中文摘要
由於利用光纖傳輸資訊可以有較大的頻寬，可以傳輸大量的資料，而DWDM更是可以大量增加光纖傳輸頻寬的技術，其中AWG為現在最熱門的DWDM的分波原件之一。所以我們希望能夠研究、瞭解AWG的設計技巧、特性和製作技術，最後能夠有能力自行設計出陣列波導光柵。
雖然說在市面上有很多設計AWG的軟體，例如BPM等等，但是其實其中在設計AWG時，最困難的問題是在於AWG的光罩佈線，還有最後光罩圖案要以AutoCAD檔案的形式，輸入機器製作光罩。其他設計的參數，都可依想設計的條件和AWG的公式來得出。
本篇論文主要貢獻在於：一、討論AWG每區的功能。二、提出並解釋AWG分波幾何原理。三、提出Rowland Circle光行程差公式。四、解決AWG通道波導中的繞線問題，使其不會有大角度的轉彎和小區率半徑。五、具備Matlab畫圖轉到AutoCAD的能力，可用Matlab來畫AutoCAD的光罩圖。

Design and Analysis of Arrayed Waveguide Grating
Abstract

Fiber optic communication provides extremely broad bandwidth making transferring large quantities of voice/data possible. Dense Wavelength Division Multiplexing (DWDM) is the most critical technology of the optical communication system. It allows the simultaneous transmission of up to hundreds of channels within a single fiber across a distance of thousands of kilometers. Arrayed waveguide grating (AWG) is the most critical component in the DWDM system. It takes a single input and separates different optical “channels” into different output fibers. It is critical that we develop our own ability to design and fabricate such a device, so that we will not be left behind in the technological realm.

Although there are many commercially available AWG designing software such as the Phaser package of the BPMPRO software, they fail to provide a solution to aide in the final design of the optical mask for the AWG. In this thesis, we present a detailed, step-by-step analysis of an AWG device, as well as a description of how the AWG device works. In the process, we have classified the free parameters from that of depending parameters and have solved the routing problem in the layout of the waveguides.

To summarize the primary result of this thesis, we use five main points, which are:
1) We discuss the function of each block, the subsystems of the AWG.
2) We propose a novel, yet intuitive theory based on geometric optics – how the device is able to perform its de-multiplexing functions.
3) We present an analytic formula showing the linear property of the optical path difference along the source and the receiver arrays.
4) We solved the routing problem of the various waveguide sections of the AWG.
5) We have automated the process of generating optical masks in AutoCAD format from within a Matlab environment.

目錄 頁次
誌謝……………………………………………………………..I
中文摘要……………………………………………………….II
英文摘要……………………………………………………. III
目錄…………………………………………………………...Ⅳ
圖目錄………………………………………………………Ⅵ
表目錄……………………………………………………... Ⅷ
第一章、導論………………………………………………….1
1-1：簡介………………………………………………….1
1-2：研究動機………………………………………………3
1-3：研究方法…………………………………………….4
第二章、設計步驟與參數…………………………………..5
2-1：陣列波導光柵的工作原理……………………………5
2-2：板片波導( Slab Waveguide) ……………………….8
2-3：基本參數和設計出的AWG參數……………………11
2-4：使用純量波動光學來模擬…………………………12
2-5：解釋最後聚光原理…………………………………13
2-6：AWG的主要設計公式…………………………….15
2-7：主要設計步驟…………………………………………21
2-8：極化與幾何形狀對AWG通道波導的有效折射率改變的探討………………………………………………………23
第三章、結果與討論………………………………………34
3-1：能量對角度分佈圖…………………………………34
3-2：造成AWG的損失主原因……………….……………38
3-3：輸入損失、平坦度與不同極化的差異損失之討論…40
3-4：隔離閘處之損失( Gate Loss)進步討論……………42
3-5：AWG設計之技巧和要特別注意事項………………44
3-6：AWG五項規格和設計結果…………………………56
3-7：和現有套裝軟體的比較……………………………57
第四章、結論………………………………………………61
4-1：結論………………………………………………… 61
附錄…………………………………………………………63
參考文獻……………………………………………………64
中英對照表…………………………………………………66


