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研究生： 黃柏勝
Huang, Po-Sheng
論文名稱： 基於超穎介面之多自由度光場調控與進階應用
Metasurface-Based Multi-degree-of-Freedom Light-Field Control: From Fundamental Design to Advanced Applications
指導教授： 吳品頡
Wu, Pin Chieh
學位類別： 博士
Doctor
系所名稱： 理學院 - 光電科學與工程學系
Department of Photonics
論文出版年： 2026
畢業學年度： 114
語文別： 中文
論文頁數： 291
中文關鍵詞： 超穎介面 、超穎透鏡 、可變焦超穎透鏡 、偏振調控 、向量波前調控 、非厄米光學 、例外點 、拓撲相位 、幾何相位 、單偏振通道 、手性超穎介面 、二維材料 、二硫化鉬 、光致發光 、谷光子學 、結構光 、VCSEL 陣列 、三維感測 、奈米光子學
外文關鍵詞： Metasurface, Multi-degree-of-freedom light-field control, Metalens, Varifocal metalens, Polarization control, Polarization group delay, Structured light, VCSEL array, Non-Hermitian optics, Exceptional points, Chiral metasurface, Monolayer MoS2
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    • 超穎介面由次波長奈米結構組成，可在極薄平面中調控光的相位、振幅、偏振、傳播方向與發光通道，具備微型化、高設計自由度與易於整合等優勢。本研究以「多自由度光場調控平台」為核心，發展多種基於超穎介面的平面光學元件與混成奈米光子系統，並將其應用拓展至可調式成像、結構光三維感測、非對稱向量波前控制與二維材料發光偏振調控。
    首先，本研究提出偏振相依強度疊加式可變焦超穎透鏡，利用各向異性氮化鎵奈米結構，使兩個正交線偏振通道分別對應不同焦距。藉由改變入射線偏振角，可連續調整兩個聚焦通道的相對強度權重，使總軸向強度峰值在兩個焦距之間移動，實現不依賴機械位移或折射率調變的連續變焦。進一步地，本研究提出基於偏振角相位響應之可變焦超穎透鏡，並引入偏振群延遲概念，將相位對入射偏振角的變化率視為額外設計自由度，透過相位－PGD 雙重匹配方法實現偏振角控制之焦距調變。
    其次，本研究將超穎介面與 VCSEL 陣列整合，提出分散激發式結構光投影架構。此設計將不同發光點的位置納入相位設計，使單一共享超穎介面可同時補償發散波前並產生多通道偏折，將各 VCSEL 發光點轉換為低發散結構光束，進一步支援三維深度重建。另一方面，本研究利用非厄米成對例外點與幾何相位建立非對稱圓偏振轉換通道，使正交圓偏振分量可被獨立調控，進而實現任意偏振態與非對稱向量波前控制。最後，將此偏振通道工程延伸至二維材料發光控制，透過單偏振通道手性超穎介面與單層二硫化鉬整合，導引室溫光致發光至特定圓偏振通道，建立激發自旋、結構手性與發光自旋之間的關聯。整體而言，本研究展示超穎介面可作為連接光場、光源、偏振通道與發光材料的多自由度光場調控平台，並展現其於微型成像、三維感測、偏振資訊處理與晶片尺度光子發射控制中的應用潛力。

    Metasurfaces composed of subwavelength nanostructures provide a compact platform for controlling the phase, amplitude, polarization, propagation direction, and emission pathway of light. Compared with conventional bulky optics, they offer high design flexibility and strong potential for integrated nanophotonic systems. In this dissertation, metasurfaces are developed as multi-degree-of-freedom light-field control platforms for tunable imaging, structured-light projection, asymmetric vectorial wavefront modulation, and two-dimensional-material emission control.
    First, a polarization-dependent varifocal metalens is demonstrated by assigning two focal lengths to two orthogonal linear polarization channels, enabling continuous focal tuning through polarization-angle-controlled intensity superposition. A second varifocal design further introduces polarization group delay, using the phase response with respect to incident polarization angle as an additional design degree of freedom. Next, a VCSEL-array-integrated metasurface is developed for distributed-excitation structured-light projection, where emitter positions are incorporated into the phase design to generate low-divergence structured-light beams for three-dimensional sensing. Non-Hermitian metasurfaces based on paired exceptional points are then used to realize asymmetric polarization channels and arbitrary vectorial wavefront control. Finally, chiral metasurfaces integrated with monolayer MoS₂ are employed to control circularly polarized photoluminescence emission.
    These results show that metasurfaces can go beyond passive wavefront modulation and serve as versatile platforms connecting light fields, light sources, polarization channels, and emitting materials.

