Nonstationary Time-Domain Statistics of Multiply Scattered Broadband Terahertz Pulses

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We examine the time-domain statistics of randomly varying electric fields generated by multiple scattering of single-cycle electromagnetic pulses in a random medium. This analysis emphasizes the fact that these measured random fields are not stationary, as is commonly assumed for diffusing photons generated with a narrowband light source. We demonstrate that the nonstationarity is a consequence of the time dependence of the configurationally averaged intensity, and that the statistical properties of the random field can be predicted if this quantity is known. We also discuss an approach for describing the transition from nonstationary to stationary behavior by investigating the degree of stationarity during a short time window. A parameterization of the statistics using a gamma distribution provides a quantifiable measure of the approach to stationarity. Our predictions are in good agreement with experimental observations.

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