Propagation-induced reshaping of the energy-information tradeoff in turbulent optical channels

Atmospheric turbulence reshapes the energy-information relation in simultaneous lightwave information and power transfer (SLIPT) through irradiance fluctuations. We derive a second-order approximation that isolates a variance penalty and use it as the prior for a differentiable residual surrogate. Under log-normal fading, the surrogate is trained with Gauss-Hermite references and independently tested by Monte Carlo simulation on disjoint grids. Under held-out extrapolation conditions, it improves rate and gradient accuracy over the second-order approximation and a task-equivalent data-only multilayer perceptron (MLP). Retraining under plane-wave Gamma-Gamma fading yields normalized root-mean-square errors (NRMSEs) below 0.14% for rate and 1.11% for gradient. The framework provides a compact, physically interpretable approximation for propagation-aware SLIPT analysis.