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.