本論文研究如何對一具有空間反射對稱的準一維光子晶體結構計算其札克相，並藉札克相來判斷此光子晶體結構在何種情況下會有介面態。本論文探討的第一類系統是含一排或多排週期分布介電質柱，上下以完美導體為邊界的準一維光子晶體結構。本論文探討的第二類系統則是以二維光子晶體系統為背景的光子晶體波導，並在其中置入一排週期分布介電質柱所形成的波導。對這兩類準一維光子晶體結構，介面態的出現都符合根據札克相所做的拓樸判斷。

This thesis investigates how to calculate the Zak phase for a quasi-one-dimensional photonic crystal structure with spatial reflection symmetry and then uses the Zak phase to determine under what conditions this photonic crystal structure will exhibit interface states.
The first type of systems explored in this paper are quasi-one-dimensional photonic crystal structures consisting of one or more rows of periodically distributed dielectric columns, with perfect conductors as boundaries on the top and bottom. The second type of systems studied are photonic crystal waveguides based on a two-dimensional photonic crystal system, with one row of periodically distributed dielectric columns forming the waveguides. For both kinds of quasi-one-dimensional photonic crystal structures, the appearance of interface states confirms the topological predictions made based on the Zak phase.

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