Fluctuations in photon local delay time and their relation to phase spectra in random media

The temporal evolution of microwave pulses transmitted through random dielectric samples is obtained from the Fourier transform of field spectra. Large fluctuations are found in the local or single-channel delay time, which is the first temporal moment of the transmitted pulse at a point in the output speckle pattern. Both positive and negative values of the local delay time are observed. The widest distribution is found at lowintensity values near a phase singularity in the transmitted speckle pattern. In the limit of long duration, narrow-bandwidth incident pulses, the single-channel delay time equals the spectral derivative of the phase of the transmitted field. @S1063-651X~99!13102-7# PACS number~s!: 41.20.Jb, 05.40.2a, 71.55.Jv Statistical optics has concentrated on fluctuations of reflected and transmitted intensity. The Rayleigh distribution describes large fluctuations in intensity at the output of a scattering medium excited by monochromatic radiation. The intensity of a single polarization component normalized to its ensemble average has a negative exponential distribution exp(2I/^I&) @1#. This distribution obtains under the assumption that the field E5Ae if can be represented as a superposition of uncorrelated partial waves. However, in multiplescattering media, the coherent nature of wave propagation inevitably leads to both short- and long-range contributions to the intensity correlation function @2‐4#. These give rise to enhanced fluctuations in the intensity @5#, total transmission @6‐10#, and electronic conductance @11‐13#, which have been studied intensively in the past decade. The degree of nonlocal intensity correlation is a measure of the closeness to the localization threshold @2‐13# and determines the statistical distributions of key transmission quantities. In this paper we consider fluctuations in pulse propagation. This is in contrast to previous studies of the statistics of steady-state propagation in random media and to measurements of the time of flight distribution @14‐17#. Fluctuations in the pulse evolution are averaged over an ensemble of samples and one obtains the arrival time distribution for transmitted photons, which is proportional to the path length distribution P(s). This corresponds to the particle transport picture and gives a mix of ballistic and diffusive components. Here we consider fluctuations in the dynamics of transmission for a given incident and outgoing channel for different realizations of a random medium. Specifically, we define the local or singlechannel delay time t ab as the first temporal moment for a transmitted pulse associated with an incident pulse of bandwidth Dv centered at t50 in the time domain and at v 0 in the frequency domain,