OP: Scattering and Imaging of Subwavelength Nanostructures: Asymptotics and Algorithms

纳米光学是指研究纳米材料或器件与光学光相互作用时的显著性质和现象。它是一门蓬勃发展的学科，为现代科学技术开辟了广泛的可能性。随着创新的图案化技术的出现，允许以纳米精度雕刻材料，目前有望制造出能够以高速度和高效率完成传统光学无法达到的任务的光学器件。本项目致力于纳米结构的光学散射和成像。理论工作的结果将为理解亚波长纳米结构中新型的光-物质相互作用提供进展。此外，计算框架将提供廉价、快速和准确的光波在这种微小结构中传播的建模，并增强近场光学成像技术。此外，正向建模和反向成像工具的快速实现也将为具有与光学光相互作用的所需性质的纳米器件的设计提供现实指导。该项目专注于研究基本的数学问题，并为由纳米结构的光波散射和成像而产生的新的重要问题开发计算方法。这包括对金属纳米结构中超高场增强的数学研究及其通过反向散射实现的超分辨率成像。模型问题的技术焦点是复杂和多尺度介质中的麦克斯韦方程。基于边界积分方程法和渐近分析技术相结合的新的分析工具将被开发用于严格研究纳米孔/孔中的严格限制的光波场。在计算上，为了解决孔径大小和辐射波长之间的极大尺度差异带来的重大挑战，将设计快速和高阶水平和垂直模式匹配的数值格式来模拟纳米结构中的波传播。最后，基于逆散射理论的高效数值算法将被应用于多尺度亚波长结构的成像和突破衍射极限。

Nano-optics refers to the study of the remarkable properties and phenomena associated with nano-scale materials or devices when interacting with optical light. It is a vigorously growing discipline that has opened up a broad range of possibilities for modern science and technology. With the advent of innovative patterning techniques allowing for the sculpting of materials with nanometer precision, it is presently promising to fabricate optical devices that can perform tasks at scales unattainable with conventional optics, and with great speed and efficiency. This project is devoted to the optical scattering and imaging of nano-structures. The outcome of the theoretical work will provide advances in the understanding of new types of light-matter interactions in subwavelength nano-structures. In addition, the computational frameworks will provide inexpensive, fast, and accurate modeling of optical wave propagation in such tiny structures and enhance near-field optical imaging techniques. Furthermore, the fast implementations of forward modeling and inverse imaging tools will also provide realistic guidance for the design of nano devices with the desired properties in their interactions with the optical light.The project focuses on examining fundamental mathematical issues and developing computational methods for new and important classes of problems arising from the optical wave scattering and imaging of nano-structures. This consists of mathematical studies of extraordinary field enhancement in metallic nano-structures and their super-resolution imaging via inverse scattering. The technical focus of the model problems is on Maxwell's equations in complicated and multi-scale media. New analytical tools based upon a combination of the boundary integral equation approach and asymptotic analysis techniques will be developed for rigorous studies of the tightly confined optical wave fields in nano apertures/holes. Computationally, in order to address the significant challenges brought by the extreme scale difference between the aperture size and the wavelength of radiation, fast and high-order horizontal and vertical mode matching numerical schemes will be designed for the simulation of wave propagations in nano-structures. Finally, efficient numerical algorithms based on the inverse scattering theory will be applied for imaging multi-scale subwavelength structures and for breaking the diffraction limit.