本論文中，我們利用有限時域差分法，來分析微米以下週期性結構之繞射特性，並針對藍光Thin-GaN LED設計具指向性之繞射光學結構。論文內容主要分為兩大部分：(一) 在數值計算上，我們將以有限時域差分法做為主要計算方法，並分析不同結構參數對指向性之貢獻與影響。(二) 以此優化之週期性結構參數做二維排列，進而設計具指向性、高效率藍光Thin-GaN LED。

In this thesis, we apply finite-difference time domain algorithm to analyze the characteristic of diffraction of the sub-wavelength periodic structure. Accordingly, we design optical diffraction structures with high directionality for Thin-GaN blue LED.
The content of this thesis can be divided into two parts: a.)In numerical calculation, we use finite-difference time domain algorithm to calculate the directionality of various structures, and try to optimize the structure. b.)According to the optimized result, we extend the structure to a two-dimensional form. Finally we try to design the structure for a Thin-GaN blue LED with high directionality and high efficiency.

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