本論文主要是關於寬頻帶特性之二維光子晶體三角晶格波導轉彎的設計與分析。所設計之三角晶格波導轉彎結構，係改良自一個具有圓形空氣孔反射面的波導轉彎，因而獲得兩種較佳之結構，第一種是增大半徑的圓形空氣孔反射面結構，第二種是單模態波導的圓形空氣孔反射面結構。設計的目的是要提高脈衝波通過光子晶體波導轉彎的傳輸率，設計結果並與簡易型光子晶體波導轉彎及矩形空氣孔反射面波導轉彎之傳輸率作比較。由模擬結果得知，本設計可將傳輸率由簡易型的1~8%大幅提昇到圓形空氣孔反射面波導轉彎的99%。
在分析的方法上，先以平面波展開法計算光子晶體能隙，並希望能隙的範圍包含光纖通訊所使用之1.55μm波長，使光侷限在光子晶體波導中，再以時域有限差分法模擬光場在轉彎結構中光傳播的情形並計算傳輸率。由分析結果可知，本論文所提出的兩種改良之圓形空氣孔反射面波導轉彎結構，皆具有結構簡單、高傳輸率及寬頻帶等優點。

In this work, design and analysis of broadband photonic crystal (PhC) waveguide bend in two-dimensional triangular lattice is presented. By modifying a waveguide bend with a reflecting plane consisting of circular air holes, two better structures are obtained. The first is designed by enlarging the radii of the circular air holes of the reflecting plane. The second is designed by making the line-defect waveguide single- mode. The design purpose is to make the transmission efficiency of a launched pulse through the PhC waveguide bend as high as possible. Transmission results are compared to those obtained for a simple PhC bend and a bend with a rectangular reflecting plane. Simulation results show that transmission efficiency is dramatically enhanced to 99% for the bend with a reflecting plane consisting of circular air holes, compared to only 1~8% for a simple PhC bend.
As for the method of analysis, the plane wave expansion method is employed to calculate the photonic bandgap. And the 1.55 μm wavelength is required to be within the photonic bandgap to ensure the light-guiding condition. The finite-difference time-domain method is employed to simulate light propagation and to calculate transmission efficiency. It is shown that the proposed PhC waveguide bends exhibit the advantages of simple structures, high transmission, and broadband characteristics.

目 錄
中文摘要...................................................................................................i
英文摘要.....................................................................................................ii
致謝.............................................................................................................iii
目錄.............................................................................................................iv
表目錄.........................................................................................................vi
圖目錄.........................................................................................................vii
第一章 緒論..............................................................................................1
1.1光子晶體簡介..............................................................................1
1.2光子晶體波導轉彎之介紹..........................................................7
1.2.1利用鏡面反射面的方式......................................................8
1.2.2在轉彎處加缺陷的方式......................................................9
1.2.3拓撲優化設計的方式.........................................................10
1.2.4模態及波數匹配的方式......................................................11
1.2.5低折射率溝渠的方式..........................................................12
1.2.6利用雙轉彎間之共振現象的方式.......................................13 1.3研究動
機....................................................14
1.4論文架構......................................................................................14
第二章 數值分析方法..............................................................................16
2.1光在介質中傳遞的行為..............................................................16
2.2平面波展開法..............................................................................19
2.2.1 橫向電場模態....................................................................20
2.2.2 橫向磁場模態....................................................................21
2.3時域有限差分法..........................................................................22
2.4吸收邊界條件...........................................................................29
2.5高斯脈衝法的介紹.......................................................................31
第三章 寬頻帶之光子晶體波導轉彎結構...............................................34
3.1三角晶格空氣孔光子能隙分析....................................................36
3.2簡易型光子晶體波導轉彎..........................................................39
3.3矩形空氣孔反射面的光子晶體波導轉彎...................................42
3.4圓形空氣孔反射面的光子晶體波導轉彎...................................48
3.4.1增大圓形空氣孔反射面的空氣孔半徑................................52
3.4.2進一步設計使線缺陷波導呈單模態....................................55
3.5設計結果討論..............................................................................59
第四章 結論..............................................................................................61
參考文獻.....................................................................................................62

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