Photonic Topological Insulators: A Beginner's Introduction [Electromagnetic Perspectives]
Dia'aaldin Bisharat, Robert Davis, Yun Zhou, Prabhakar Bandaru, Dan Sievenpiper
Abstract
The control and manipulation of electromagnetic (EM) waves has reached a new level with the recent understanding of topological states of matter. These metamaterials have the potential to revolutionize many areas in traditional EM design, from highly robust cavities to small-footprint waveguides. Much of the past literature has been on the cutting edge of condensedmatter physics, but there are now ample opportunities to explore their usage for practical microwave and optical devices. In this tutorial, we have given an overview of the concepts, mathematics, and implementations of PTIs. The central idea that relates the topics together is the geometric phase, which lies at the heart of both theory and physical realization. This concept is readily applied to a 2D PhC, which is a simple platform to engineer topological modes. Computations of the Berry curvature, Chern number, and other topological invariants for a given design illuminate how the geometric phase influences the system and can be readily calculated with numerical tools to aid in design.