  Scattering has usually be considered as detrimental for optical focusing or
imaging. Recently, more and more research has shown that strongly scattering
materials can be utilized to focus coherent light by controlling or shaping the
incident light. Here, purposeful focusing of second-harmonic waves, which are
generated and scattered from nonlinear turbid media via feedback-based
wavefront shaping is presented. This work shows a flexible manipulation of both
disordered linear and nonlinear scattering signals, indicating more
controllable degrees of freedom for the description of turbid media. This
technique also provides a possible way to an efficient transmission of
nonlinear signal at a desired location in the form of a focal point or other
patterns. With the combination of random nonlinear optics and wavefront shaping
methods, more interesting applications are expected in the future, such as
nonlinear transmission matrix, multi-frequency imaging and phase-matching-free
nonlinear optics.
