Photon information efficient communication through atmospheric turbulence

High photon-efficiency (many bits/photon) optical communication is possible with pulse-position modulation and direct detection, and high spectral efficiency (many bits/sec-Hz) optical communication is possible with quadrature-amplitude modulation and coherent detection. These high efficiencies, however, cannot be achieved simultaneously unless multiple spatial modes are employed. Previous work for the vacuum-propagation channel has shown that achieving 10 bits/photon and 5 bits/sec-Hz is impossible with coherent detection, and it requires 189 low diffraction-loss spatial modes at the ultimate Holevo limit, and 4500 such modes at the Shannon limit for on-off keying with direct detection. For terrestrial propagation paths, however, the effects of atmospheric turbulence must be factored into the photon and spectral efficiency assessments. This paper accomplishes that goal by presenting upper and lower bounds on the turbulent channel’s ergodic Holevo capacity for M-mode systems whose transmitters use either focused-beam, Hermite-Gaussian (HG), or Laguerre-Gaussian (LG) modes, and whose receivers do M-mode detection either with or without adaptive optics. The bounds show that use of adaptive optics will not be necessary for achieving high photon efficiency and high spectral efficiency through atmospheric turbulence, although receivers which do not use adaptive optics will need to cope with considerable crosstalk between the spatial patterns produced in their entrance pupils by the M-mode transmitter. The bounds also show the exact theoretical equivalence of the HG and LG mode sets for this application, generalizing a result previously established for the vacuum-propagation channel. Finally, our results show that the FB modes outperform the HG and LG modes in operation with and without adaptive optics.