Spatially-Resolved Atmospheric Turbulence Sensing with Two-Dimensional Orbital Angular Momentum Spectroscopy

Atmospheric turbulence characterization is crucial for technologies like free-space optical communications. Existing methods using a spatially-integrated one-dimensional (1D) orbital angular momentum (OAM) spectrum, P(m), obscure the heterogeneous nature of atmospheric distortions. This study introduces a two-dimensional (2D) OAM spectroscopy, P(m, n), which resolves the OAM spectrum (topological charge m) across discrete radial annuli (index n). Integrating this high-dimensional spectral analysis with a Support Vector Machine (SVM) classifier significantly improves the accuracy of atmospheric turbulence parameter inversion. The full potential of complex probe beams, such as multi-ringed Bessel-Gaussian beams, is realized with this radially-resolved 2D analysis. Through a co-design of the probe beam's spatial structure and the OAM spectral analysis dimensionality, a median classification accuracy of 85.47% was achieved across 20 turbulence conditions, a 23% absolute improvement over 1D techniques. The radial index also mitigates insufficient OAM spectral range, and a targeted feature-selection protocol addresses noise from low signal-to-noise ratio outer radial regions. This framework emphasizes co-design of the optical probe field and its OAM spectral analysis for enhanced fidelity in turbulence characterization.