Optimal transmission modes under atmosphere turbulence with transmitter/receiver aperture size constraint.

In this paper, an optimal mode set is proposed to maximize the receiving power for free space transmission under atmosphere turbulence with transmitter/receiver aperture size constraint. The optimal beam profiles are evaluated through eigenmode analysis of the Fredholm integral equation, which is mathematically equivalent to the eigen vector analysis of an infinitely large matrix. The matrix is formed by orthonormal basis expansion, and its element is the overlap integral of the orthonormal basis functions and the Fredholm kernel. If circular aperture is implemented, then it is rigorously proven in this work that the eigenmodes possess certain topological charges (i.e., they are the OAM modes). These OAM modes have specific radial beam profiles, which have been optimized to minimize the power loss and the inter-mode crosstalk. While the traditional OAM beams, such as the Laguerre-Gauss (LG) beams, suffer significant energy loss and inter-radial-mode crosstalk, the optimized beam profiles will remarkably reduce the penalties.