Photon Budget Estimation for Long-Range Underwater Free-Space Optical Communications Through Realistic Levels of Oceanic Absorption and Scattering

Optical communications (OC) through water bodies is an attractive technology for a variety of applications. Thanks to current single-photon detection capabilities, OC receiver systems can reliably decode very weak transmitted signals. This is the regime where pulse position modulation is an ideal scheme. However, there has to be at least one photon that goes through the pupil of the fore optics and lands in the assigned time-bin. We estimate the detectable photon budget as function of range for propagation through ocean water, both open and coastal. We make realistic assumptions about the water's inherent optical properties, specifically, absorption and scattering coefficients, as well as the strong directionality of the scattering phase function for typical hydrosol populations. We adopt a path-integral small-angle solution of the radiative transfer equation for multiple forward-peaked scattering across intermediate to large optical distances. Integrals are performed both along the directly-transmitted beam (whether or not it is still populated) and radially away from it. We use this modeling framework to estimate transmission of a 1-Joule pulse of 532 nm light through open ocean and coastal waters. Thresholds for single-photon detection per time bin are a few km and a few 100 m respectively.