Computational & Applied Mathematics (CAM) Seminar

Time: 3:15pm, Oct. 31 (周一下午 3:15)

Location: Conference Room 4, Jin Chun Yuan West Bldg.
(近春园西楼二楼第四会议室)

Title: Electromagnetic waves in honeycomb structures

Speaker: Yi Zhu,（朱毅，周培源中心）

Abstract: In the past two decades, the words "Graphene" and "Topological Insulator" are the most popular scientific terminologies which attract so many attentions in physics, chemistry, engineering and mathematics. Stimulated by their success, analog phenomena in other systems have been investigated. In this talk, we discuss the electromagnetic waves of Maxwell equations in media with honeycomb symmetry. Different form many photonic setups in which the Schr\"odinger equation is used, we work on the Maxwell equation directly. We first show the existence of the Dirac cones in the band structure of the Maxwell equation. This is an analogy to the material graphene. We then discuss ``edge states", electromagnetic modes which propagate parallel to a line defect in the bulk structure (a domain wall potential) and are localized transverse to it. We focus, in particular, on edge states which are topologically protected. We also discuss the bi-directional and uni-directional propagations of the electromagnetic waves with breaking different symmetries. This gives a complete description of the photonic analogy to the topological insulator. This talk is based on the joint work with Michael I. Weinstein at Columbia University and James Lee-Thorp in Courant Institute of Mathematical sciences.