Evolution and reversal of topological edge states at optical frequencies from a two-dimensional photonic crystal

Abstract

The nonreciprocal, defect-immune and backscatter suppression of topological waveguides will play an important role in future optical communication systems. For a long time, researchers have studied such waveguides through magneto-optical media. On one hand, for gyromagnetic media, they have a large magneto-optical effect, but also have large losses at high frequencies; on the other hand, for gyroelectric media, they have small losses at optical frequencies, but their magneto-optical effect is too small. In this paper, we study a magneto-optical photonic crystal (PC) based on a metamaterial design with gyroelectric media, ordinary media and metal. The PC not only can work at optical frequencies, but it also has a large magneto-optical effect. From the PC, we have found some unique properties of non-trivial topological edge states. Different from the ordinary topological edge states that result from the broken band gap from the band degeneration, the topological edge states in the current structure can directly occur in the lowest band gap. For a small magneto-optical effect, the topological edge state and ordinary edge state can coexist in the lowest gap. Through adjusting the external magnetic field, the first trivial band leaves off the zero-frequency point at the center of the first Brillouin zone and becomes non-trivial. With the increase of the external magnetic field, the first and second bands undergo a process of separation–intersection–separation. Following the process, the reversal of modes and Chern number from the two bands occurs. The direction of the topological edge states have also been reversed by the band reversal. The design in this paper has not only realized a topological waveguide working at optical frequencies, but it has also achieved dynamical control of topological edge states.