Atmospheric turbulence strength distribution along a propagation path probed by longitudinally structured optical beams

mospheric turbulence can cause critical problems in many applications. To effectively avoid or mitigate turbulence, knowledge of turbulence strength at various distances could be of immense value. Due to light-matter interaction, optical beams can probe longitudinal turbulence changes. Unfortunately, previous approaches tended to be limited to relatively short distances or large transceivers. Here, we explore turbulence probing utilizing multiple sequentially transmitted longitudinally structured beams. Each beam is composed of Bessel-Gaussian ( BG_𝓁=0,k_z ) modes with different k_z values such that a distance-varying beam width is produced, which results in a distance- and turbulence-dependent modal coupling to 𝓁0 orders. Our simulation shows that this approach has relatively uniform and low errors (<0.3 dB) over a 10-km path with up to 30-dB turbulence-structure-constant variation. We experimentally demonstrate this approach for two emulated turbulence regions ( 15-dB variation) with <0.8-dB errors. Compared to previous techniques, our approach can potentially probe longer distances or require smaller transceivers.