Scattering medium is a substance commonly found in nature such as turbid atmosphere, smoke, and biological tissues. Coherent light beams propagating through scattering media will be disrupted due to random scattering effects. The wavefront will be destroyed, and the transmission direction will deviate from the original input direction and becomes chaotic. Random scattered light interference will form a particle-like intensity pattern, known as an “optical speckle”. In multi-mode fibers, due to mode dispersion and inter-modal interference, a similar scattering distribution will be formed. Thus, multi-mode fibers are also regarded as a special class of scattering medium.

Due to the scattering phenomenon, it is difficult to maintain the original spatial distribution of the light beam, and the energy is exponentially attenuated with the increasing penetration depth, which greatly limits the applications of advanced technologies such as optical tweezers, optical communications, and biomedicine in a strong scattering environment. However, in 1990, Freund proposed that light scattering in static scattering media is a deterministic linear process, a property that reveals the possibility of reutilizing the energy of the scattered light field. Due to the existence of a deterministic response relationship between incident and scattered lights, suitable input conditions can lead to the formation of the desired distribution of the output light field after passing through the scattering medium. In 2007, Vellekoop and Mosk put forward the concept of optical wavefront shaping whereby optimizing the distribution of the incident light wavefront leads to an in-phase coherent superposition of the light field at the target point, which thus achieves a focused light field that reaches the diffraction limit after the scattering medium. The focusing spot that reaches the diffraction limit is realized after the scattering medium. The emergence of wavefront shaping technology makes it possible to effectively employ the scattered light, thereby overcoming the limitations of the scattering problem for the above optical applications.

With the development of modulation devices and computer technology in recent years, increasingly more wavefront shaping methods have been applied to scattering medium focusing, mainly including iterative optimization methods, transmission matrix methods, and phase conjugate methods. The focusing quality and speed have been continuously improved, and exciting progress has been made in the applications based on this. By adopting wavefront shaping techniques, precise light manipulation through strong scattering media has become possible. The intensity of fluorescence excitation in deep biological tissues can be greatly enhanced to expand the penetration depth of fluorescence imaging. Additionally, even the scattering media can be adopted to improve the numerical aperture of the focusing objective lens and thus achieve focusing beyond the diffraction limit. Thanks to the wavefront shaping technology, the scattering medium has become a new type of optical device with the ultra-high degree of freedom of operation, which can realize some special applications that cannot be accomplished by ballistic light, such as functional modules in optical computing, super-resolution imaging, and directional energy delivery. Therefore, it is necessary to sort out the representative studies of wavefront shaping-based optical focusing technology for scattering media in recent years and the outlook on the future development direction.

Focusing through turbid medium based on wavefront shaping technique is mainly divided into three technical routes of the iterative optimization method, transmission matrix method, and phase conjugate method, with the basic principles shown in Fig. 1. Among them, the iterative optimization method relies on the set feedback physical quantities, improves the evaluation value by changing the input conditions, and finally realizes the light focusing at the target position. Meanwhile, this method plays an important role in complex optimization scenarios and dynamic scattering media. Currently, the most employed ones are intelligent optimization algorithms (Fig. 3) and neural network algorithms (Fig. 4). Diverse feedback signals further broaden the applications of this method (Fig. 7). On the other hand, the transmission matrix method relies on the measurement of the transmission matrix to establish a correlation between the input optimized wavefront and the scattered light field on the target focusing plane. Additionally, it employs the operation of time inversion to calculate the optimized wavefront for achieving focusing, which provides a powerful theoretical research tool for studying the mechanism of light transmission and focusing in scattering media (Fig. 8). By depending on the physical quantities of interest, various types of transport matrices have been developed (Figs. 9-11) and adopted in a variety of fields such as energy transport, optical communication, and particle manipulation (Figs. 12-13). The phase conjugate method relies on the light source placed at the target focusing position and utilizes the reversibility principle of the optical path to solve the phase of the received scattering light field. The utilization of the conjugate phase as the input condition can achieve focusing, which requires the fewest number of calculations and is currently applied to internal focusing of dynamic scattering media (Figs. 15-16).

Till now, scattering medium focusing based on wavefront shaping has successfully realized dynamic focusing inside or through the scattering medium, providing powerful technical support for applications including optical manipulation, long-distance communication, and deep biological tissue imaging. In future development, researchers should further improve the optical field transport mechanism inside the scattering medium, build a more refined physical model, and explore more dimensions of controllable physical quantities. Finally, broader scattering focusing and optical field modulation can be achieved, with the application scope of wavefront shaping technology in optics expanded. Additionally, combined with emerging optical computing, artificial intelligence, and other technologies, it is expected to achieve more compact optical path structure and faster and more efficient optimization. In conclusion, under the traction of cutting-edge exploration and the impetus of technological innovation, the scattering medium focusing technology based on wavefront shaping will continue to break through the limitations of traditional optical scattering and provide brand-new possibilities for optical applications in strong scattering environments.