本研究主要為設計平面聚焦透鏡並可達到傳統聚焦透鏡之效果，其主要結構為利用不規則的光子晶體結構來構成傳統聚焦透鏡所需要的相位差，我們將光子晶體以正方晶格的方式排列成一二維平面，此種方式可以提供我們更多設計上的自由。我們所設計之光子晶體聚焦透鏡工作波段為1310 nm，除了計算整體的光穿透率(Overall Transmission)，因為我們亦計算其焦平面之能量聚集度(Concentration)。在此論文中，其中分別有兩個不同數值孔徑 (Numerical Aperture) 的設計，在最後模擬結果中，其整體的穿透率皆可達到85%以上，甚至可以到93%，在能量聚集度上，在較大數值孔徑結果與單模光纖比較並無較好的能量聚集的效果，然而較小數值孔徑之設計結果在半徑為3.7m的圓內下包含90%的能量，與單模光纖之光源相比較有良好的聚焦效果。

Our research is mainly about designing flat focuser by using photonic crystal structure. By arranging non-periodic photonic crystal with square lattice, we can distribute the phase for a focusing element like traditional curved focusing lens. It let us have much more design of freedom by using square lattice, we can either gradually vary the period between lattices or the radius of cylindrical holes. The center wavelength we design is at 1310 nm, and the not only concern about the overall transmission of the photonic crystal slab (PCS), we also introduce the concentration of the focusing spot at focal plane. In this thesis, we design two cases of the PCS focuser, one has bigger numerical aperture (NA), the other one has a smaller NA. The overall transmission is above 85% for both cases, and for smaller NA case is up to 94%. But for the application of receiver, the concentration of the focusing spot is also a key factor. At last, the PCS focuser of large NA has no improvement compared to single mode source. But the smaller NA case has great improvement for concentration. The 90% of the power can be confined within circle radius of 3.7 micron meter.

致謝 I
摘要 II
Abstract III
目錄 IV
圖目錄 V
第1章 緒論 1
第2章 基本理論背景 5
2.1 波導模態共振 (Guided-Mode Resonance) 5
2.2 聚焦透鏡理論 9
2.2.1 傳統聚焦透鏡理論 9
2.2.2 平面聚焦透鏡設計 12
第3章 光子晶體平面聚焦透鏡 19
3.1 設計與模擬方式 19
3.2 元件設計結果與分析 32
第4章 結論 39
附錄 I 42
參考文獻 45

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