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.
