Magnetic topological photonic crystals

Abstract

In this paper, I discuss the motivation and theory behind Photonic Topological Insulators. In particular, I focus on using gyromagnetic materials such as microwave ferrites and Indium Antimonide (InSb) to create a Chern Photonic Topological Insulator. By breaking Time Reversal Symmetry, one is able to lift quadratic degeneracies in the bandstructure of photonic crystals, which if it results in a non-trivial Gap Chern Number, implies the existence of robust one-way edge states that suppress backscattering. I use ANSYS HFSS to compute the band structure, verifying the data by comparing it to Wang et al’s work in 2008. I also use ANSYS HFSS and MATLAB to compute the Berry Curvature Plot across the second frequency band, as well as the Chern Number (also known as the TKNN number), but the results are invalid due to a lack of convergence on a proper value, which was cross-referenced once again with Wang et al’s work. I then utilise the theory of Effective Hamiltonians to prove a non-trivial Gap Chern Number of the second band, thus showing the presence of a robust one-way edge state in the crystals through breaking of Time Reversal Symmetry.