一般光的反應控制包含穿透、反射和吸收，在光電系統、微電子系統以及節能系統等微奈米結構中扮演著關鍵的角色。隨著奈米製程技術以及一維、二維、三維等週期性奈米結構的發展，在特定領域需要強化或調整光反應狀態時經常性會使用像彩色濾光片、偏振片、光激發器或光吸收器、偵測器以及感測器等光學元件與儀器。隨著目前的學術研究致力於一維週期性奈米結構的應用於光電機構的數值研究發展，一維結構在理論分析和實驗論證據深具研究潛力的優勢。包括整合性偏振片以及彩色濾光片(紅、綠、藍)的設計；彩色濾光片的設計具備高性能、設計偏振鈍化thermophotovoltaic發射器研究以及紅外光(IR)吸收比光譜或在近紅外光與可見光區域光穿透的控制。

本論文的數值模擬方法建構於嚴格耦合波理論(RCWA)、有限差分時間域法(FDTD)以及基因演算法(GA)等基礎理論與方法。其中RCWA與GA是使用MATLAB程式語言完成撰寫，而FDTD則是使用商用軟體(OptiFDTD)。RCWA是計算結構的光反應變化，而GA則是在特定波長光反應變化的幾何參數求取最佳化的方法。然而，耦合波理論原是使用於連續以計算電磁場、波印庭向量(Poynting vector)的分佈及繞射效率的有效計算方法。

針對整合性偏振片與RGB彩色濾光片，本研究提供了一個方便且有效率的方法在使用單一機構建立於次波長金屬光柵(SWMGs)液晶顯示面板時，能同時達到偏振與濾波的機制。依照次波長金屬光柵(SWMGs)的應用，建議RGB 彩色濾光片使用高穿透率、寬波段以及無額外穿透峰值的回音金屬波導器(SWGs)。再者，一綜合研究探討關於如何引發進而增強奈米結構輻射的物理機制，希望能設計出簡單的光柵如同thermophotovoltaic發射器同時包含橫向電波與磁波效應。同樣地，一包含入射光入射角鈍化之紅外光(IR)吸收比光譜的單層波長金屬光柵(SWMGs)結構也會在此論文提及並以可調式吸收比光譜伴隨幾何參數與光柵層的改變為例子介紹。此外，一新式雙層混和光柵結構(DCG)的概念也會介紹如何控制光穿透，例如：移動、開放或遮蔽任何在可見光和近紅外光區域的電磁波視窗，可應用在位置感測或其它應用。本論文所得到的結果與物理現象探究期將提供如何設計一維奈米光柵光電機構的潛力方法並能輕易的使用目前一維微奈米製造技術。

Control of optical responses including transmittance, reflectance, or absorptance spectra using micro/nanostructures plays a key role in such tremendous applications as photonics, microelectronics, and energy conversion systems. With developments of nanofabrication technology, periodic nanostructures based on one, two, and three dimensions (1, 2, and 3D) have been considerable as promising candidates in enhancing or modifying optical responses. Accordingly, this dissertation aims to numerically investigate 1D periodic nanograting structures used for color filters, polarizers, emitters or absorbers, and sensors since the 1D structures possess potential benefits of theoretical analyses and experimental demonstrations. These applications include the design of integrated polarizer and RGB (red, green, and blue) color filters, the design of RGB color filters featuring high performance, investigation on physical mechanisms to design a polarization-insensitive thermophotovoltaic emitter, and controlling infrared (IR) absorptance spectra or optical transmission spectra in near IR and visible regions.

The numerical methods used in this dissertation are based on the rigorous coupled-wave analysis (RCWA), the finite-difference time-domain method (FDTD), and a genetic algorithm (GA). The RCWA and GA are the developments of the working codes based on the MATLAB programming language while the FDTD is a commercial software, namely OptiFDTD. The RCWA method is utilized to calculate optical responses of nanostructures, while the GA is used to optimize geometrical parameters of the nanostructures in such a way as to maximize or minimize the optical responses at the wavelengths of interest. Physical origins are, however, demonstrated by plotting electromagnetic field patterns and Poynting vector distributions within the structures using the FDTD method.

For the integrated polarizer and RGB color filters, the study provides a convenient and effective means of achieving the polarizing and filtering functions in liquid crystal display panels using a single device constructed on different subwavelength metallic gratings (SWMGs). In accordance with applications of SWMGs, RGB color filters-based resonant waveguide-metallic SWGs are proposed with high transmission efficiencies, broad bandwidths, and no redundant transmission peaks. Next, a comprehensive study is performed to investigate physical mechanisms, which cause the emittance enhancement of nanostructures, in order to design a very simple grating as a thermophotovoltaic emitter working under both transverse magnetic and transverse electric waves. Similarly, a single-layered SWMG owning an IR absorptance spectrum insensitive to the angle of incidence is recommended and features a tunable absorptance spectrum with a change in geometrical parameters and grating layers. Furthermore, a new concept of double-layered compound grating structure (DCG) is represented for actively controlling optical transmission spectra, e.g., shifting, opening, or blocking any special electromagnetic window in the visible and near IR regimes, which can be applied for displacement sensors or other applications. Overall, the numerical results and physical investigation obtained from the dissertation will provide a potential means of designing optoelectronic devices based on the 1D nanograting structures which is easily manufactured using current micro/nanofabrication technology.

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