  Scattering hinders the passage of light through random media and consequently
limits the usefulness of optical techniques for sensing and imaging. Thus,
methods for increasing the transmission of light through such random media are
of interest. Against this backdrop, recent theoretical and experimental
advances have suggested the existence of a few highly transmitting
eigen-wavefronts with transmission coefficients close to one in strongly
backscattering random media.
  Here, we numerically analyze this phenomenon in 2-D with fully spectrally
accurate simulators and provide rigorous numerical evidence confirming the
existence of these highly transmitting eigen-wavefronts in random media with
periodic boundary conditions that is composed of hundreds of thousands of
non-absorbing scatterers.
  Motivated by bio-imaging applications where it is not possible to measure the
transmitted fields, we develop physically realizable algorithms for increasing
the transmission through such random media using backscatter analysis. We show
via numerical simulations that the algorithms converge rapidly, yielding a
near-optimum wavefront in just a few iterations. We also develop an algorithm
that combines the knowledge of these highly transmitting eigen-wavefronts
obtained from backscatter analysis, with intensity measurements at a point to
produce a near-optimal focus with significantly fewer measurements than a
method that does not utilize this information.
