本研究設計並分析四種具有不同幾何排列的光子晶體單元結構（簡稱 PCS1 至 PCS4），透過 COMSOL Multiphysics 5.6 模擬其頻帶結構與模態分佈，探討結構對稱性與排列方式對拓樸性質與邊界態形成的影響。PCS1 為單一中心環狀孔洞，作為對照基準；PCS2 採單一環狀而四角切除設計，以誘導邊界模態局域化；PCS3 為四個環狀對稱四角排列結構，模擬多重耦合與邊界干涉行為；PCS4 也是四個環狀為中央集中排列，用以比較模態集中與對稱性破壞之差異。亦輔以 MATLAB 計算 札克相 與拓樸極化，進一步判斷各結構間之拓樸分類與性質變化。整體模擬結果呈現幾何排列對拓樸相位、邊界模態以及場分佈的顯著影響，提供一個簡潔直觀的幾何平台，作為深入理解光子晶體中拓樸性質起源與控制機制的理論基礎。;In this study, four photonic crystal unit cell structures with distinct geometric arrangements (denoted as PCS1 to PCS4) are designed and analyzed. Their band structures and mode distributions are simulated using COMSOL Multiphysics 5.6 to investigate the effects of structural symmetry and arrangement on topological properties and the formation of edge states. PCS1 consists of a single central annular hole and serves as the reference structure; PCS2 adopts a corner-cut configuration to induce localization of edge modes; PCS3 features a symmetric arrangement at the four corners, enabling the exploration of multimode coupling and edge interference; and PCS4 exhibits a centrally concentrated configuration, allowing comparison of mode localization and symmetry breaking. Additionally, Zak phase and topological polarization are computed using MATLAB to further determine the topological classification and property variations among the different structures. The overall simulation results demonstrate that geometric arrangement significantly influences topological phase, edge modes, and field distribution. This study thus provides a simple yet intuitive geometric platform for understanding the origin and control mechanisms of topological properties in photonic crystals.
