Reflection-Free One-Way Edge Modes in a Gyromagnetic Photonic Crystal

TLDR

Electromagnetic one‑way edge modes analogous to quantum Hall states can arise in photonic crystals beyond those with Dirac‑point band gaps. TM modes in a gyromagnetic photonic crystal map to electronic wave functions in a periodic electromagnetic field, so a nonzero Chern number below a gap guarantees one‑way edge modes; in a square‑lattice YIG crystal at microwave frequencies, strong time‑reversal breaking makes the effect readily observable. With realistic material parameters the edge modes occupy a 10 % band gap, and numerical simulations of a one‑way waveguide using this crystal achieve 100 % transmission across strong defects.

Abstract

We point out that electromagnetic one-way edge modes analogous to quantum Hall edge states, originally predicted by Raghu and Haldane in 2D photonic crystals possessing Dirac point-derived band gaps, can appear in more general settings. We show that the TM modes in a gyromagnetic photonic crystal can be formally mapped to electronic wave functions in a periodic electromagnetic field, so that the only requirement for the existence of one-way edge modes is that the Chern number for all bands below a gap is nonzero. In a square-lattice yttrium-iron-garnet crystal operating at microwave frequencies, which lacks Dirac points, time-reversal breaking is strong enough that the effect should be easily observable. For realistic material parameters, the edge modes occupy a 10% band gap. Numerical simulations of a one-way waveguide incorporating this crystal show 100% transmission across strong defects.