We explore the nature of coherent propagation of light and microwave radiation in disordered samples from a number of perspectives, including the statistics of (1) the random speckle patterns of transmitted field and intensity, (2) the electromagnetic modes of the medium and (3) the transmission eigenchannels. Our focus is on universal aspects from these three perspectives, the relationship between them, and applications of these findings to focusing and imaging in and through random media, random lasing, enhanced transmission and energy deposition and selective coupling to modes and channels of the medium. Some issues and findings regard these perspectives are:

• Speckle: The statistics of transmitted intensity, transmission integrated over the output and of transmittance, which is analogous to the electronic conductance have been found in terms of a single parameter. The variances of intensity, total transmission, or optical conductance indicate the precise point in the crossover from diffusive to localized photons within the medium. We are also exploring the statistics of the energy density within random samples. The diffusion of features of the speckle patterns in transmission provide a possible approach to imaging motion in dynamic samples that may have biomedical applications. The evolution of the speckle pattern with frequency shift yields the diffusion coefficient of photons propagating through the medium.
• Modes: We find that the statistics of the shape, spectral spacing of central frequencies, linewidth and the correlation between modal speckle patterns determines the nature of transmission.
• Transmission eigenchannels: We seek a universal description for the average profile of intensity inside random media. The description applies broadly to samples in which wave propagation is quasi-ballistic, diffusive and localized.
• Photonic topological insulator: We are currently exploring robustness of transmission along domain boundaries within the bulk of metamaterials.