The transport of waves is of wide interest since waves are the means by which we probe our environment and communicate with one another. Our group seeks to understand the way waves propagate within and through disordered systems, nearly periodic structures and metamaterials.

We seek a statistical description of transport because the field within an individual random sample and between samples varies in a random fashion. In addition, the microscopic structure of random samples is generally not fully specified. In key respects, such a description would apply equally to classical waves, such as light, sound and microwave radiation, and to quantum mechanical waves such as electrons or atoms.

The statistics of wave propagation depends on the degree to which transmission is suppressed as they interfere within the sample. This leads to Anderson localization. The statistics of the intensity is found in terms of the closeness to the crossover to Anderson localization. Microwave and optical measurements are used to explore the statistics of wave transport from many different perspectives including the random field speckle patterns of waves, the modes or resonances within the medium, and the natural transmission channels through the medium. These approaches provide a means for controlling waves for applications in imaging, communications and lasing.

Discoveries and demonstrations of a range of phenomena have stimulated applications ranging from low-threshold lasing at the band edge of periodic liquid crystals and at localized modes of random systems, chiral fiber polarizers and optical fiber couplers, acousto-optic imaging, control of intensity through and within random systems, and robust propagation in the interior of metamaterials.