有限時域差分法(finite-difference time-domain method，FDTD)在近幾年已成為光學元件經常使用的電磁場數值計算 方法之一。對於未來光學元件越來越小的趨勢上，FDTD相關的方法在光學共振腔、波導甚至是光子晶體的設計以及分析都是不可或缺的技術。而微共振腔(microcavity)的小體積優勢、在光學集成線路的應用性、以及可令共振頻率較為稀疏而達成單頻雷射的特性，成為近期光學 領域研究的重點。
本論文探討不同尺寸的半球形微共振腔之共振頻譜 ，以FDTD模擬計算生長於雲母基板上之鈣鈦礦半球形微共振腔的共振頻譜以及場強度分布，透過改變微共振腔尺寸以及分析不同共振波長，得到不同模態數以及偏振的相關性。並比較半球形微共振腔對於不同共振波長的光學侷限性 。最後，為探究FDTD對於半球形微共振腔其 對應光致發光量測實際應用的可行性，將FDTD計算出之頻譜與本實驗室的CsPbBr3半 球形微共振腔之光致發光光譜做比對，並進一步以其微共振腔內的數值計算場強分佈，結果顯示光致發光頻譜中的波峰是TM模態，得知在樣品的光致發光量測上觀察到的兩個不同波長的尖峰之角方位模態數以及徑向模態數不同。

The finite-difference time-domain (FDTD) method has become one of the most popular electrodynamics numerical simulation tool for optical components in recent years. As the demand for smaller optical components increases, FDTD-related techniques are essential in the design and analysis of optical resonators, waveguides, and photonics. Moreover, the microcavity, which is characterized by its small size, its applicability in optical integrated circuits, and the ability to make resonance frequency sparse and achieve a single-frequency laser, has become the focus of research on optics. This study investigated the resonance spectrum of different sizes of perovskite hemispherical microcavities grown on mica using FDTD simulation. By changing the size of microcavities and analyzing the resonant wavelength, we obtained the relationship between different mode numbers and polarization. Finally, the spectrum calculated by FDTD was compared with that by the photoluminescence. The results showed that the peaks in the photoluminescence spectrum were the TM modes which were different azimuthal and radial mode numbers.

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