利用奈米球鋪排成六角晶格形狀，來製作奈米等級的結構，具有製作方便、大面積及較佳的規律性等優點，可應用於生物檢測器及彩色濾波器等方面。本論文提出以單層鋪排奈米球取代黃光微影製程，製作大面積週期性奈米結構的二維共振波導，達到製程簡單的目標。
本論文利用嚴格耦合波理論方法模擬與設計出在週期780 nm時，分別探討填充因子，蝕刻深度以及旋轉角度對共振波長的影響。由以上參數改變的模擬結果可以得知，以週期780 nm的參數為例，其填充因子須大於0.6，才會有共振波長產生。蝕刻到底部的共振波導對於角度有較大的容忍度。我們以直徑750 nm的奈米球分別製作出不同週期之試片A:780 nm，B:753 nm及C:780 nm的二維共振波導濾波器其中試片C:780 nm的光柵為蝕刻到底部的結構。經由量測穿透頻譜的結果得知，試片A共振波長與半高寬λ(nm):Δλ(nm)為1106:17、1142: 22、1368:30，試片B共振波長為1155:27、1235:40、1365:24，試片C共振波長為1276:102、1624:151。同樣的驗證了其具有多模態的效果，而且試片C，在旋轉角度上有較高的容忍度。本研究驗證了以奈米小球製作二維共振波導濾波器的可行性，且可應用在寬頻濾波器，未來可改變奈米球週期來調製所需波長，應用到更多元件。

This study fabricated a nano-structure in the shape of a hexagonal-lattice grating through the arrangement of nanospheres. This structure offers a number of advantages, including easy fabrication, excellent coverage, and structural regularity. Such structures have been applied to the development of biosensors and color filter. This study proposes that a single layer sedimentation of nanospheres be used as an easily fabricated alternative to photolithography .
This study observed the resonance behavior of the proposed two dimensional guided-mode resonant through rigorous coupled-wave analysis (RCWA). Incident wavelength, grating thickness, and grating fill ratio were selected as the parameters for simulations. Using period = 780 nm as an example, when the fill ratio ≧ 0.6, resonance was achieved. By broadening the angular tolerance of the self-suspended subwavelength grating, this study fabricated a three two-dimensional guided-mode resonant filter.
The measurement results of wavelength and full width half maximum (FWHM) were λ(nm):Δλ(nm), respectively. Sample A: 1106:17, 1142: 22, 1368:30; Sample B: 1155:27, 1235:40, 1365:24; Sample C: 1276:102, 1624:151. This study demonstrated that Sample C in multi-mode showed broadening of angular tolerance at an oblique angle of incidence.
This study demonstrated that two-dimensional guided-mode resonance filters can be fabricated through the use of nanospheres, which can simplify the process of fabricating such devices.

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