Discrete Approximation of Topologically Protected Modes in Magneto-Optical Media

Abstract

Topologically protected waves in the linearly polarized Maxwell's equations with gyrotropic, magneto-optic media were studied a decade ago both computationally and experimentally. This paper develops a robust tight-binding model for this system that makes careful use of Wannier function representations. The model provides very good approximations to the underlying band structure. When solved on a semi-infinite strip, it produces exponentially localized edge modes whose corresponding eigenvalues span the frequency band gaps. A set of coupled differential equations are derived which allows one to find how the electromagnetic field propagates unidirectionally, without backscatter from defects. Furthermore, the discrete model predicts topologically protected edge modes with nontrivial Chern number which are consistent with direct simulation.

References in corpus (5)

• Topological Photonics
• Reflection-Free One-Way Edge Modes in a Gyromagnetic Photonic Crystal
• Analogs of quantum Hall effect edge states in photonic crystals
• Exponential localization of Wannier functions in insulators
• Tight-binding methods for general longitudinally driven photonic lattices -- edge states and solitons