A modeling framework for OAM integrity of super Lorentz–Gauss beams in turbulent free-space optical communications

This paper presents a rigorous semi-analytical model for characterizing the propagation behavior and quantifying the orbital angular momentum (OAM) integrity of super Lorentz–Gaussian vortex beams (SLGVBs) through atmospheric turbulence. By projecting the received field over the full two-point spatial mutual coherence function via the extended Huygens–Fresnel integral and employing a Hermite–Gaussian expansion of the SLGVB’s non-Gaussian amplitude profile, we derive a closed-form expression for the average received OAM mode power spectrum. This framework allows for the systematic analysis of how the SLGVB’s unique structural parameters—the topological charge ( l ), amplitude orders ( a , b ), and the Lorentz–Gaussian mixing ratio ( \(wₗₛ/wgs\) )—influence link viability. Our findings reveal that structural complexity imposes a significant penalty: the OAM mode purity is inversely proportional to both the topological charge and the amplitude complexity, with high-order configurations collapsing rapidly under turbulent conditions. To bridge the spatial statistics to the temporal domain, we utilize Taylor’s frozen turbulence hypothesis to derive a closed-form analytical expression for the time-averaged OAM purity as a function of the receiver integration window. Furthermore, we evaluate communication performance using a physically grounded on-off keying bit error rate model under spatial crosstalk and receiver noise. The entire theoretical framework is independently validated against classical analytical limits and numerical split-step Fourier wave-optics simulations, showing close quantitative agreement with a root-mean-square error of less than \(2.4%\) in the weak-to-moderate regime. This verified framework provides essential tools for designing and optimizing structured light sources in high-capacity free-space optical communication systems.