Propagation of short infrared/optical pulses in dilute random media (e.g., atmospheric clouds, fog, dust, or aerosols) consisting of large, compared to the wavelength, scatterers is analyzed. A rigorous approach based on analytic complex-contour integration of numerically determined cut and pole singularities of the radiative transport equation solution in the Fourier space is presented. It is found that the intensity of a propagating pulse, in addition to the coherent ("ballistic") contribution and a long late-time diffusive tail, also exhibits a sharply rising early-time component that (i) can be attributed to the small-angle diffractive part of the scattering cross-section on medium particles, (ii) is attenuated proportionally to the nondiffractive rather than total cross-section, and (iii) can be extracted by high-pass filtering of the received pulse.
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