If I were again beginning my studies, I would follow the advice of Plato and start with mathematics.
We probe our environment and communicate with one another with classical waves. Because of wave-particle duality, studies of classical waves also serve as models of electronic transport, involving quantum mechanical electron waves in the solid state. The goal of our studies of microwave and optical propagation is to provide a universal description of wave propagation in random systems and to apply the understanding gained to imaging and communications. We explore the diversity of propagation phenomena in ensembles of sample realizations which reflect the openness, scattering strength, internal reflection, dissipation or gain, and topology of the system. The work in the lab has demonstrated Anderson localization, the statistics of transport in space and time, including short-, long- and infinite-range intensity correlation in space and frequency; crossovers between ballistic, diffusive and localized wave transport, acousto-optic tomography, band-edge lasing, the photon localization laser, correlation of non-orthogonal modes in open media, and robust transport of edge states in photonic topological insulators, which emulate the spin and valley degrees of freedom in condensed matter. Research in the lab contributed to the formation of Chiral Phonics, Inc. (https://www.chiralphotonics.com/), which develops and produces microfabricated optical fiber-based components and assemblies for applications in coupling and sensing.
The microwave laboratory was started together with Dr. Narciso Garcia.