## Mathematical Challenges for Wave Propagation in Nanostructures

- March 28, 2016
- 1:15 p.m.
- LeConte 312

## Abstract

Remarkable phenomenon would occur when light interacts with nanoscale devices. The development of innovative nano optical devices for applications in physics and engineering has presented new challenges and opportunities in applied and computational mathematics. In this talk, I will focus on two mathematical problems arising from the control of electromagnetic waves in engineered nanostructures. The first one concerns the extraordinary electric field enhancement in a metallic naogap. A rigorous mathematical theory is presented based on the study of the perfect electric conductor model. The upper and lower bounds on the enhancement factors are established. The second one is devoted to near-field imaging of nanostructures. We introduce a novel numerical method to break the so-called Rayleigh diffraction limit and obtain super-resolution images of locally perturbed surface profiles. The ongoing work along this research direction will also be discussed.