  Propagation of light beams through scattering or multimode systems may lead
to randomization of the spatial coherence of the light. Although information is
not lost, its recovery requires a coherent interferometric reconstruction of
the original signals, which have been scrambled into the modes of the
scattering system. Here, we show that we can automatically unscramble four
optical beams that have been arbitrarily mixed in a multimode waveguide,
undoing the scattering and mixing between the spatial modes through a mesh of
silicon photonics Mach-Zehnder interferometers. Using embedded transparent
detectors and a progressive tuning algorithm, the mesh self-configures
automatically and reset itself after significantly perturbing the mixing,
without turning off the beams. We demonstrate the recovery of four separate 10
Gbits/s information channels, with residual cross-talk between beams of -20dB.
This principle of self-configuring and self-resetting in optical systems should
be applicable in a wide range of optical applications.
