  Transmission eigenchannels are building blocks of coherent wave transport in
diffusive media, and selective excitation of individual eigenchannels can lead
to diverse transport behavior. An essential yet poorly understood property is
the transverse spatial profile of each eigenchannel, which is critical for
coupling into and out of it. Here, we discover that the transmission
eigenchannels of a disordered slab possess localized incident and outgoing
profiles, even in the diffusive regime far from Anderson localization. Such
transverse localization arises from a combination of reciprocity, local
coupling of spatial modes, and nonlocal correlations of scattered waves.
Experimentally, we observe signatures of such localization despite finite
illumination area. Our results reveal the intrinsic characteristics of
transmission eigenchannels in the open slab geometry, commonly used for
applications in imaging and energy transfer through turbid media.
