13 October 1998 Validity of the diffusion approximation for the description of a short pulse diffusely reflected from a resonant random medium
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Abstract
A recently derived radiative transfer equation with three Lorentzian kernels of delay is applied to an albedo problem on a scalar wave field quasi-monochromatic pulse diffuse reflection from a semi-infinite random medium consisting of resonant point-like scatterers. The albedo problem is solved exactly in terms of the Chandrasekhar consisting of resonant point-like scatterers. The albedo problem is solved exactly in terms of the Chandrasekhar H-function, extended analytically into the single scattering complex albedo (lambda) -plane. Simple analytical asymptotics for the non- stationary scattering function is obtained in the limit related to large values of the time variable. The exact analytic solution for the time-evolution of a diffusely reflected short pulse is used to analyze an accuracy of the non-stationary scattering function calculated in the diffusion approximation. It is shown that the diffusion asymptotics describes the exact solution with a relative error not exceeding one percent only at larger values of dimensionless wave propagation time t equals t/to > 200 where to stands for a mean free time of wave radiation between scattering events defined in terms of the wave phase in a random medium consisting of point-like scatterers tuned to the Mie resonance. Besides, the accuracy of the diffusion asymptotics falls off providing that wave scattering approaches the resonance conditions.
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Mikhail Yu. Barabanenkov, Vitalii V. Aristov, "Validity of the diffusion approximation for the description of a short pulse diffusely reflected from a resonant random medium", Proc. SPIE 3467, Far- and Near-Field Optics: Physics and Information Processing, (13 October 1998); doi: 10.1117/12.326816; https://doi.org/10.1117/12.326816
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