    口試合格證明 I 中文摘要 II 英文摘要 III 致謝 XVI 目錄 XVIII 圖目錄 XXV 第一章 緒論 1 1.1 前言 1 1.2 超穎介面簡介 2 1.2.1 超穎介面發展脈絡 2 1.2.2 電漿子超穎介面與介電質超穎介面 5 1.2.3 超穎介面相位調控機制：傳播相位、共振相位與幾何相位 9 1.2.3.1 傳播相位 10 1.2.3.2 共振相位 12 1.2.3.3 幾何相位 16 1.2.4 超穎介面光場調控自由度 19 1.2.4.1 廣義斯乃爾定律與相位梯度調控 20 1.2.4.2 惠更斯原理與波前重建 22 1.2.4.3 偏振通道與多自由度光場調控 23 1.3 超穎透鏡、可調式變焦超穎透鏡以及消色散超穎透鏡 26 1.3.1 超穎透鏡之聚焦原理 26 1.3.2 可調式超穎透鏡 28 1.3.3 消色散超穎透鏡工作原理 34 1.4 結構光投影與三維感測 36 1.4.1 結構光簡介與三角量測原理 36 1.4.2 傳統結構光生成方法 39 1.4.3 超穎介面於結構光生成之應用 43 1.5 非厄米光學與例外點超穎介面 46 1.5.1 非厄米光學系統以及例外點介紹 47 1.5.2 超穎介面在非厄米光學之應用 50 1.6 過渡金屬二硫族化物以及其與超穎介面的應用 52 1.6.1 過渡金屬二硫族化物之結構與光學特性 52 1.6.2 能谷選擇律、圓偏振光致發光與室溫退偏振機制 55 1.6.3 超穎介面整合 TMDCs 之發光與偏振調控應用 58 1.7 論文架構與研究主軸 61 第二章 數值模擬與實驗方法 65 2.1 前言 65 2.2 數值模擬與光場分析方法 66 2.2.1 有限元素法 66 2.2.2 嚴格耦合波分析法 69 2.2.3 結構資料庫建立與相位匹配方法 72 2.2.4 波前分析、角譜法以及遠場傳播投影原理 75 2.3 材料平台與製程技術 77 2.3.1 氮化鎵超穎透鏡樣品製程 77 2.3.2 非晶矽結構光超穎介面製程 79 2.3.3 金屬－介電質－金屬反射式電漿子超穎介面製程 80 第三章 偏振相依強度疊加之連續變焦超穎透鏡 83 3.1 研究動機 83 3.2 偏振相依強度疊加之變焦原理 84 3.2.1 正交偏振通道之焦距配置 85 3.2.2 Malus law 與軸向強度疊加模型 85 3.2.3 焦距差異與單一焦點形成條件 87 3.2.4 數值孔徑、焦深與變焦範圍之取捨 90 3.3 氮化鎵超穎透鏡設計方法 90 3.3.1 偏振選擇性聚焦之設計需求 91 3.3.2 聚焦相位與隨機相位配置 92 3.3.3 氮化鎵異向性奈米結構資料庫 93 3.3.4 結構選擇與相位匹配流程 94 3.3.5 光場傳播模擬與偏振選擇性驗證 95 3.4 光學量測與分析方法 96 3.4.1 光學量測架構與偏振控制 96 3.4.2 焦距與軸向強度分布量測 97 3.4.3 點擴散函數與焦點品質分析 98 3.4.4 聚焦效率量測與計算方法 99 3.5 連續變焦特性與成像結果 100 3.5.1 偏振角控制下的焦距連續調變 100 3.5.2 不同數值孔徑樣品之變焦特性比較 102 3.5.3 聚焦效率與可見光波段響應 104 3.5.4 MTF 分析與空間解析能力 105 3.5.5 Strehl ratio 與FWHM焦點品質分析 107 3.6 總結 108 第四章 基於偏振角相位響應之可變焦超穎透鏡 113 4.1 研究動機 113 4.2 偏振群延遲之物理概念 115 4.2.1 以 Jones 矩陣描述各向異性超穎原子的偏振角相位響應 115 4.2.2 偏振群延遲之定義與平均 PGD 近似 116 4.2.3 結構旋轉與 PGD 符號反轉 121 4.2.4 PGD 對變焦超穎透鏡設計的意義 122 4.3 反射式電漿子超穎結構資料庫建立 123 4.3.1 反射式金屬－介電質－金屬超穎原子結構 123 4.3.2 多幾何形狀資料庫設計 125 4.3.3 偏振角掃描與資料庫參數萃取 126 4.3.4 相位、反射率與 PGD 響應分析 127 4.4 PGD 變焦理論與PGD匹配方法 128 4.4.1 偏振角相依之透鏡相位分布與目標PGD 128 4.4.2 對稱化 PGD 配置與調變深度提升方法 129 4.4.3 相位-PGD 雙重匹配方法 130 4.5 正向與反向PGD變焦超穎透鏡設計結果 132 4.5.1 設計參數與焦距調變方向 132 4.5.2 目標 PGD 分布與結構匹配結果 133 4.5.3 偏振角相依相位演變與 MATLAB 角譜法模擬 134 4.5.4 焦距調變範圍與聚焦品質比較 136 4.6 總結 139 第五章 基於 VCSEL 陣列整合超穎介面之分散激發結構光投影 142 5.1 研究動機 142 5.2 