基于表面积分方程的二维非线性材料电磁建模研究

Two dimensional (2D) materials, including graphene, transition-metal dichalcogenide, phosphorene, silicone, and germanene, exhibit remarkable linear and nonlinear optical properties that are not attainable in bulk ones. They show great potentials to substitute for traditional silicon and III-V compound semiconductors and to become widely-adopted functional materials in emerging electromagnetic, optical, and optoelectronic devices. Until now, no accurate, fast, efficient, and universal solver exists for simulating nonlinear electromagnetic responses from 2D materials in both academia and industry. This project aims at studying integral equation and its fast algorithms named rotated mixed-form fast multipole algorithm (R-MFFMA) to model nonlinear electromagnetic processes from 2D materials. Based on this model, the nonlinear properties of 2D material will be explored and the physical mechanisms of nonlinear light-matter interaction will be studied in detail. This project will have great significance in the investigation of nonlinear electromagnetic algorithms, physical understanding of nonlinear optics in 2D materials, extended applications of integral equation and its fast solvers, and training innovative talents in multidisciplinary fields. Moreover, the project will lay a solid theoretical foundation on the industrial development of 2D materials in China.

二维材料如石墨烯、过渡金属硫属化合物、黑磷、硅烯、锗稀等，由于具有块体材料不可获得的线性和非线性的电磁和光学特性，被认为有巨大潜力替代传统的硅和三五族半导体材料，成为未来电磁、光及光电器件中广泛应用的功能材料。目前，无论是学术界还是工业界，缺乏对二维材料非线性电磁响应模拟的精确、快速、高效和通用的求解器。该项目拟采用积分方程及其旋转混合模式快速多极子算法，建模二维材料非线性电磁响应。基于建立的模型，深入研究二维材料的非线性电磁特性及波-物非线性互作用机理。该项目对非线性电磁学的计算方法研究、二维材料非线性光学的物理机制理解、积分方程及快速算法的拓展应用及复合型人才培养有重大意义。该项目也为我国二维材料的产业化发展奠定了坚实的理论基础。

二维材料如石墨烯，过渡金属硫属化合物，黑磷，硅烯，锗稀等，由具有块体材料不可获得的线性和非线性的电磁和光学特性，被认为有巨大潜力替代传统的硅和三五族半导体材料，成为未来电磁、光及光电器件中广泛应用的功能材料。目前，无论是学术界还是工业界，缺乏对二维材料非线性电磁响应模拟的精确、快速、高效和通用的求解器。项目基于表面积分方程方法开发了二维材料的线性及非线性电磁特性求解器。该求解器对二维材料的电磁建模拥有天然的算法优势，同时弥补了商业软件无法考虑二维材料非线性极化率的张量特性及非局域特性等不足，实现对二维材料的线性及非线性电磁响应的准确仿真。项目研究了二维材料的电磁特性及波-物作用机制，实现了利用结构对称性破坏对贵金属表面二次谐波进行增强。探索了高次谐波生成的物理机制，及如何控制线性及非线性散射波的幅度、极化、波前和方向性。设计了石墨烯加载的线性电可调极化器及基于过渡金属硫属化合物超表面结构生成幅度及相位可调的径向极化，方位角极化及涡旋光束等非线性可结构化波。该项目对非线性电磁学的计算方法研究、二维材料非线性光学的物理机制理解、积分方程及快速算法的拓展应用有重大意义。该项目也为二维材料的产业化发展提供了理论基础及数值仿真工具。