Wave scattering, diffusion, and localization have long been central research topic in our study of the physical world. This thesis is focused on theoretical study of the dynamic intensity fluctuations for mesoscopic 1D and quasi-1D systems in the localized regime, providing an underlying-mode explanation for 1D numerical simulations and quasi-1D experiments. A dynamic single-parameter scaling (DSPS) model was adopted and further developed by including the effects due to a finite pulse width and keeping the interference terms back for the dynamic transmission in mesoscopic 1D systems, which turns out to be an essential step especially when the second moment of normalized transmission was concerned. Such a developed model becomes able to predict not only the decay rate of dynamic transmit...[ Read more ]

Wave scattering, diffusion, and localization have long been central research topic in our study of the physical world. This thesis is focused on theoretical study of the dynamic intensity fluctuations for mesoscopic 1D and quasi-1D systems in the localized regime, providing an underlying-mode explanation for 1D numerical simulations and quasi-1D experiments. A dynamic single-parameter scaling (DSPS) model was adopted and further developed by including the effects due to a finite pulse width and keeping the interference terms back for the dynamic transmission in mesoscopic 1D systems, which turns out to be an essential step especially when the second moment of normalized transmission was concerned. Such a developed model becomes able to predict not only the decay rate of dynamic transmitted intensity but also the variance of normalized transmission at long times when the energy within the sample is increasingly stored in long-lived localized modes, indicating its ability to capture the dynamic behavior of long-lived localized modes. This was later confirmed by the comparison between simulations and the model on the probability distributions of normalized dynamic transmitted intensity at different time delays. However, at short times, since it accounts only for the localized modes, the model underestimates the decay rate while overestimates the variance when the necklace-state effect still dominates the transport properties.

For dynamic correlation in mesoscopic quasi-1D systems, both variance of normalized total transmissin and that of dimensionless conductance are compared with the DSPS model. The DSPS model always underestimates the variance of normlalized total transmission in the experimental time range; however, its prediction for the variance of dimensionless conductance is as good as for that of normalized transmitted intensity in 1D systems. This study concludes that the variance of dimensionless conductance is the quantity in quasi-1D random media that should be chosen to be compared with the DSPS model.

Both simulations for 1D systems and experimental results from quasi-1D setups show that dynamic intensity fluctuations initially drop towards a minimum after which they increase nearly exponentially. The time corresponding to such a minimum in the intensity fluctuations, i.e., the variance dip, is not sensitive to the incident pulse width. It stands for a characteristic time when a transition from a state dominated by the necklace states to a state dominated by the localized modes happens, and corresponds to time at which the largest number of modes participate in transmission. In terms of the sample size, the variance dip has a linear dependence for small sample sizes but will increase exponentially for large samples. The DSPS model starts to overlap the variance at about three times the corresponding dip time. This overlapping time corresponds to when the dynamic correlation is about to deviate from an exponential increase.