  The impact of surface reflection on the statistics of transmission
eigenvalues is a largely unexplored subject of fundamental and practical
importance in statistical optics. Here, we develop a first-principles theory
and confirm numerically that the distribution of transmission eigenvalues of
diffusive waves exhibits a nonanalytic `transition' as the strength of surface
reflection at one surface passes through a critical value while that at the
other is fixed. Above the critical value, the highest transmission eigenvalue
is strictly smaller than unity and decreases with increasing internal
reflection. When the input and output surfaces are equally reflective, the
highest transmission eigenvalue is unity and the transition disappears
irrespective of the strength of surface reflection.
