在此論文，我們探討單一散射體在外在入射波刺激下的光散射反應。經由適當條件下，這些多層且次波長尺度的奈米散射裝置可具有異常的波特性，如超級光吸收體、完美吸收體、隱形斗篷、零點前向散射和超級散射體。在這篇論文中，我們有三個主要課題探討：1.奈米粒子的光催化反應、2.量子隱形斗篷、3.被動式散射粒子的光反應物理極限特性。

第一部分，我們推導所需的米式散射公式，並討論幾個重要的物理量、光學定理、長波長下的近似到因果律。我們應用堆導的米式散射來了解二氧化鈦的光吸收和催化反應關係。藉由調整幾何大小與簡化複雜的光化學問題為純光學現象，我們的理論計算結果與實驗符合。此外，儘管光散射訊號受幾何影響，這是由於共振模態的激發，但是我們發現對能量吸收而言，它是對幾何厚薄相當不敏感，在大尺度散射體，即使厚薄程度已達0.4，能量的吸收可維持相同。這有助於對設計光觸媒反應的最佳幾何達到簡省材料的地步。在最佳的幾何情況，我們理論預測可將產氫的效率達到五倍以上。

第二部分，我們從不同方式來設計量子隱形斗篷。雖然，從變換光學的方式也能得到量子隱形斗篷，但是此斗篷具有複雜的材料結構，而且在斗篷內的等校質量是一個奇異點。這裡，我們提供一個新的概念古斯-漢欣位移在球殼中產生全反射。並藉由調整殼內的參數來消除s和p波來達到量子散射消去。以此種方法，我們不僅可以隱藏內部區域，並且可以大幅降低量子散射訊號。這個方法大幅降低工程的難度，而且只需要均勻的球殼結構。

在最後一章，我們發展相圖來了解散射係數在所有頻道的振幅和相位。散射係數不僅與能量分配有關也與外在表徵狀態有關。經由此相圖，可完整呈現所有在米式散射下可能的解，超越各種可能的設計和結構，並且說明散射的最大最小能量分配。選擇任何在相圖的路徑，我們可找出相對的材料參數，這也表示我們能由此控制光場。

In this thesis, we investigate the general wave scattering response of an individual scatterer excited by incident waves. Through choosing the suitable conditions,
we show that these subwavelength scatterers could have anomalous wave features, analogous to metamaterial counterparts, for example superabsorber, perfect absorber, invisible cloak, zero-forward scattering and superscattering.
There are three major studies of interests in this thesis: nano-light harvesting for photocatalysis, design of quantum invisible cloak and physical limitation on
general passive scatterers.
In the first part, we derive the formulas from exact Mie theory and integrate basic physics: various characteristic cross sections, long wavelength approximation, optical theorem and causality of frequency dispersive relation. We apply this Mie theory to understand the relationship between absorption of light and the photocatalytic activity of TiO2 compared with experimental data. By tuning geometries and simplifying the complicated photochemistry reaction as pure optical
problem, we nd that our calculation could agree with experimental results.
Although scattering signal is really affected by geometries due to exciting modes and channels as well as function of cavity, we show that in large-sized parameters the absorbed power could maintain the same by tuning thickness up to 0.4 . This non-sensitive absorbed power on the thickness ratio may bring a lot of benefits on saving cost of material. In optimized situation, our theory predicts that one could raise the efficiency of hydrogen generation up to 500%.
In the second part, we design a new quantum invisible cloak from different methods. Following the recipe of transformation optics, the solution to design
quantum cloaks would need complicated anisotropic and inhomogeneous material parameters and have infinite singular point for effective mass at the inner cloak.
In this part, we introduce a new concept of Goos-Hanchen effect, producing total internal reflection happened at the boundary of core-shell cloak. Choosing the proper core parameters, we could eliminate the scattering contributions from s and p waves based on conventional scattering cancellation method. We could not only create a hidden region but also largely compress the total scattering signals.
This method could largely reduce the difficult of engineering level because of its simple core-shell isotropic and homogeneous only.
In the final part, we develop the phase diagram to recognize the limitation of phase and amplitude of complex scattering coefficient for each harmonic channel.
Scattering coefficient not only connects various cross sections but also has an influence on extrinsic characteristic. Through this phase diagram it can completely display possible solutions of Mie theory beyond any design and structures, including
minimum or maximum of the power assigned toward different extrinsic states. Choosing any paths or any specific positions in the allowable territory in diagram,
the corresponding parameters could be calculated, highlighting the possibility of manipulation of light.

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