Fig. 1: Concept of using longitudinally structured optical beams for probing turbulence along a propagation path.

a A general scheme for transmitting forward-propagating optical beams at the transmitter (Tx) to probe turbulence along a path. At the receiver (Rx), beam-turbulence interactions are measured to retrieve turbulence information. b One prior turbulence probing technique transmits two beams from two separate sources, crosses them at different distances, and detects them using a multi-element Rx aperture array. c Our approach designs and sequentially transmits multiple longitudinally structured beams. Our longitudinally structured beams are superpositions of multiple \({{BG}}_{{{{{{\mathscr{l}}}}}}{{{{{\mathscr{=}}}}}}0,{k}_{z}}\) modes with different longitudinal wavenumbers \({k}_{z}\) and an OAM \({{{{{\mathscr{l}}}}}}{{{{{\mathscr{=}}}}}}0\) order. The three numerically generated transverse (y)-longitudinal (z) intensity distributions exemplify three different beams with narrower beam widths only in limited regions of choice. At the Rx, based on measured modal coupling from \({{{{{\mathscr{l}}}}}}{{{{{\mathscr{=}}}}}}0\) to \({{{{{\mathscr{l}}}}}}{{{{{\mathscr{\ne }}}}}}0\) orders, the distributed turbulence strength along the propagation path is extracted.