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 本篇論文考量三維幾何結構對光作用力與光力矩變化。我們選用不同波長的圓偏振入射光源，透過有限元素法得到介電質表面電磁場分布，代入馬克斯威爾應力方程得到每一網格點之的光應力，將每網格點光作用力，對位置向量進行外積，接著加總每網格的光力矩，得到全體三維結構之光力矩。接著分析局部結構電場分布與光力矩振盪表現，透過篩選不同入射波長，達到光操作物體旋轉方向的成效，並以圓盤結構為基礎，延伸設計為各樣結構進行分析，觀察其光力矩振盪行為變化。最後給出我們自行提出的5-layer結構，此設計於1.66 um ~0.62 um處皆為正光力矩，而0.62 um ~0.51 um皆為負光力矩，在特定波長達到正負力矩一分為二的效果，除此之外，y分量與z分量之光力矩於1.66 um~0.51 um波長內皆趨於零，成功降低其正負光力矩對波長之振盪行為，其設計優勢將光操作物體旋轉領域，帶來全新穩定操作微米物質旋轉的成果。
 In this thesis, we discuss the optical force and optical torque of circularly polarized incident light on three-dimensional objects. We use circularly polarized light as incident light in different wavelengths. The electromagnetic field distribution on the grid surface is obtained by the finite element method, and the light stress on each grid point is obtained from Maxwell's stress equation, and the overall optical force is evaluated by summing over the contributions from all grid points. Similarly, to calculate the optical torque of a three-dimensional object, we first calculate at each grid point the cross product of the position vector and the optical force, then sum over the surface contributions from the whole geometric structure. We analyzed the surface distribution of the electric field and the local oscillation behavior of the optical torque density on the surfaces of various three-dimensional structures. These results provide us with the information on how to change the wavelength of incident light to control the direction of rotation. Based on the knowledge obtained in the study of disc structures, we further designed various structures and analyzed their optical torque oscillation characteristics.Finally, we proposed a 5-layer structure. This design has positive optical torque in 1.66 um ~ 0.62 um, and negative optical torque in 0.62 um ~ 0.51 um. In addition, the optical torque of the y and z components approach zero within the wavelength of 1.66 um ~ 0.51 um. This structure successfully reduces the unwanted oscillation behavior of the optical torque appearing in the positive or negative region, and thus has the advantage of providing the necessary stability in controlling the rotation direction of microscopic structures.
 摘要 VAbstract I致謝 II目錄 i圖目錄 iv第一章 緒論 11-1 前言 11-2 歷史背景 21-3 文獻回顧 31-3-1光鉗 31-3-1矩形共振波導 51-3-2光子晶體波導 61-3-3 環形共振波導 81-3-2光學角動量的力矩效應 101-4 論文架構 13第二章 理論與方法 142-1 馬克斯威爾方程組與邊界條件 142-1-1波動方程 162-1-2馬克斯威爾張量應力 172-1-3光力矩計算 192-2平面波與圓偏振光線 20第三章 結果與討論 223-1 模擬架構 223-1-1 基本參數設定 223-1-2 邊界條件設定 233-1-3 網格設定 243-2 圓盤介電質 263-2-1 Fabry-Perot 反射率計算 273-2-2 圓盤光作用力和力矩 283-2-2 圓盤區域光力和光力矩分析 303-2-3 圓盤力矩反轉歸一電場分布 333-2-4 圓盤z方向切線力矩變化趨勢分析 343-2-4-1 z方向切線力矩下降區段電場分析 353-2-4-2 z方向切線力矩上升區段電場分析 383-2-5 圓盤x方向力矩變化趨勢分析 413-2-5-1 x方向力矩下降區段電場分析 423-2-5-1 x方向力矩上升區段電場分析 453-2-6 圓盤折射率分析 483-2-7 圓盤半徑分析 493-2-8 圓盤厚度分析 513-2-9 圓盤不同角度入射分析 553-2-10 圓盤於線偏振入射光分析 563-2-11 圓盤於橢圓偏振入射光分析 573-3 橢圓盤介電質 593-3-1 橢圓盤光作用力與光力矩 603-2-3 圓盤缺角介電質 623-2-4 5-layer介電質 64第四章 結論與未來展望 684-1 結論 684-2 未來與展望 71參考文獻 72
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