Transmission eigenchannels, the density of states and intensity profiles inside opaque media

We find a single expression for the average intensity profile of eigenchannels of the transmission matrix inside single and multichannel random media for quasi-ballistic, diffusive and localized waves. The intensity profiles are built upon the simple form of the completely transmissive channel and depend only upon the transmission eigenvalue, τ, the sample length and the localization length. We show that eigenchannel intensity profiles are related to the auxiliary localization lengths introduced by Dorokhov to parameterize τ. The integral of the spatial intensity distribution over the sample volume for unity incident flux , which is the contribution of each eigenchannel to the density of states (DOS), is equal to the derivative of the average phase of the transmission eigenchannel with angular frequency of the incident radiation. The sum of the eigenchannel DOS over all eigenchannels gives the density of states (DOS) which controls spontaneous and stimulated emission and wave localization. This is demonstrated in microwave experiments in the equivalence of spectra of the DOS determined from a decomposition of the wave into transmission eigenchannels and quasi-normal modes.