  The propagation of waves through transmission eigenchannels in complex media
is emerging as a new frontier of condensed matter and wave physics. A crucial
step towards constructing a complete theory of eigenchannels is to demonstrate
their spatial structure in any dimension and their wave-coherence nature. Here,
we show a surprising result in this direction. Specifically, we find that as
the width of diffusive samples increases transforming from quasi
one-dimensional ($1$D) to two-dimensional ($2$D) geometry, notwithstanding the
dramatic changes in the transverse (with respect to the direction of
propagation) intensity distribution of waves propagating in such channels, the
dependence of intensity on the longitudinal coordinate does not change and is
given by the same analytical expression as that for quasi-$1$D. Furthermore,
with a minimal modification, the expression describes also the spatial
structures of localized resonances in strictly $1$D random systems. It is thus
suggested that the underlying physics of eigenchannels might include
super-universal key ingredients: they are not only universal with respect to
the disorder ensemble and the dimension, but also of $1$D nature and closely
related to the resonances. Our findings open up a way to tailor the spatial
energy density distribution in opaque materials.
