  The propagation of light through samples with random inhomogeneities can be
described by way of transmission eigenchannels, which connect incoming and
outgoing external propagating modes. Although the detailed structure of a
disordered sample can generally not be fully specified, these transmission
eigenchannels can nonetheless be successfully controlled and utilized for
focusing and imaging light through random media. Here we demonstrate that in
deeply localized quasi-1D systems, the single dominant transmission
eigenchannel is formed by an individual Anderson localized mode or by a
"necklace state". In this single-channel regime, the disordered sample can be
treated as an effective 1D system with a renormalized localization length,
coupled through all the external modes to its surroundings. Using statistical
criteria of the single-channel regime and pulsed excitations of the disordered
samples allows us to identify long-lived localized modes and short-lived
necklace states at long and short time delays, respectively.

Disordered Systems and Neural Networks;Mesoscale and Nanoscale Physics;Chaotic Dynamics;Optics