Mesoscopic correlation within transmitted speckle pattern and wave localization

This thesis is an experimental study of the statistical character of the field distribution within one-dimensional and transmitted through quasi-1D random samples.; We measured the spatial extent of the field for extended, evanescent, and localized wave in random single-mode waveguide. We find that spectrally and spatially overlapping modes in a nominally localized region of an open dissipative system can be decomposed into quasi-normal-modes.; Microwave field measurements of the near-field transmitted speckle pattern through random quasi-one-dimensional samples were carried out with polarization rotation, along a line, on a tight grid covering the full output surface. The field spectrum is Fourier transformed to give the temporal evolution of the speckle pattern. Field and intensity correlation versus displacement, frequency shift, and polarization rotation were studied to exhibit the growing impact of mesoscopic fluctuation and photon localization with time delay from a exciting pulse. The variation of key distributions and correlation functions with delay time were examined. We find a universal expression for the intensity correlation function which is valid for localized and diffusive waves in steady-state and in the time domain. It is a function only of the field correlation function which is the same in steady state and in the time domain and the degree of correlation, kappa, which also indicates the closeness of the random system to the localization transition. We also studied the microstatistics of the transmitted field in individual sample realizations, as opposed to the traditional focus on fluctuations relative to the ensemble average. We find that the field distribution in each configuration is Gaussian and that mesoscopic correlation arises as a result of fluctuation of the total transmission. The degree of correlation kappa is just the variance of total transmission normalized by its ensemble average.; Other aspects on phase statistics of the speckle pattern are also reported. The distributions and correlations of phase, the first spatial derivation of the phase, and the transverse current density, which may be expressed as the product of the intensity and the first spatial derivative of phase, are all determined by a parameter derived from spatial correlation function of the field.