氧化鋅(ZnO)具有高原子鍵結能且寬能帶隙之特性，使其在紫外光或可見光光學元件應用上有很大的發展與願景。另外，氧化鋅晶格屬於六方纖鋅礦結構 (Wurtzite hexagonal structure)，因此其六角形切面便成為分析六角形迴廊模態(WGMs, whispering gallery mode)與三角形準迴廊模態(quasi-WGMs, quasi- whispering gallery mode) 很好的材料。由於WGMs與quasi-WGMs為利用全內反射將光束侷限在腔內，使得此兩種模態皆擁有很高的品質因子。因此，本篇論文將利用有限時域差分法(FDTD, Finite Difference Time Domain)探討此兩種共振模態在六角形共振腔內之光學效應。我們在結構尺寸較小的情況下，找出低階模態WGMs的場值分布圖、等效折射率、共振位置與線寬等，並發現低階模態的線寬趨勢有著特殊多角形共振腔之特性；接著，在大尺寸共振腔中分析並探討高階quasi-WGMs，藉由改變單一共振腔的結構使其簡併模態分裂，並利用兩個相鄰共振腔之間的耦合觀察到模態分裂之光學特性。

Zinc oxide (ZnO) is a promising semiconductor material for UV or visible photonic devices due to its large exciton binding energy and wide band gap. Furthermore, crystal structure of ZnO is usually the hexagonal wurtzite type. Therefore, the hexagonal cross sections provide a unique subject for the analysis of hexagonal WGMs and triangle quasi-WGMs. Those two types of resonance mode use internal reflection for light confinement, which can provide a very high quality factor. Therefore, in this thesis, we investigated those two types of resonance in the hexagonal cavity via FDTD calculations. For the case of the small-scale structure, we present a numerical analysis of low-order WGMs. Our investigations include mode patterns, effective refractive-index, resonance positions and linewidths, etc. And found that the tendency of linewidths exhibits a characteristic of polygonal-shaped cavities. Subsequently, we studied high-order quasi-WGMs in the large-Scale Structure. We demonstrate two split resonances of quasi-WGMs by varying the height of the lower edge of the dielectric hexagonal. We also demonstrate the mode splitting effect by putting two hexagonal cavities close to each other.

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