週期性金屬狹縫和非週期金屬狹縫皆可用於設計光學繞射元件，透過材料特性與幾何結構的設計，可以實現一般傳統光學元件無法達到的特性，本研究利用二維有限元素法設計週期性和非週期性的光學繞射元件。首先，非週期性金屬狹縫主要是利用中心狹縫與兩側狹縫之繞射光的光程不同，使繞射光的相位發生延遲，透過適當設計狹縫位置，焦點處會在我們所預期的地方形成聚焦光斑。我們可透過增加狹縫數或降低焦距長度降低焦點處光斑的半高全寬，但同時也會讓景深變小。當我們的非週期性繞射元件的焦距長度為3μm時，狹縫數僅5個，元件寬度只有6.16μm且厚度僅100nm，即可達到光斑的半高全寬及景深分別為494nm及1.58μm的效果。
關於週期性繞射元件，我們利用週期性的金屬狹縫耦合的方式激發水平方向的表面電漿子模態與狹縫電漿子的耦合模態。隨著環境折射率發生變化，共振峰值將產生位移，故可作為環境感測元件。元件經過優化之後，折射率靈敏度為464nm/RIU。另外，我們也在元件上填入溫度敏感材料以應用於溫度感測，其靈敏度為-119.67nm/oC。與過去的文獻相比，我們的元件在頻譜上的峰值極窄，較容易進行峰值追蹤，量測的準確性也較佳。

Periodic and aperiodic metallic slit arrays can be applied to design optical diffractive elements. They can provide some properties that are hard to be achieved by conventional optical elements. In this study, we design periodic and aperiodic optical diffractive elements by using a two-dimensional finite element method. We first consider aperiodic metallic slit arrays containing a central slit with other slits on both sides. By appropriately arranging positions of the slits, the phase difference for diffractive light from each slit can be well designed to form a focused spot at the expected position. We can reduce the FWHM by increasing the number of slits or decreasing the focal length. However, the DOF is decreased. By using only five slits, we can realize a device with the FWHM is only 494nm as the designed focal length is 3μm. In addition, the width and thickness of our element are only 6.16μm and 100nm, respectively.
Besides, we also design periodic metallic slit arrays to excite the surface plasmon polariton mode and slit plasmon polariton mode. They will couple with each other as their propagation constants are the same. The element can be used in sensing applications due to the resonance peak can be shifted by the variation of environmental refractive index. After optimization, the sensing sensitivity of the device is 464nm/RIU. In addition, we can infiltrate the temperature-sensitive material into our device to achieve a temperature sensitivity of -119.67nm/oC. Compared with other reports, the resonance peak of our device is much more narrower to make it easy to track the peak and enhance the measurement accuracy.

誌謝 i
摘要 ii
Abstract iii
目錄 v
圖目錄 vii
表目錄 xi
第一章 緒論 1
1-1繞射元件簡介 1
1-2表面電漿子原理 6
1-3研究動機 11
第二章 狹縫的繞射 12
2-1狹縫的繞射原理 13
2-1.1 Fresnel繞射原理(近場繞射) 14
2-1.2 Fraunhofer繞射原理(遠場繞射) 17
2-1.3 狹縫的干涉原理 18
2-2異常光學穿透現象 23
第三章 非週期性狹縫之數值分析 29
3-1繞射透鏡的重要參數解釋 29
3-2非週期狹縫透鏡 32
3-3非週期狹縫透鏡之特性分析 35
3-3.1 狹縫尺寸對元件表現的影響 36
3-3.2 狹縫數量對元件特性的影響 39
3-3.3 焦距長度對元件特性的影響 42
第四章 週期性狹縫之數值分析 46
4-1週期性金屬狹縫之感測元件 46
4-2週期性金屬狹縫之共振特性 47
4-2.1 共振模態分析 48
4-2.2 結構參數對共振點的影響 50
4-3週期性金屬狹縫的感測特性與結果 55
第五章 結論 61
參考文獻 62

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