There are significant differences between Ishimaru’s theory [ J. Opt. Soc. Am. 68, 1045 ( 1978)] and Furutsu’s theory [ J. Opt. Soc. Am. 70, 360 ( 1980)] on pulse propagation in discrete random media, although both deal with the same physical problem. In this paper we attempt to clarify the confusion created by the two theories. A simple numerical example is shown to illustrate the difference and the range of validity of the theory. It is shown that if a delta-function pulse is initiated at r = 0 and t = 0 in a discrete random medium, Furutsu’s diffusion theory predicts. that the pulse diffuses instantly and arrives at all points with infinite speed for t > 0; therefore its range of validity is limited to the time interval t ≫ L/C, where L is the propagation distance and C is the velocity of light. Ishimaru’s theory gives a delta-function pulse propagating out at a finite velocity of followed by a diffusing tail. Therefore Ishimaru’s is not a usual diffusion theory, but it includes both propagation and diffusion, and its range of validity is different from that of the pure diffusion theory. The limitations of both theories are also discussed.
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