Solutions of the time-dependent radiative transfer equation (RTE) are used to describe propagation of a pulsed collimated beam through a random medium consisting of discrete scatterers of sizes large compared to the wavelengths—a situation particularly relevant to free-space optical communication through atmospheric obscurants. The RTE is solved in the spherical-harmonics basis with no approximations other than a truncation in the angular momenta; the results confirm convergence of the solution for a fixed beam width and growing . The obtained time-resolved radiance includes both the usual “late-time diffusion” (LTD), responsible for the well known reduction of the “coherence bandwidth” and, thus, a serious limitation in the transfer rate, and the more recently identified “early-time diffusion” (ETD) component, attenuated at a rate significantly lower than for the coherent (ballistic) signal and characterized by a very short rise time, allowing a high-rate data transfer. The ratio of the ETD to the LTD signal for the considered collimated beams is much (orders of magnitude) higher than in the previously examined problem of an omnidirectional source, increasing its potential usefulness in communication and related imaging applications.
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