Effect of a pulse entrapping on weak localization of waves in a resonant random medium

Abstract

We consider theoretically a new physical effect in coherent backscattering enhancement (CBE) of electromagnetic or acoustic non-stationary waves from a discrete random medium under condition of Mie resonant scattering. The effect manifests itself as an angle-cone broadening of a short pulsed signal CBE from the resonant random medium, compared with the case of a non-resonant random medium. The cone broadening is associated with a pulse-entrapping effect when the pulse, while propagating within the resonant random medium, spends most of the time being ‘entrapped’ inside scatterers. A theory for the predicted effect is based on, first, the well known relation between the contributions of the ladder and cyclical diagrams to the time spectral density of the wave electric field coherence function and, second, a recently derived radiative transfer equation with three Lorentzian kernels of delay describing a pulse entrapping in an ensemble of resonant point-like scatterers. Using the generalized Chandrasekhar H-function, we obtain an exact analytic expression for the non-stationary albedo of the semi-infinite resonant random medium, taking into account the phenomena of a pulse CBE and entrapping. A simple analytic asymptotics is found for the albedo of the later part of the scattered pulse. This asymptotics shows quantitatively how the entrapping affects the peak amplitude and peak line shape of the CBE of a short pulse.