  Optical absorption is omnipresent and very often distributed non-uniformly in
space. We present a numerical study on the effects of inhomogeneous absorption
on transmission eigenchannels of light in highly scattering media. In the weak
absorption regime, the spatial profile of a transmission channel remains very
similar to that without absorption, and the effect of inhomogeneous absorption
can be stronger or weaker than homogeneous absorption depending on the spatial
overlap of the localized absorbing region with the field intensity maximum of
the channel. In the strong absorption regime, the high transmission channels
redirect the energy flows to circumvent the absorbing regions to minimize loss.
The attenuation of high transmission channels by inhomogeneous absorption is
lower than that by homogeneous absorption, regardless of the location of the
absorbing region. The statistical distribution of transmission eigenvalues in
the former becomes broader than that in the latter, due to a longer tail at
high transmission. Since the maximum transmission channel is the most efficient
in bypassing the absorbing region, the ratio of its transmittance to the
average transmittance increases with absorption, eventually exceeds the ratio
without absorption.

Optics