分散激發超穎介面設計概念 144 5.2.1 分散激發與全域照明架構之差異 144 5.2.2 發射源位置與局部相位取樣 144 5.2.3 1-to-3 波束轉換之物理圖像 145 5.3 非晶矽超穎介面單元與相位分布設計 147 5.3.1 非晶矽奈米柱單元與相位響應 147 5.3.2 準直相位設計方法 147 5.3.3 偏折相位與三通道方向設計 148 5.3.4 相位疊加與正負階偏折通道設計 148 5.3.5 多通道權重與面積比例設計 150 5.4 單點光源激發之波束整形驗證 152 5.4.1 入射位置掃描與波束整形效率定義 152 5.4.2 大範圍入射位置下之效率分布與樣品影像 153 5.4.3 代表性入射位置之遠場驗證 154 5.4.4 發射源位置相依之遠場映射 155 5.4.5 單點光源與效率量測架構 157 5.5 VCSEL 陣列整合式結構光投影 158 5.5.1 VCSEL 陣列座標與超穎介面整合架構 158 5.5.2 光線追跡模型與遠場位置計算 159 5.5.3 VCSEL 陣列結構光圖樣之數值預測 161 5.5.4 VCSEL 陣列整合實驗與效率比較 161 5.5.5 完整VCSEL陣列座標之輔助驗證 163 5.6 結構光圖樣之發散角、視場與幾何失真分析 165 5.6.1 投影光束發散角量測方法 165 5.6.2 低發散角光束輸出結果 166 5.6.3 結構光圖樣視場分析 166 5.6.4 幾何失真定義與量測結果 167 5.7 三維深度重建之概念驗證 169 5.7.1 結構光深度重建之量測架構 169 5.7.2 參考圖樣與物體圖樣之光點位移 170 5.7.3 深度重建結果 171 5.8 總結 173 第六章 成對例外點於任意偏振控制之非對稱向量波前調控 174 6.1 研究動機 174 6.2 成對例外點之理論基礎與偏振轉換機制 176 6.2.1 非厄米 Jones matrix 與例外點條件 176 6.2.2 鏡像對稱操作與成對例外點形成 177 6.2.3 幾何相位與任意偏振態重建 179 6.3 成對例外點超穎介面之結構設計與數值驗證 181 6.3.1 反射式金屬－介電質－金屬超穎介面架構 181 6.3.2 原始結構與鏡像結構之偏振響應 182 6.3.3 例外點參數掃描與零反射奇點 183 6.3.4 頻譜響應與本徵態簡併驗證 185 6.3.5 參數空間中的本徵態分布 186 6.4 非對稱任意偏振超穎全像 188 6.4.1 幾何相位編碼與單一繞射階次控制 188 6.4.2 任意偏振輸出超穎全像設計 190 6.4.3 非對稱全像影像之實驗驗證 191 6.4.4 龐加萊球偏振分析 192 6.5 非對稱向量超穎全像 193 6.5.1 向量超穎全像之設計概念 193 6.5.2 改良式 Gerchberg–Saxton 演算法 195 6.5.3 強度、方位角與橢圓率角之解耦控制 197 6.5.4 實驗量測與非對稱向量全像驗證 197 6.5.5 向量資訊編碼之意義與限制 199 6.6 光學量測與偏振態重建方法 201 6.6.1 反射式超穎全像光學量測架構 201 6.6.2 固定偏振超穎全像之偏振態量測 202 6.6.3 向量超穎全像之 Stokes 參數重建 203 6.6.4 量測結果判讀與誤差來源 204 6.7 總結 205 第七章 單偏振通道手性超穎介面輔助之單層二硫化鉬光致發光偏振控制 207 7.1 研究動機 207 7.2 單偏振通道手性超穎介面之設計概念 208 7.2.1 室溫二硫化鉬光致發光退偏振問題 209 7.2.2 單偏振通道之物理意義 211 7.2.3 激發自旋、結構手性與發光自旋之關係 214 7.3 手性金屬－介電質－金屬超穎介面設計與數值驗證 217 7.3.1 L 型複合手性超穎原子結構 217 7.3.2 normal-L 與 mirrored-L 結構之圓偏振反射響應 219 7.3.3 近場分布與單偏振通道選擇性 223 7.4 MoS₂－手性超穎介面混成結構與量測方法 226 7.4.1 混成結構之量測對象與樣品區域確認 227 7.4.2 偏振解析反射量測與分析 228 7.4.3 偏振解析光致發光量測與DOP分析 230 7.5 單偏振通道輔助之光致發光控制 232 7.5.1 混成結構之偏振解析反射光譜 233 7.5.2 裸MoS₂ 與混成結構之偏振解析光致發光對照 235 7.5.3 面內偶極發光模擬與偏振通道分析 237 7.5.4 室溫 PL 圓偏振度、手性反轉與發光自旋控制機制 243 7.6 總結 246 第八章 結論與未來展望 248 參考文獻 251 附錄：個人著作和獲獎紀錄 257

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