Mathematical Physics and Harmonic Analysis Seminar

Date: April 12, 2024

Time: 1:50PM - 2:50PM

Location: BLOC 302

Speaker: Wei Li, DePaul University

Title: Edge States on Sharply Joined Photonic Crystals

Abstract: Edge states are important in transmitting information and transporting energy. We investigate edge states in continuous models of photonic crystals with piecewise constant coefficients, which are more realistic and controllable for manufacturing optical devices. First, we show the existence of Dirac points on honeycomb structures with suitable symmetries. Then we show that when perturbed in two appropriate ways, the perturbed honeycomb structures have a common band gap, and when joined along suitable interfaces, there exist edge states which propagate along the interfaces and exponentially decay away from the interfaces. The main tools used are layer potentials, asymptotic analysis, the Gohberg-Sigal theory and Lyapunov-Schmidt reductions.

This is joint work with Junshan Lin, Jiayu Qiu, Hai Zhang.