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

纳米光学是指研究纳米尺度材料或器件与可见光相互作用时的显着特性和现象。它是一个蓬勃发展的学科，为现代科学技术开辟了广泛的可能性。随着允许以纳米精度雕刻材料的创新图案化技术的出现，目前有希望制造能够以传统光学器件无法达到的规模执行任务的光学器件，并且具有很高的速度和效率。该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，计算框架将为此类微小结构中的光波传播提供廉价、快速和准确的建模，并增强近场光学成像技术。 此外，正向建模和逆向成像工具的快速实现也将为纳米器件的设计提供现实的指导，这些纳米器件在与可见光的相互作用中具有所需的特性。该项目侧重于研究基本的数学问题，并为纳米结构的光波散射和成像所产生的新的重要问题开发计算方法。这包括在金属纳米结构和它们的超分辨率成像通过逆散射非常场增强的数学研究。模型问题的技术重点是复杂多尺度介质中的麦克斯韦方程组。基于边界积分方程方法和渐近分析技术相结合的新的分析工具，将开发严格的研究在纳米孔径/孔的严格限制的光波场。在计算方面，为了解决孔径尺寸和辐射波长之间的极端尺度差异所带来的重大挑战，将设计快速和高阶水平和垂直模式匹配数值方案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成像多尺度亚波长结构和突破衍射极限。

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.