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

通过等离子体纳米孔共振成像和传感：定量分析和数值反演

• 批准号: 2011148
• 负责人: Junshan Lin
• 金额: $ 22.15万
• 依托单位: Auburn University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2020
• 资助国家: 美国
• 起止时间: 2020-09-01 至 2024-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2011148&HistoricalAwards=false
• 关键词: Imaging; Sensing; via; Plasmonic; Nanohole

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.

在等离子体结构中引入亚波长孔可以引起各种类型的共振，从而产生所谓的非寻常光透射（EOT）和孔附近的强局域光场。这种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所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人员提供用于生物化学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培训和研究经验。该项目将解决等离子体纳米孔共振及其在成像和传感中的应用的数学研究中的关键科学挑战。 首先，分析工具的基础上结合边界积分方程的方法，渐近分析，和Gohberg-Sigal理论将开发用于表征光谱灵敏度时，等离子体纳米孔用于生化传感。此外，为了加速相关的逆谱问题的解决方案，高效的有限元边界积分方程特征解算器将被设计来解决潜在问题的多尺度性质所带来的重大计算挑战。最后，受等离子体纳米孔共振研究的启发，PI提出了一种新的超分辨率成像模式，通过使用从亚波长孔共振器的集合产生的照明图案。新的照明模式允许探测成像样品的高空间频率分量，以突破衍射极限。在这方面，PI将研究数学建模，并为相应的逆问题开发反卷积和优化类型的数值方法。该奖项反映了NSF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。

项目成果

Dirac Points for the Honeycomb Lattice with Impenetrable Obstacles

• DOI: 10.1137/22m1505116
• 发表时间: 2022-06
• 期刊: SIAM J. Appl. Math.
• 作者: Wei Li;Junshan Lin;Haifeng Zhang

Scattering resonances for a three-dimensional subwavelength hole

三维亚波长孔的散射共振

• DOI: 10.1007/s42985-021-00111-w
• 发表时间: 2021
• 期刊: SN Partial Differential Equations and Applications
• 作者: Fatima, Maryam;Lin, Junshan.
• 通讯作者: Lin, Junshan.

Sensitivity of resonance frequency in the detection of thin layer using nano-slit structures

使用纳米狭缝结构检测薄层时共振频率的灵敏度

• DOI: 10.1093/imamat/hxaa041
• 发表时间: 2020
• 期刊: IMA Journal of Applied Mathematics
• 影响因子: 1.2
• 作者: Lin, Junshan;Oh, Sang-Hyun;Zhang, Hai
• 通讯作者: Zhang, Hai

Mathematical theory for topological photonic materials in one dimension

• DOI: 10.1088/1751-8121/aca9a5
• 发表时间: 2021-01
• 期刊: Journal of Physics A: Mathematical and Theoretical
• 作者: Junshan Lin;Hai Zhang

Mathematical Theory for Electromagnetic Scattering Resonances and Field Enhancement in a Subwavelength Annular Gap

亚波长环形间隙中电磁散射共振和场增强的数学理论

• DOI: 10.1137/22m1508881
• 发表时间: 2023
• 期刊: Multiscale Modeling & Simulation
• 影响因子: 1.6
• 作者: Lin, Junshan;Lu, Wangtao;Zhang, Hai
• 通讯作者: Zhang, Hai