圖目錄 頁次
圖(1.1-1) 陣列波導光柵的示意圖……………………………2
圖(2.1-1) 設計的陣列波導光柵的示意圖……………………7
圖(2.2-1) 羅倫圓結構的示意圖………………………………9
圖(2.2-2) 羅倫圓結構的線性路徑示意圖………………….10
圖(2.5-1) 最後聚光原理示意圖…………………………….13
圖(2.6-1) 板片波導的示意圖………………………………..15
圖(2.6-2) 通道波導長度簡示圖…………………………….16
圖(2.6-3) 與相鄰之間繞射階數簡示圖……………………..17
圖(2.6-3) 板片波導聚光長度公式的示意圖………………..19
圖(2.8-1)二個嵌入型通道波導示意圖………………………24
圖(2.8-2)二個山脊型通道波導示意圖………………………25
圖(2.8-3)水平極化與垂直極化(基礎模態場型) ……………27
圖(2.8-4)垂直極化(第二、第三模態場型) …………………28
圖(3.1-1) 全部32個通道的輸出波形……………………….35
圖(3.1-2) 32個通道中最低的兩個頻率的通道輸出波形…...36
圖(3.1-3) 32個通道的頻率中，中心兩個頻率的波形……….36
圖(3.1-4) 32個通道中最高的兩個頻率的通道輸出波形…..37
圖(3.3-1)設計的通道波導橫切面圖形………………………40
圖(3.4-1) 隔離閘處之損失( Gate Loss)的說明圖………….42
圖(3.5-1)設計的AWG大概圖形介紹……………………….44
圖(3.5-2)通道波導與板片波導連接處圖形…………………45
圖(3.5-3)通道波導與板片波導連接處圖形（錯誤示範）……46
圖(3.5-4)通道波導起始、結尾處的特殊設計………………47
圖(3.5-5)羅倫圖結構所造成彎曲的和理想平面的誤差……47
圖(3.5-6) 波導通道特殊繞線圖形式一……………………48
圖(3.5-7) 波導通道特殊繞線圖形式二……………………48
圖(3.5-8) 波導通道每區分段佈局說明圖…………………50
圖(3.5-9) AWG輸入部分和光纖連接處細節圖………………51
圖(3.5-10) AWG輸出部分和光纖連接處細節圖……………51
圖(3.5-11)AWG中通道波導佈線Lay Out放大圖……………52
圖(3.5-12)把波導通道分出對稱的一半，再分成七個相等的等分的示意圖…………………………………………………………………53
圖(3.7-1)某套裝軟體之AWG示意圖……………………………57
圖(3.7-2)某套裝軟體之通道波導示意圖……………………58


表目錄 頁次
表(2.3-1) 基本參數和設計出的AWG參數……………………11
表(2.8-1) 折射率參數表………………………………………25
表(2.8-2) 嵌入型的垂直和水平極化…………………………29
表(2.8-3) 山脊型的垂直和水平極化…………………………30
表(2.8-4) 改變波核幾何形狀之山脊型的垂直和水平極化…31
表(3.4-1) 隔離閘處之損失( Gate Loss)的討論表…………42
表(3.5-1) 通道波導和其相鄰通道的距離……………………54
表(3.6-1)五項目標規格達成表…………………………………56
表附錄國際標準( ITU)通道頻率表……………………………63

參考文獻
[1]Hiroshi Takahashi, Member, IEEE, Kazuhiro Oda, Member, IEEE, Hiroma Toba, Member, IEEE,and Yasuyuki Inoue, Member, IEEE, “Transmission Characteristics of Arrayed Waveguide N×N Wavelength Multiplexer,” Journal of Lightwave Technology. vol. 13, No. 3, pp.447-455, March 1995.
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[9]Tso-Lun Wu and Hung-Wen Chang, “Guiding mode expansion of a TE and TM transverse-mode integral equation for dielectric slab waveguides with an abrupt termination,” J. Opt. Soc. Am. A, vol. 18, pp.2823-2832 No. 11/November 2001.
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[11]極化與幾何形狀對AWG通道波導的有效折射率改變的探討，2002年台灣光電研討會( OPT)，作者張弘文、林政衛、張世明、吳宙秦、曹碩芳、周逸軒。
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