Back to Departmental Colloquium: Spring 2022
Departmental Colloquium
Date: Monday, Jan 10, 2022
Time: 4:00PM
Location: JWB 335
Junshan Lin
Auburn University
Title |
Electromagnetic Wave in Novel Materials and Devices: Mathematical Analysis and Numerical Computation |
Abstract |
The advance in fabrication technology allows for the manipulation of electromagnetic waves at various scales and with high efficiency by novel materials and devices. The significant applications of these materials and devices in physics and engineering have driven the need for mathematical studies to guide their experimental designs. In particular, rigorous mathematical theories need to be established for new types of wave-matter interactions and efficient computational methods need to be developed for the modeling of wave phenomena in complex media. Furthermore, the mathematical problems arising from the design of materials/devices and their realistic applications in many cases are inverse problems or optimization problems. In this talk, I will exemplify how mathematical research contributes to these aspects by two research topics. The first topic is resonant wave scattering in nano-hole structures. I will present quantitative mathematical theories for various resonant scattering phenomena and fast numerical methods for their computational modeling. I will also introduce the mathematical framework for the application of resonances in biosensing and imaging. The second topic is on topological photonic materials. I will present mathematical theory to quantify the Dirac point and the interface mode induced from the topological index for one-dimensional photonic structures with both time-reversal and inversion symmetry. The studies for the two-dimensional photonic structures and related inverse design problems will also be discussed. |
Computational Mathematics