  The universal bimodal distribution of transmission eigenvalues in lossless
diffusive systems un- derpins such celebrated phenomena as universal
conductance fluctuations, quantum shot noise in condensed matter physics and
enhanced transmission in optics and acoustics. Here, we show that in the
presence of absorption, density of the transmission eigenvalues depends on the
confinement geometry of scattering media. Furthermore, in an asymmetric
waveguide, densities of the reflection and absorption eigenvalues also depend
of the side from which the waves are incident. With increas- ing absorpotion,
the density of absorption eigenvalues transforms from single-peak to
double-peak function. Our findings open a new avenue for coherent control of
wave transmission, reflection and absorption in random media.
