Deep Learning Driven Enhancement of Optical Vortex Line Robustness in Atmospheric Turbulence

The stability of optical vortex structures in turbulent environments is critical for their applications in optical communication, quantum information, and structured light technologies. Although topological invariants, such as crossings and linking numbers, are fundamentally invariant, recent studies reveal that their observed values deteriorate considerably in turbulent conditions due to environmental effects. In this study, we introduce an alternative approach based on the geometric stability of three-dimensional singularity line shapes, demonstrating that shape-based tracing of singularities outperforms both topological and spectral methods in turbulence. To test this concept, we propose Flower Beams, a novel class of structured optical fields featuring controllable petal-like singularity morphologies. We construct an 81-element optical alphabet and classify these structures after turbulence using deep learning. Our findings reveal that shape-based tracing achieves classification accuracy exceeding 90% in the weaker turbulence regimes and remains highly competitive even in stronger turbulence, significantly outperforming spectral and topology-based approaches. Experimental results confirm that the predicted shape stability holds in real-world conditions. This study stablishes the shape of the singularities' lines as a scalable and resilient alternative for structured light tracing and transmission, opening new avenues for turbulence-robust-applications.