  The impact of surface reflection upon transmission through and energy
distributions within random media has generally been described in terms of the
boundary extrapolation lengths $z_b, z_b'$ at the input and output end of an
open sample, which are the distance beyond the sample surfaces at which the
energy density within the sample extrapolates to zeroThe importance of
reflection at the sample boundaries plays a key role in the scaling of
transmission. Here we consider the impact of surface reflection on the
propagation of diffusive waves in terms of the modification of the distribution
of transmission eigenvalues (DTE). We review our finding of a transition in the
analytical form of the DTE at the point that the sample length equals
$|z_b-z_b'|$. The highest transmission eigenvalue for stronger asymmetry in
boundary reflection is strictly smaller than unity. The average transmission
and profiles of energy density inside the sample can still be described in
terms of the sample length, $L$, and the boundary extrapolation lengths on both
sides of the sample, $z_b, z_b'$. For localized waves, we find the energy
density profile within the sample is a segment of the distribution that would
be found in a longer sample with length $L+z_b+z_b'$. These results suggest new
ways of controlling wave interference in both diffusive and localized systems
by varying boundary reflectivity.
