Universality of eigenchannel structures in dimensional crossover

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 (1D) to two-dimensional (2D) 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-1D. Furthermore, with a minimal modification, the expression describes also the spatial structures of localized resonances in strictly 1D random systems. It is thus suggested that the key ingredients of eigenchannels are not only universal with respect to the disorder ensemble and the dimension, but also of 1D nature and closely related to the resonances. Our findings open up a way to tailor the spatial energy density distribution in opaque materials.