Statistics of the near-field speckle pattern in transmission through random media

In this paper, we explore the specific nature of wave propagation in multiple scattering media and examine how this is revealed in various aspects of the speckle pattern measured at the output surface of an ensemble of disordered media. We present near-field measurements of the speckle pattern transmitted through random samples in a quasi-one dimensional geometry. The microwave field - amplitude and phase - is measured as a function of frequency along perpendicular transverse polarizations on a close grid of points on the output surface of samples composed of randomly positioned dielectric spheres. The field spectrum is Fourier transformed to access the temporal evolution of the speckle pattern. The field and intensity correlation functions versus displacement and frequency shift are measured and reveal non-Gaussian behavior, namely long range correlation. The key distributions and correlation functions of the delay time are also measured and compared to calculations, to show the interplay between the delay time and the intensity in the speckle pattern. The widest fluctuations of the phase derivative with frequency are found at low intensity values near a phase singularity in the transmitted speckle pattern. The position of these phase singularities at which the intensity vanishes is reconstructed for the entire speckle pattern.