Light waves will propagate without distortion in a uniform medium according to its wave equation and are widely employed for energy and information transmission. However, absolutely uniform media do not exist in the real world, and there are various defects and impurities in various media, especially in completely disordered media. Small particles within the scattering medium can make light waves deviate from their original propagation direction, which results in a disordered light field, forms speckles, and thus hinders energy and information transmission. Since in the early stages scattering was believed to be irreversible, most conventional methods relied on extracting ballistic photons from the scattering photons to address scattering-induced aberrations. As the ballistic photons decay exponentially with the increasing propagation distance, and it is difficult to extract ballistic photons from scattering photons after a certain depth, scattering correction based on ballistic photons is only applicable to weakly scattering media.

With the rapid development of spatial modulation devices such as spatial light modulators and digital micromirrors, it has become possible to realize the spatial light modulation with high accuracy. In 2007, Vellekoop and Mosk proposed a landmark new technique based on spatial light modulators that can compensate for the strong scattering effect, which is the wavefront shaping method to pre-compensate for the wavefront aberrations due to scattering by iteratively optimizing the wavefront of the input light. Meanwhile, the scattering light field manipulation has become possible. Additionally, light propagation in complex media is characterized by the transmission matrix. In just over a decade, scattering light field manipulation based on the wavefront shaping method has been widely adopted in many fields. For example, wavefront shaping methods can be employed to achieve light focusing beyond the diffraction limit by strongly scattering media and compensate for light scattering effects, further enabling high-resolution imaging at high transmission depths. In addition to the imaging field, scattering light field manipulation can transform the inherently harmful scattering medium into a variety of optical elements such as beam splitters, angular momentum generators and converters, and polarization controllers. In the field of communication, the scattering light field manipulation can increase the scattering light intensity received by an optical receiver and realize high-speed non-line-of-sight communication with lower power consumption. Additionally, mode selection of the outgoing field of a multi-mode fiber can be performed by scattering light field manipulation and the spectrum modulation of a nonlinear output field.

We focus on scattering light field manipulation, introduce the research progress in related fields and highlight the new applications of scattering light field manipulation in various research fields. Meanwhile, we first introduce the light field scattering characteristics, followed by the introduction of scattering and its light field modulation methods based on transmission matrix, feedback-based wavefront shaping, optical phase conjugation, and artificial intelligence-assisted wavefront shaping. Subsequently, the studies of the modulation methods of multiple degrees of freedom of the scattering light field, such as spatial (Figs. 1-3), polarization (Figs. 4-5), spectral (Figs. 6-8), energy (Fig. 9), and orbital angular momentum (Fig. 10) are presented. Finally, the existing applications in various fields of scattering light field manipulation are introduced. For example, the fluorescence-based transmission matrix is employed to achieve non-invasive imaging of biological tissues (Fig. 12). Orbital angular momentum communications in a complex environment are realized by exploiting the transmission matrix method (Fig. 18). Manipulation of nonlinear scattering optical field is achieved by adopting the transmission matrix method (Fig. 22). Scattering compensation of entangled photon pairs is performed by optimizing the pump wavefront (Fig. 24). Discrete Fourier transform can be achieved by utilizing the transmission matrix method (Fig. 27).

In summary, we introduce in detail the manipulation methods of each degree of freedom of the scattering light field, and the latest progress of the scattering light field manipulation in various fields, such as imaging, optical communication, nonlinear optics, quantum optics, optical sensing, integrated optics, and optical computing. Although scattering light field manipulation has made great progress, there are still some limitations to be broken through. 1) The energy utilization of scattering light is low with only part of the fully modulated scattering field. 2) The modulation speed is slow, and real-time scattering light field manipulation should be realized under dynamic scenarios. 3) It is difficult to modulate multiple physical quantities simultaneously, and most of the scattered light modulation can only realize the manipulation of a single physical quantity. With the further development of optimization algorithms, artificial intelligence, and modulation devices, scattering light field manipulation will move towards more precision, higher resolution, and deeper detection depth. The high degree of freedom brought by the combination of scattering light field manipulation and strong scattering media will also provide new solutions for the development of new optical components in the future. We believe that the further development of scattering light field manipulation will lead to many new applications.