自2016年諾貝爾物理學獎頒給拓撲絕緣體的研究以來，這個領域在固態物理學界引起了大量的關注。拓撲絕緣體的研究不僅在凝聚態物理學中有廣泛的應用，而且在光子系統中也表現出卓越的性能。近年來的拓撲研究中有重大突破，提出了新的性質和應用，例如邊緣態和自旋極化。由於光子系統的能帶易於控制，因此在拓撲物質的研究中起著關鍵的作用。光子系統中的拓撲概念被用來描述物體在連續變化中仍能保持其能帶的拓撲完整性，這已經成為一個不可或缺的自由度。本篇論文通過谷霍爾理論模型和有限時域差分法(FDTD)的數值模擬方法研究了介電質拓撲絕緣體的拓撲性質，探討邊緣態的各種性質，與以其製成的共振腔對於缺陷的表現。這些結果對於深入理解光子拓撲物質的機制具有重要意義，並為拓撲光子態的應用提供了新的思路。這些研究可為未來量子計算、量子通信和光電器件等領域的應用提供了新的可能性。

Since the awarding of the 2016 Nobel Prize in Physics for research on topological insulators, this field has attracted a great deal of attention in the solid-state physics community. The study of topological insulators not only has broad applications in condensed matter physics, but also exhibits excellent performance in photonic systems. Recent breakthroughs in topological research have revealed some properties and applications, such as edge states and spin polarization. Due to the ease of controlling the energy bands in photonic systems, they play a key role in the study of topological materials. The concept of topology in photonic systems is used to describe how an object can maintain the topological properties of its energy bands during continuous changes, which has become an indispensable degree of freedom. This paper studies the topological properties of dielectric topological insulators of the Valley Hall model through the numerical simulation method of Finite-Difference Time-Domain (FDTD), explores various properties of edge states, and the performance of resonant cavities made from them with or without defects. These results are of great significance for a deep understanding of the mechanisms of photonic topological insulators and provide new ideas for the application of topological photonic states. These studies offer new possibilities for future applications in the fields of quantum computing, quantum communication, and optoelectronic devices.

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