Applied Mathematics Seminar

Speaker: Junshan Lin
Subject: 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. In particular, for a finite one dimensional symmetric photonic crystal with a defect, it is shown that the near bound-state resonances converge to the point spectrum of the infinite structure with an exponential rate when the number of periods increases. Such an exponential decay rate also holds for the Schrodinger operator with a potential function that is a low-energy well surrounded by a thick barrier. We introduce a general method that is suitable for the Schrodinger operator in both low and high dimensions, and has the potential to be extended to the photonic case.