Abstract: Edge states are important in stably transmitting information and energy. We investigate edge states in full PDE models of photonic crystals with sharp interfaces, 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. Our rigorous analysis confirms the heuristic effective theory results. 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.

 

 

Host: Junshan Lin