Radial spectrum spread of Laguerre-Gaussian beam transmission in weak compressible turbulence

Turbulence effects can seriously affect the propagation of structured light, especially for orbital angular momentum (OAM) modes, causing spread and crosstalk. We derive an analytical solution to the mode spectrum of a Laguerre-Gaussian beam (LGB) propagating in weak compressible turbulence. The influence of the radial number and turbulence strength in the mode spectrum on the probability of LGB propagation is mainly considered. The results show that the weak compressible turbulence interferes strongly with the LGB, and this effect is mainly reflected in the sharp drop of the signal mode energy at short transmission distance. We find that the pure radial mode has a higher signal mode energy than the pure OAM mode, which means that the pure radial mode is more resilient to compressible turbulence than the pure OAM mode. In addition, the increase of radial number can improve the performance of the OAM dimension, but on the other hand, it reduces the probability of the radial dimension. Finally, we discussed the propagation properties of higher-order modes. Our research clarifies the interaction of OAM mode and radial mode in turbulence, and provides a theoretical basis for applications based on radial modes in the field of free-space communication.