了解被動元件與外部場的電磁波交互作用是近年來最熱門的研究課題，從超材料(metamaterials)、超平面(metasurfaces)、電漿雷射共振腔(plasmonic laser cavity)到早期的金屬與介電面的表面電漿共振(surface plamonics polariton)。其物理內涵與可能應用層面極具廣泛且引人注目，從克服因繞射極限而造成生物成像問題、增強生物分子的信號等等，皆凸顯深刻了解光散射的極限是相當重要課題。
儘管光散射的理論以於上世紀的德國科學家古斯塔夫·米(Gustav Mie)建立理論，但近期的理論發展如反雷射裝置（coherent perfect absorption）、用散射場相消機制的隱型斗篷、超級散射體共振腔(superscattering cavity)，顯示了從一些有趣的看法與引入吸引人的物理概念，可以發現有多種不同方式的散射體。
本論文專注在圓柱體的散射特性與了解其物理極限。相較於球型散射系統，圓柱體的對稱特性只在方位角，也因此對於不同的電場偏振會有不同的散射性質。
本研究期望從這種特性中去了解整個物理圖相，並進而增進如何控制光散射的場:遠場與近場，增進未來可能的奈米光學應用。
本論文第一部分由馬克斯威爾方程組，推導出圓柱的散射理論。
第二部分，基於能量守恆，我們說明如何描畫出相圖，與稍為討論相圖的意義與特性。
第三部分，展示如何利用相圖，設計1.特定方向隱形的散射體。2.超極吸收體。3.兩道入射光來控制散射光場。
最後，我們總結本論文研究的成果與未來方向。

Understanding of light-passive materials interaction is a hot subject related to a variety of applications from metamaterials, metasurfaces, plasmonic laser cavity, and surface plasmonic polarity. The physics insight and proposed applications attract much attention, because it could be believed to overcome diffraction limit, which is fundamentally constrained to biological imaging and enhancing molecule signal. Although the theory of light scattering was established over the past century by Gustav Mie,it is interesting to adopt different viewpoint of physics to comprehend this old theory. Now, theoretical physicist have found that for passive system, one can have coherent perfection absorption, invisible objects based on cancellation method, and superscattering cavity.
This thesis discusses the fundamental scattering limit by passive objects, in order to
explore possible scattering states and physical bounds.
Compared to spherical symmetrically object, in cylindrical system it only has an azimuth symmetry to exciting field.
As a result, it has different field response to different field polarization.
This study wants to understand this intrinsic characteristic to recognize its picture, i.e., phase diagram.
The first part of this thesis develops a theory of light scattering in cylindrical systems based on Maxwell equations.
The second part, we plot the phase diagram due to power conservation and discuss the meaning and properties of diagram.
The third part, we display how to use the diagram to design functional devices, such as 1. directional emission, 2. superabsorbers, 3. manipulation of intrinsic light scattering by two counter-waves.

1. 緒論 1
2. 圓柱空間的米氏散射 4
2.1 柱諧函數的波 4
2.2 平面坡展開 6
2.3 散射係數與邊界條件 7
2.4 等效散射截面積 11
3. 相圖 16
3.1 相圖 16
4. 相圖應用 18
4.1 特定方向隱形的散射體 18
4.2 超極吸收體 25
4.3 兩道光控制散射光場 27
5. 結論 31
參考資料 32

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