磁光材料柱構成的方形晶格中的光學量子反常霍爾態之操控

Abstract

本文以有限元素法來探討方形晶格光子晶體加入磁光材料後，是否具有由拓樸性質所產生單一行進表面態，藉由分析此結構之能帶結構和在不同材質介面產生之能帶，我們確定其在頻率大約在512太赫茲至534太赫茲時，具有一個單一行進表面態，除此之外，在頻率為516太赫茲時，我們使用線波源激發表面態和用理想導體作為阻礙展示表面態不受阻礙繞過雜質的特性。最後我們分別利用改變光子晶體柱中的介電常數和半徑來在不同的特徵模態上產生能帶對調，並利用貝里曲率和陳數字的計算，發現能帶對調會造成貝里曲率在各個被翻轉的能帶上改變，而光學量子反常霍爾態則沒有發生改變。

In this thesis, we use the finite element method to investigate whether there is a chiral edge state protected by the property of topology after adding a magneto-optical medium into a photonic crystal. We analyze the band structure of this system. We discover that there will be a chiral edge state during the frequency is set at the range from 512 THz to 534 THz. Furthermore, we use a line source as a stimulation of the chiral edge state and a perfect electric conductor as an obstacle to demonstrate the property of circumventing the obstacle at 516 THz. We also change the square-lattice rod’s permittivity and radius to generate a band inversion in different eigenmode respectively. We find that the Berry curvature will change under the band inversion by calculating the Chern number and the Berry curvature distribution. However, the photonic quantum anomalous Hall phase for our system remains the same.