Statistics of Electromagnetic Propagation and Localization

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9973959GenackThis project will provide a detailed examination of the statistics of electromagnetic propagation in random media. Because of the strong analogy between quantum mechanical and classical transport, these studies will address fundamental issues of electronic transport in the context of photonics. Microwave measurements made with high spectral and spatial resolution in ensembles of statistically equivalent samples will be used to chart both the static and dynamic aspects of transport in the transition from diffusive propagation to localization. Samples will include low-density mixtures of dielectric spheres with various degrees of translational order, and metallic and dielectric periodic structures with various concentrations of scatterers floated in the sample. Only a statistical description is adequate to capture the essence of wave propagation in the presence of disorder. This research will provide a universal description of wave propagation in terms of the closeness to the localization transition. In the absence of inelastic processes, this can be specified by a single parameter - the ensemble average of the dimensionless conductance. Measurements of the probability distribution of microwave intensity, total transmission, and conductance will bridge the gap between the statistics of classical waves and electronic mesoscopic physics. The relationship between the moments of these distributions and the connection between the statistics of local and averaged quantities will be examined. The dynamics of diffusing waves will be extended to localized waves and their connection to intensity statistics will be explored together with the correlation between delay time and transmitted intensity for localized states. Transport will be studied in samples that display sharp line spectra associated with resonances with localized states to unify mesoscopic physics and statistical optics, which will enlarge the range of phenomena studied in these disciplines.%%%Electronic, electromagnetic and acoustic propagation in the presence of disorder are related fundamental problems with wide ranging applications in electronics, imaging, communication and photonics. The statistical analysis of electromagnetic propagation using diagnostic tools that are not available in the study of electronic insulators and conductors will be used. This project will thereby shed light on the connection between microscopic and global aspects of conductance and wave propagation. The distributions of static transmission quantities, such as intensity, total transmission and conductance, as well as dynamic quantities, such as the dwell time of energy in the sample will be obtained for diffusing and for localized waves. The nature of waves, which are strongly trapped inside nearly periodic samples, will be studies and their use in photonic devices will be elucidated. The high school, undergraduate, and graduate students as well as the postdoctoral fellows who will be involved in this research will receive training in fundamental problems, which are of importance in photonics, microwave cellular phone communication, and imaging.