Georgia Institute of Technology College of Sciences

Resonances are important in the study of transient phenomenaassociated with the wave equation, especially in understanding the largetime behavior of the solution to the wave equation when radiation lossesare small. In this talk, I will present recent studies on the scatteringresonances for photonic structures and Schrodinger operators. I will beginwith a study on the finite symmetric photoinc structure to illustrate theconvergence behavior of resonances. Then a general perturbation approachwill be introduced for the analysis of near bound-state resonances for bothcases. In particular, it is shown that, for a finite one dimensionalphotonic crystal with a defect, the near bound-state resonances converge tothe point spectrum of the infinite structure with an exponential rate whenthe number of periods increases. An analogous exponential decay rate alsoholds for the Schrodinger operator with a potential function that is alow-energy well surrounded by a thick barrier. The analysis also leads to asimple and accurate numerical approach to approximate the near bound-stateresonances. This is a joint work with Prof. Fadil Santosa in University ofMinnesota.