雙曲超穎材料因為有著獨特的雙曲色散的光學特性，近年來吸引了許多研究者的注意，在本研究中我們主要探討奈米柱雙曲超穎材料於增益自發性輻射的性質。由於雙曲超穎材料所產生的模態具高波數特性，造成能量要耦合出來相當困難，因此本研究藉由改變奈米金屬柱的幾何結構、光源擺放位置、添加增益結構與改變外部介電質材料的折射率來增加雙曲超穎材料耦合的效率並觀察光學特性。而結果顯示，我們可以藉由提升介電質材料的折射率，有效的將系統的高波數模態耦合出雙曲超穎材料，而在特定波長下其發光增益最大可達 18.4。

另外，我們在模擬奈米柱雙曲超材料與外部介電質材料之間能量耦合時，發現了特別的波前現象，當環境的介電質折射率變化時，由雙曲超穎材料耦合出的能量會有不同的發散與匯聚現象，因此我們以數值方法去模擬這些特性，並藉由電磁理論所運算的解析解來探討這些現象，這些分析結果都有助於設計雙曲超穎材料於高效率光學元件的應用。

Hyperbolic metamaterials have attracted considerable attention owing to many unique optical properties deriving from the hyperbolic dispersion characteristics. In this study, we investigate enhanced spontaneous emission characteristics in nanowires hyperbolic metamaterials. Due to the high-k feature of modes in hyperbolic metamaterials, energy is difficult to be coupled out from the structure. Therefore, we examine the coupling efficiency and optical properties by varying the geometry of the nanowires and excitation conditions, adding an enhanced structure, and changing the refractive index of the dielectric material. The results show that by increasing the refractive index of the dielectric material, the coupling efficiency can be enhanced by a maximum of 18.4 at a specific wavelength, by virtue of efficient coupling of high-k modes.

In addition, we have observed interesting features of the wavefront for waves coupled out from the structures. Depending on the refractive index of the surrounding dielectric materials, the wavefront may exhibit various converging or diverging profiles. We study these properties by both numerical simulations and analytical electromagnetic derivations. The results are important for the design of hyperbolic metamaterials in the applications of highly efficient optoelectronic devices.

致謝 I
摘要 III
Abstract IV
目錄 V
第一章 緒論 1
1.1 超穎材料介紹 1
1.2 雙曲超穎材料介紹 4
1.2.1 多層狀雙曲超穎材料 4
1.2.2 奈米柱雙曲超穎材料 5
1.3 雙曲超穎材料共振腔 6
1.3.1 共振腔大小與偶極子光源位置 6
1.3.2 三維光學共振腔 8
1.4 雙曲超穎材料的耦合與特性 9
1.4.1 一維光柵增益結構 9
1.4.2 二維光柵增益結構 10
1.4.3 楔形增益結構 11
1.4.4 雙軸雙曲超穎材料的掌性表面波 12
1.5 研究動機 12
第二章 實驗方法 14
2.1 時域有限差分法 14
2.2 等效介質理論 15
2.3 增益參數 17
2.3.1 Purcell factor 17
2.3.2發光增益 17
2.4 能量頻譜圖 18
2.5 平面電磁波之解析解 19
2.5.1 電磁波於各向異性介質中的傳播特徵 20
2.5.2 電磁波於各向異性介質與各向同性介質界面的反射與折射 21
2.5.3 電磁波於界面的布魯斯特角與反射率 24
2.5.4 數值解與解析解之穿透頻譜 25
2.6模擬結構 25
第三章 提升奈米柱雙曲超穎材料的光耦合效率 27
3.1 光學特性 27
3.1.1 等效介電常數 27
3.1.2 Purcell factor與發光增益 28
3.1.3 穩態電場分佈圖 29
3.2 增益結構 30
3.2.1 不規則奈米柱長度 31
3.2.2 表面粗糙 32
3.2.3 反射層 33
3.2.4 靶心光柵 34
第四章 雙曲超穎材料與介電質材料耦合特性 38
4.1 光學特性 38
4.1.1 雙曲超穎材料共振腔 39
4.1.2 偶極子光源於雙曲超穎材料內不同激發位置 40
4.1.3 雙曲超穎材料之體積分率 41
4.1.4 Purcell factor與發光增益 42
4.2 雙曲超穎材料之耦合波前特性 43
4.2.1 Purcell factor於不同折射率的周圍介電質之光學特性 43
4.2.2 不同介電質折射率波前之變化與不同激發波長耦合波前之變化 44
4.2.3 二維等頻率線圖 46
4.2.4能量頻譜圖 46
4.2.5不同介電質折射率之發光增益 49
4.2.6 遠場能量分佈圖 49
4.3 等效雙曲超穎材料的波前特徵 50
4.4 折射率匹配層 53
4.4.1 有限厚度介電質之發光增益 54
4.4.2 折射率匹配 55
4.4.3能量頻譜圖 57
第五章 結果與未來展望 60
參考文獻 61

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