Focusing coherent light through a nonlinear scattering medium

Wavefront shaping is a powerful technique that can be used to focus light through scattering media, with the limitation that the obtained focus contains a small fraction of the total power. The method is based on the assumption that the field at the output 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 that using adaptive optimization of the wavefront light can still be controlled and focused through a nonlinear scattering medium, and that the focused fraction of power can be significantly enhanced in the presence of moderate positive nonlinearity. Our results suggest that the use of short pulses for focusing through scattering media with a mild self-focusing response might be favorable to the use of continuous-wave light.