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.

散射矩阵是描述介质散射特性的重要参数，该参数对介质的理化特性敏感。为研究利用该参数对气溶胶进行识别及理化特性获取的可行性，设计并实验测量了聚α烯烃和氯化钠两种气溶胶样品的散射矩阵，讨论了二者矩阵元素的角度分布规律，并基于Mie散射理论，采用模板匹配的方法利用测量结果对聚α烯烃气溶胶的粒径分布进行了反演。结果表明通过矩阵元素的角度分布规律可以对两种气溶胶进行有效识别与区分，结合相关散射模型与反演方法还可以获得气溶胶的理化特性。该研究为气溶胶识别及其理化特性的获取提供了方法参考。

将适用于复杂系统各个节点电磁响应同步求解的电磁拓扑方法引入到配电网络雷电过电压问题的分析中。首先，给出了传输线网络的BLT方程及其元素构建方法；然后，通过一个复杂的配电网络对电磁拓扑的分析流程进行了详细说明，并重点展示了理想节点散射矩阵的求解步骤。结果表明：电磁拓扑方法可以应用在配电网络节点雷电过电压的分析中，其计算结果与CST的结果非常吻合，且耗时远远低于CST。

针对临近空间飞行器的黑障问题，根据模拟的RAM C-III飞行器周围的流场分布结果，计算了等离子体电子密度和碰撞频率，并根据其分布建立了非均匀的等离子体模型。在此基础上，利用散射矩阵方法分析了太赫兹波在等离子体中的传输特性随着等离子体密度、等离子体厚度、等离子体碰撞频率的变化以及外加磁场对传输特性的影响。结果表明，太赫兹波的传输损耗随着等离子体电子密度和等离子体厚度的增加而增加，而碰撞频率的增加会使得透射率先减小后增加。在外加磁场的作用下，左旋太赫兹波的传输特性会得到改善；而对于右旋太赫兹波，磁场的施加会引入吸收峰，并且随着磁感应强度的增加向高频方向移动。