拓撲相變和拓撲物質的研究自2016年獲得諾貝爾物理學獎後引起了固態物理學界的廣泛關注。這些研究的目標是探索物質能帶中的拓撲性質及其在物理現象中的應用，為我們揭示了拓撲在現代物理學中的重要地位。拓撲物質的研究廣泛應用於凝聚態物理學中，也在光子系統中有優異的表現。近年來，科學家們在拓撲的研究中取得了重要突破，並提出了一些令人驚訝的性質和應用，如邊緣態和自旋極化。光子系統因其能帶容易操控，在拓撲物質的研究中發揮著關鍵作用。而光子系統中的拓撲概念用於描述物體在連續變化中仍能保持其能帶之拓撲完整性的特性，並且成為一個不可或缺的自由度。本篇論文通過自旋霍爾與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與表面電漿光子拓撲絕緣體的拓撲性質，並提出了有限離散倒空間晶格陳數FDTD計算方法來確定結構的拓撲特性。並探討了不同激發方式如hard/soft source及偽自旋相位與激發點相對位置，對不同拓撲絕緣體其陳數的影響。這些結果對於深入理解陳數於光子拓撲物質和拓撲相變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。

The research of topological phase transitions and topological phase of matter has drawn significant attention in the field of solid-state physics with the award of the 2016 Nobel Prize in Physics. The study of topological matter has found extensive applications in condensed matter physics and has shown remarkable performance in photonic systems. In recent years, scientists have made important breakthrough in topological research and discovered surprising properties and applications such as edge states and spin polarization. Photonic systems, known for their manipulability of band structures, play a critical role in the study of topological matter.
This paper investigated the topological properties of dielectric and surface plasmon photonic topological insulators using the spin Hall and valley Hall theoretical models, along with the numerical simulation method of finite-difference time-domain (FDTD). It proposed a finite-discrete reciprocal lattice Chern number FDTD calculation method to determine the topological characteristics of the structures. The influence of different excitation methods such as hard/soft sources and pseudo-spin phases, as well as the relative positions of excitation points, on the Chern number of various topological insulators is explored. These findings hold significant importance for a deeper understanding of the mechanisms of Chern numbers in photonic topological matter and topological phase transitions, providing new insights for the application of topological photonic states. These studies open up new possibilities for future applications in fields such as quantum computing, quantum communication, and optoelectronic devices.

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