  Light-matter interactions inside turbid medium can be controlled by tailoring
the spatial distribution of energy density throughout the system. Wavefront
shaping allows selective coupling of incident light to different transmission
eigenchannels, producing dramatically different spatial intensity profiles. In
contrast to the density of transmission eigenvalues that is dictated by the
universal bimodal distribution, the spatial structures of the eigenchannels are
not universal and depend on the confinement geometry of the system. Here, we
develop and verify a model for the transmission eigenchannel with the
corresponding eigenvalue close to unity. By projecting the original problem of
two-dimensional diffusion in a homogeneous scattering medium onto a
one-dimensional inhomogeneous diffusion, we obtain an analytical expression
relating the intensity profile to the shape of the confining waveguide.
Inverting this relationship enables the inverse design of the waveguide shape
to achieve the desired energy distribution for the perfectly transmitting
eigenchannel. Our approach also allows to predict the intensity profile of such
channel in a disordered slab with open boundaries, pointing to the possibility
of controllable delivery of light to different depths with local illumination.
