Scattering Resonances for Photonic Structures and Schrodinger Operators
Speaker: Dr. Junshan Lin from the Department of Mathematics and Statistics, Auburn University Thursday, Febr. 12, 3.30 pm, room DM 100.
Title: Scattering Resonances for Photonic Structures and Schrodinger Operators
Abstract: 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 Fadil Santosa in University of Minnesota.