Transmission eigenchannels in a disordered medium

While the distribution of the transmission eigenvalues of a disordered medium is well understood in the context of random-matrix theory, the properties of eigenchannels have remained unexplored. In this study, we have solved electromagnetic wave propagation through a disordered medium using the finite-difference time-domain method, we numerically constructed a transmission matrix in an optical regime, and we obtained its eigenchannels as well as its eigenvalues. We observe that open eigenchannels enhance the energy stored inside the disordered medium. From mode decomposition, we prove that eigenchannels contribute to a single-channel optimizing mode, which is realized in recent experiments by I. M. Vellekoop et al. [Phys. Rev. Lett 101, 120601 (2008)], in proportion to their eigenvalues. Our study will pave the way for experimental approaches to finding open eigenchannels and their potential use for imaging through turbid media and random lasers.