in Linear and Nonlinear Regimes

The topological properties of vector optical fields are traditionally considered strictly conserved during continuous deformations and linear propagation. However, while structured light has been extended into nonlinear regimes, previous studies have predominantly focused on the intensity modulation of specific orbital angular momentum (OAM) components and the pure frequency conversion of structured light. The critical question of whether macroscopic topological invariants remain robust or experience fundamental breakdown during nonlinear light–matter interactions remains largely unexplored. To address this specific gap, we propose and generate multiple fractional vector optical fields (MF-VOFs), establishing their dynamic topological evolution and inherent conservation laws in free space. It should be noted that our experimental results are limited to free-space propagation. Strikingly, we report a significant departure from this paradigm during light–matter interactions: topological nonconservation anomalies manifest when these optical fields interact with nonlinear materials via second- and third-harmonic generation. Through a comprehensive quantitative analysis of the OAM spectrum, we confirm that the asymmetrical reconstruction and spatial transition of the total OAM along the propagation direction serve as the physical origins driving this topological symmetry breaking. These findings provide a fundamentally novel perspective on topological manipulation in nonlinear optical processes, offering advanced strategies for complex structured light generation and high-dimensional optical information processing.