Shaping the propagation of light in complex media

The main obstacle for optical imaging or for sending information through turbid media such as paint, clouds and biological tissue is the random scattering of light. Owing to its immense complexity, the process of multiple scattering has long been described by the diffusion equation, which ignores the interference of scattered light. Recent developments in optical wavefront shaping and phase recording techniques have enabled the breaking of the diffusion limit and the control of coherent light transport in complex media, including strongly scattering tissues and multimode optical fibres with random mode mixing. Great advances have been made in focusing and controlling the transmission of light through such complex systems and in performing various tasks behind them, such as optical micro-manipulation. Here, we summarize the amazing power and the fundamental limits of controlling multiple light scattering, which lay the physical foundation to harness multiply-scattered light for imaging and communication purposes. Connections to practical applications are illustrated, in particular in those areas covered in the companion articles in this issue. Multiple scattering fundamentally complicates the task of sending light through turbid media, as many applications require. This Review summarizes the theoretical framework and experimental techniques to understand and control these processes.