  A central question in free-space optical communications is how to improve the
transfer of information between a transmitter and receiver. The capacity of the
communication channel can be increased by multiplexing of independent modes
using either: (1) the MIMO (Multiple-Input-Multiple- Output) approach, where
the communication is done with modes obtained from the singular value
decomposition of the transfer matrix from the transmitter array to the receiver
array, or (2) the OAM (Orbital Angular Momentum) approach, which uses vortex
beams that carry angular momenta. In both cases, the number of usable modes is
limited by the finite aperture of the transmitter and receiver, and the effect
of the turbulent atmosphere. The goal of this paper is twofold: First, we show
that the MIMO and OAM multiplexing schemes are closely related. Specifically,
in the case of circular apertures, the usable singular modes of the transfer
matrix are essentially the same as the commonly used Laguerre-Gauss vortex
beams, provided these have a special radius that depends on the wavelength, the
distance from the transmitter to the receiver and the ratio of the radii of
their apertures. Second, we study the effect of atmospheric turbulence on the
communication modes using the phase screen method put in the mathematical
framework of beam propagation in random media.
