本研究可分為兩部份，其一為量子點的光學特性，另一為量子點在光學上的應用。 量子點的光學特性是根基於其量子侷限的能階概念，有鑑於相關的數學模型眾多，但都各自有其限制及適用的量子位能結構。因此我們自行發展一套計算量子能階、能帶的方法，Iterative Boundary Method (IBM)，並由一系列的計算，比對文獻資料或實驗數據，證明它確實適用於所有型態的量子位能系統。此部份的成果並藉由CdS及CdSe/ZnS兩種量子點，經實驗驗証計算的正確，甚至指出許多文獻中對CdSe/ZnS此一核殼量子點光學特性的誤解。 在量子點的光學應用方面，我們首先以理想中的-k材料做有系統的研究，成功地拓展現有薄膜理論，以之描述-k材料在光學薄膜上的行為及優化策略，本論文是第一個提出此”負k薄膜”概念的研究。接著我們成功製鍍出含有量子點的介電質薄膜，以窄帶濾光片為例，證實量子點在該光學薄膜內的貢獻。依據量子點特有的光學特性，此一濾光片在激發光源的開與關狀態下具有不同的穿透率，甚至可超越100%。此一現象與傳統的-k在物理意義上並不相同，文末亦指出其解釋。 本論文成果不僅證明，量子點用在光學薄膜確實可行，且可預見此一新穎概念將為光學薄膜開啟一個全新的視野; This thesis is distributed into two parts. The first part is about the optical properties of quantum dots. And the second part is about the applications of quantum dots in optics. All of the optical properties in quantum dots are based on the concept of confined energy states, or energy bands. The known mathematics tools for this issue have individual restrictions although numerous approaches are proposed. A novel approach is proposed in this thesis, Iterative Boundary Method (IBM), which is able to calculate the confined energy levels, energy bands, of any kind of potential profile. The calculations have been verified by published data, experimental results and other known approaches. Otherwise, CdS and CdSe/ZnS quantum dots are also employed to our experiments to compare with the simulations. Moreover, we find a misinterpretation exists in many published reports about CdSe/ZnS core-shell quantum dots. This mistake is figured out in this thesis and proved by IBM. About the applications of quantum dots in optics, we starts from an ideal that a layer owns index like dielectric layer and negative extinction coefficients. The –k layer is studied systematically including spectra, admittance and optimization of multilayers. The conventional method of thin-film optics is extended for the special layers successfully. This is the first research that provides complete analysis of –k layer and optimization. Consequently, optical filters with quantum dots are fabricated. Narrow band pass filters are employed to demonstrate the contribution of quantum dots in filters. These filters have different transmittance due to characteristics while exciting light is on and off, even exceeds 100% due to participation of quantum dots. The achievements not only carry out optical filter including negative k thin-films, but also provide a new horizon for conventional thin-film optics.