Analysis of dispersive effects and enhanced medium penetrability in wide-band pulse propagation through sparse discrete media

Evolution of an oscillatory wide-band pulse in a sparse medium composed of randomly distributed, uncorrelated, discrete scatterers (such as atmospheric clouds, fog, or dust) is studied. Frequency dependent (dispersive) losses are evaluated by taking into account energy absorption in the medium constituents as well as scattering itself. A reduced, algebraic (i.e., behaving as a certain inverse power of the penetration depth) attenuation of the pulse energy is observed, provided the pulse contains a significant frequency content in the region of strongly varying medium dispersive properties. Different types of algebraic attenuation can arise, depending on the inter-relations between characteristic frequencies of the pulse spectrum and the medium dispersive properties.