Divergence-degenerated spatial multiplexing towards ultrahigh capacity, low bit-error-rate optical communications.

Spatial mode (de)multiplexing of orbital angular momentum (OAM) beams is a promising solution to address future bandwidth issues, but the rapidly increasing divergence with the mode order severely limits the practically addressable number of OAM modes. Here we present a set of multi-vortex geometric beams (MVGBs) as high-dimensional information carriers, by virtue of three independent degrees of freedom (DoFs) including central OAM, sub-beam OAM, and coherent-state phase. The novel modal basis set has high divergence degeneracy, and highly consistent propagation behaviors among all spatial modes, capable of increasing the addressable spatial channels by two orders of magnitude than OAM basis as predicted. We experimentally realize the tri-DoF MVGB mode (de)multiplexing and shift keying encoding/decoding by the conjugated modulation method, demonstrating ultra-low bit error rates (BERs) caused by center offset and coherent background noise. Our work provides a useful basis for next generation of large-scale dense data communication.