  Wavefront shaping is a powerful technique that can be used to focus light
through scattering media, which can be important for imaging through scattering
samples such as tissue. The method is based on the assumption that the field at
the output of the medium is a linear superposition of the modes traveling
through different paths in the medium. However, when the scattering medium also
exhibits nonlinearity, as may occur in multiphoton microscopy, this assumption
is violated and the applicability of wavefront shaping becomes unclear. Here we
show, using a simple model system with a scattering layer followed by a
nonlinear layer, that with adaptive optimization of the wavefront light can
still be controlled and focused through a scattering medium in the presence of
nonlinearity. Notably, we find that moderate positive nonlinearity can serve to
significantly increase the focused fraction of power, whereas negative
nonlinearity reduces it.
