| Abstract: | Because the dream of looking into natural and artificial opaque materials is ordinarily frustrated by scattering within the medium, much of what we know regarding transport within disordered media is inferred from the scattering and transmission of waves and particles. Transmission can be characterized via the transmission eigenvalues τ of coherent eigenchannels of the transmission matrix, but is mute regarding the disposition of intensity inside the sample. In this talk, I will discuss the use of numerical simulations to find an empirical formula for the average intensity profile of transmission eigenchannels within random samples that holds for quasi-ballistic, diffusive and localized waves. We demonstrate that the derivative with angular frequency of the average phase of each transmission eigenhannel, , is proportional to the energy stored in the eigenchannel and gives the contribution of the eigenchannel to the density of states (DOS). Microwave measurements of vs. τ are in accord with computer simulations, while the sum of over all channels equals the DOS determined from a decomposition of the wave into quasi-normal modes.
Work carried out with Matthieu Davy, Zhou Shi, Jongchul Park and Jing Wang |
