Abstract: In this paper we present a theoretical study of focused beam wave pulse propagation and diffusion in highly scattering discrete random media. By using Wigner distributions, we calculate an explicit closed-form expression for the reduced intensity of focused beam waves. From this analysis, we find that the extent to which the reduced intensity focuses depends upon the attenuation it experiences from scattering and absorption. We then solve the diffusion equation for continuous wave sources and delta function input pulses to examine the spatial and temporal spreading of beam wave pulses. Through numerical approximations to the obtained solutions, we find that focusing effects of the diffuse intensity are negligible. Finally, we compare these results to those of collimated beam waves and pulsed plane waves. Through these comparisons, we determine that the spatial spreading of focused beams is similar to that of collimated beams, and the temporal spreading of the focused beam wave pulse is similar to that of plane wave pulses.!22
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