Time-of-arrival fluctuations of a space–time Gaussian pulse in weak optical turbulence: an analytic solution

An analytic expression is derived for the long-term temporal broadening (fluctuations of arrival time) of a collimated space-time Gaussian pulse propagating along a horizontal path through weak optical turbulence. General results are presented for nominal parameter values characterizing laser communication through the atmosphere. Specific examples are calculated for both upper-atmosphere and ground-level cross links. It is shown that, for upper-atmosphere cross links, pulses shorter than 100 fs have considerable broadening, whereas at ground level, broadening is predicted in pulses as long as 1 ps.