  A striking prediction from the random matrix theory in mesoscopic physics is
the existence of "open channels": waves that can use multipath interference to
achieve perfect transmission across an opaque disordered medium even in the
multiple-scattering regime. Realization of such open channels requires a
coherent control of the complete incident wavefront. To date, the open channels
have only been demonstrated in scalar two-dimensional (2D) structures, both
experimentally and with numerical studies. Here, we utilize a recently proposed
"augmented partial factorization" full-wave simulation method to compute the
scattering matrix from 3D vectorial Maxwell's equations and demonstrate the
existence of open channels in 3D disordered media. We examine the spatial
profile of such open channels, demonstrate the existence of a bimodal
transmission eigenvalue distribution with full control, and study the effects
of incomplete polarization control and of a finite illumination area. This
study confirms the validity of the random matrix theory in vectorial systems.
The simulation framework provides full access to the complex multi-channel wave
transport in 3D disordered systems, filling the gap left by experimental
capabilities.
