Scattering of waves, e.g., light, due to medium inhomogeneity is ubiquitous in physics and is considered detrimental for many applications. Wavefront shaping technology is a powerful tool to defeat scattering and focus light through inhomogeneous media, which is vital for optical imaging, communication, therapy, etc. Wavefront shaping based on the scattering matrix (SM) is extremely useful in handling dynamic processes in the linear regime. However, the implementation of such a method for controlling light in nonlinear media is still a challenge and has been unexplored until now. We report a method to determine the SM of nonlinear scattering media with second-order nonlinearity. We experimentally demonstrate its feasibility in wavefront control and realize focusing of nonlinear signals through strongly scattering quadratic media. Moreover, we show that statistical properties of this SM still follow the random matrix theory. The scattering-matrix approach of nonlinear scattering medium opens a path toward nonlinear signal recovery, nonlinear imaging, microscopic object tracking, and complex environment quantum information processing.

同步辐射实验方法在研究材料的结构和物性上具有独特的优势，然而，要实现同步辐射原位高温条件，尤其温度高于2 000 K以上，对很多实验方法来说还是一个挑战。激光加热方法可以实现快速、微区的极端高温条件，已经成为高温物性研究的重要工具。上海同步辐射光源在极端高温研究领域，例如高熵合金、涡轮叶片、航空材料等还欠缺相关的原位高温条件，因此，研制了一种便携式连续激光加热装置，利用光谱仪获得样品的热辐射谱，并通过黑体辐射方法拟合出样品的温度梯度和温度稳定性。利用该装置成功实现真空环境中钨片的快速熔化（熔点约3 695 K），并在上海同步辐射光源表面衍射线站获得了1 608 K原位条件下的MoS₂和CTAB-MoS₂材料X射线衍射图谱。本工作所研制的激光加热方法拓展了上海光源在极端条件下的实验能力，为极端高温条件下的材料物性研究提供了重要手段。

Orbital angular momentum (OAM) is a fundamental physical characteristic to describe laser fields with a spiral phase structure. Vortex beams carrying OAMs have attracted more and more attention in recent years. However, the wavefront of OAM light would be destroyed when it passes through scattering media. Here, based on the feedback-based wavefront shaping method, we reconstitute OAM wavefronts behind strongly scattering media. The intensity of light with desired OAM states is enhanced to 150 times. This study provides a method to manipulate OAMs of scattered light and is of great significance for OAM optical communication and imaging to overcome complex environment interference.

Based on nonlinear wave mixing, we experimentally propose a scheme for directly generating optical orbital angular momentum (OAM) by a spirally structured fundamental wave interacting with a nonlinear medium, in which the nonlinear susceptibilities are homogenous. In the experiment, the second-harmonic generation of a fundamental wave carrying positive (negative) integers and fractional OAM states was investigated. This study presents a convenient approach for dynamic control of OAM of vortex beams, which may feature their applications in optical manipulation and optical communication.

Recently, the perfect vector (PV) beam has sparked considerable interest because its radius is independent of the topological charge (TC), which has demonstrated special capabilities in optical manipulation, microscopy imaging, and laser micromachining. Previous research about the generation and manipulation of such PV beams only focuses on the linear optical fields. Therefore, the generation of nonlinear PV beams is still lacking. Here, we propose a dual waveband generator to simultaneously generate the PV beams in linear and nonlinear wavebands. In our experiment, PV beams with different polarization states are realized. It is proved that the polarization states of the generated PV beams can be flexibly adjusted by changing the axis direction of a half wave plate. The experimental results show that the radii of the generated PV beams are equal and independent of the TCs. With proper alteration of the nonlinear crystals, this approach could be further extended to other nonlinear processes, such as sum-frequency generation and difference-frequency generation.

The generation and manipulation of optical vortices are of fundamental importance in a variety of promising applications. Here, we develop a nonlinear optical paradigm to implement self- and cross-convolution of optical vortex arrays, demonstrating the features of a vortex copier and regenerator. We use a phase-only spatial light modulator to prepare the 1064 nm invisible fundamental light to carry special optical vortex arrays and use a potassium titanyl phosphate crystal to perform type II second-harmonic generation in the Fourier domain to achieve 532 nm visible structured vortices. Based on pure cross-convolution, we succeed in copying arbitrary-order single vortices as well as their superposition states onto a prearranged array of fundamental Gaussian spots. Also, based on the simultaneous effect of self- and cross-convolutions, we can expand the initial vortex lattices to regenerate more vortices carrying various higher topological charges. Our presented method of realizing an optical vortex copier and regenerator could find direct applications in optical manipulation, optical imaging, optical communication, and quantum information processing with structured vortex arrays.