氧化鋅為雷射二極體的熱門材料之一，因為其具有寬能隙(3.37 eV)以及大的激子束縛能(60 meV)，且成本也低廉。在晶格結構方面，氧化鋅晶體屬於六方晶系，在ab平面呈現完美的六邊形共振腔結構，因而能夠產生準迴廊模態(quasi-WGM, quasi-whispering gallery mode)與迴廊模態(WGM, whispering gallery mode)，使能量被限制在六邊形共振腔之中。然而，在微米等級以下的共振腔，由於狹窄的自由頻譜範圍(FSR, free spectral range)，會產生多重的共振模態，因此可以利用游標尺效應，將不同的共振腔相互耦合，進行二次選模，以獲得單一模態。本文運用有限時域差分法(FDTD, finite-difference time-domain)進行數值模擬，使用三角形網格坐標系統以及對稱軸的設置，減低模擬的運算量，並利用共振腔的耦合效應，提高共振頻譜的強度，並改變共振腔之間的間隙大小，觀察其共振模態的變化。此外，我們也將兩邊長不同的六邊形共振腔相互耦合，改變其共振頻譜的強度分布，其共有的共振波長將會成為極大值，呈現如同光柵般的頻譜強度分布。

The hexagonal crystal structure of zinc oxide makes it easy to produce resonant modes such as quasi-WGMs and WGM. In this thesis, we used the FDTD, finite-difference time domain, method to simulate hexagonal ZnO cavities. We improved the simulation space by using triangle meshes and a symmetric axis so as to make the simulation space fit hexagonal ZnO cavities and reduce simulation time. Then, we simulated a hexagonal ZnO cavity by two kinds of the simulation space. One is square-meshed and the other is triangle-meshed. We analyzed the wavelengths of the resonant modes of the two spectra and concluded that the triangle-meshed coordinate system was a better choice than the square-meshed one when hexagonal cavities were simulated. Next, we made a hexagonal ZnO cavity couple with a silica substrate or another same-sized cavity. The intensity increased result from the coupling effect. Besides, we coupled a hexagonal ZnO cavity of which the side length was 1090 nanometers with another one of which the side length was 2000 nanometers and its spectrum looked like the one with gating effect.

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