讲座题目：Scattering Resonances for Photonic Structures and Schrodinger Operators

主讲人：Dr. Junshan Lin (Auburn University, USA)

主持人：袁健华副教授

时　间：2014年6月19日（周四）上午9:30-10:30

地　点：主楼1214

主要内容：

Resonances are important in the study of transient phenomena associated with the wave equation, especially in understanding the large time behavior of the solution to the wave equation when radiation losses are small. In this talk, I will present recent studies on the scattering resonances for photonic structures and Schrodinger operators. I will begin with a study on the finite symmetric photoinc structure to illustrate the convergence behavior of resonances. Then a general perturbation approach will be introduced for the analysis of near bound-state resonances for both cases. In particular, it is shown that, for a finite one dimensional photonic crystal with a defect, the near bound-state resonances converge to the point spectrum of the infinite structure with an exponential rate when the number of periods increases. An analogous exponential decay rate also holds for the Schrodinger operator with a potential function that is a low-energy well surrounded by a thick barrier. The analysis also leads to a simple and accurate numerical approach to approximate the near bound-state resonances. This is a joint work with Prof. Fadil Santosa in University of Minnesota.

报告人简介：

Dr. Junshan Lin ，Department of Mathematics and Statistics, Department of Mathematics and Statistics。

Research Interests：

• Applied and numerical analysis, scientific computation

• Inverse and optimal control/design problems in partial differential equations

• Mathematical problems arising in wave propagation, particularly in optics, medical imaging and geophysical exploration

http://www.auburn.edu/~jzl0097