Measurements of femtosecond temporal speckle field of a random medium

The femtosecond temporal speckle field of a random medium is studied theoretically and experimentally. Femtosecond temporal speckle arises from the interference of multiple randomly scattered electric fields. The femtosecond temporal speckle field is measured with a cross-correlation frequency-resolved optical gating method. The spatial average of the speckle field yields a smooth transmitted profile. The speckle field is a circular complex Gaussian variable because the scattered light beams from different trajectories have no correlation with each other. The field and the intensity profiles of individual speckle spots fluctuate randomly in time. The ensemble average of the temporal intensity profiles converges, thereby yielding the photon travel time probability distribution function.