Wave localization characteristics in the time domain

Abstract

We present an analytical solution to the problem of pulse backscattering from a randomly stratified half-space. It is shown that the power spectrum μ for the backscattered wave is characterized by a function of χ, where χ=(distance traveled by the pulse at time τ)/(the frequency-dependent localization length). For the matched-impedance and the total-reflection boundary conditions, μ is given by χ/(1+χ${)}^2$ and 4χ, respectively. Implications for the time-domain measurement of the localization length are discussed.