Imaging and Sensing via Plasmonic Nanohole Resonances: Quantitative Analysis and Numerical Inversion

以亚波长空穴为图案的等离子体结构可以诱导各种类型的共振，从而导致所谓的超光传输（EOT）和在空穴附近的强局域光场。这种显著的现象在生物和化学传感、光学透镜和其他新型光学器件中有着重要的应用。该项目将研究从这些等离子体结构产生的成像和传感问题中产生的基本数学和计算问题。具体而言，该项目将开发分析和计算工具，以有效和创新的方式解决潜在的逆问题。该项目的成果将为实验工作者提供用于生化传感的纳米等离子体结构应用的基本数学工具，并为超分辨率成像提供新的途径。该项目还将为研究生和本科生提供跨学科的应用数学训练和研究经验。该项目将解决等离子体纳米孔共振的数学研究及其在成像和传感中的应用中的关键科学挑战。首先，基于边界积分方程方法、渐近分析和gohberg - signal理论的分析工具将用于表征等离子体纳米孔用于生化传感时的光谱灵敏度。此外，为了加速相关逆光谱问题的求解，将设计高效的有限元-边界积分方程特征解，以解决潜在问题的多尺度特性带来的重大计算挑战。最后，在等离子体纳米空穴共振研究的推动下，研究小组提出了一种新的超分辨率成像方式，即利用亚波长空穴谐振器产生的照明模式。新的照明模式允许探测成像样品的高空间频率成分，以打破衍射极限。在这方面，PI将研究数学建模，并为相应的反问题开发反卷积和优化类型的数值方法。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

Plasmonic structures patterned with subwavelength holes can induce various types of resonances, which lead to the so-called extraordinary optical transmission (EOT) and strongly localized optical field near the hole apertures. Such remarkable phenomenon has found significant applications in biological and chemical sensing, optical lenses, and other novel optical devices. This project will examine the fundamental mathematical and computational issues arising from the imaging and sensing problems that arise from these plasmonic structures. Specifically, this project will develop analytical and computational tools to solve the underlying inverse problems in an efficient and innovative manner. The outcome of the project will provide experimentalists with essential mathematical tools in applications of nano-plasmonic structures for biochemical sensing and to provide new avenues for super-resolution imaging. This project will also provide interdisciplinary applied mathematics training and research experiences for both graduate and undergraduate students.The project will address key scientific challenges in the mathematical investigation of plasmonic nanohole resonances and their applications in imaging and sensing. First, analytical tools based upon a combination of boundary integral equation approach, asymptotic analysis, and the Gohberg-Sigal theory will be developed for characterization of spectral sensitivity when plasmonic nanoholes are used in biochemical sensing. In addition, in order to accelerate the solution of related inverse spectral problems, efficient finite element-boundary integral equation eigensolvers will be designed to address the significant computational challenges brought by multiscale nature of the underlying problems. Finally, motivated by the studies of plasmonic nanohole resonances, the PI proposes a new super-resolution imaging modality by using illumination pattern generated from a collection of subwavelength hole resonantors. The new illumination pattern allows for probing the high spatial frequency component of the imaging sample in order to break the diffraction limit. In this regard, the PI will investigate the mathematical modeling, and develop deconvolution and optimization type numerical approaches for the corresponding inverse problems.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.