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論文名稱 Title |
以全特徵模態展開法分析大角度、單方向傳播之緩變介電質波導 Effectiveness of full eigen-mode expansion technique for studying smoothly varying dielectric waveguides with wide-angle one-way traffic |
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系所名稱 Department |
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畢業學年期 Year, semester |
語文別 Language |
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學位類別 Degree |
頁數 Number of pages |
104 |
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研究生 Author |
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指導教授 Advisor |
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召集委員 Convenor |
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口試委員 Advisory Committee |
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口試日期 Date of Exam |
2007-06-20 |
繳交日期 Date of Submission |
2007-07-04 |
關鍵字 Keywords |
彎曲波導、直線波導 bending waveguide |
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統計 Statistics |
本論文已被瀏覽 5682 次,被下載 1157 次 The thesis/dissertation has been browsed 5682 times, has been downloaded 1157 times. |
中文摘要 |
積體光學中有許多大角度、單方向傳播之緩變介電質波導。如彎曲波導、多模干涉器(MMI)、錐型波導(tapered waveguide)、階梯陣列順向耦合器(GADC)等,他們都是集成光器件中不可缺少的部分。波導的側向位移和連接都需要很多的彎曲波導來實現。 而現今用來分析光電元件最佳化的近似方法有光束傳播法 (BPM)、時域有限差分法 (FD-TD)、頻域有限差分法(FD-FD)等。有別於光束傳播法沒有辦法計算大角度且計算結果不是很準確、時域有限差分法、頻域有限差分法雙向傳播使用大量的計算,因此,此篇論文中我們修改(couple transverse mode integral equation ,CTMIE)僅考慮所有角度、單方向傳播近似,我們稱做全特徵模態展開法 (full eigenmode expansion technique, FEMET)來分析各角度彎曲波導傳播及輻射損耗。FEMET不需解代數聯立方程式、可大量降低計算量。 最後我們用FEMET來計算傾斜直線波導,來驗正其FEMET的精確性。 |
Abstract |
In integrated optics, there are many adiabatic dielectric waveguides. Examples include bending waveguides, multi-mode interferometers (MMI), taper waveguides, grating assisted directional couplers (GADC), etc. Among these waveguide devices, adiabatic bending waveguides are the most important basic devices. They are used to connect various vertical or horizontally displaced waveguides. There are many approximate methods such as the beam propagation method (BPM), finite-difference time-domain, (FD-TD) and finite-difference frequency-domain (FD-FD) methods that have been used to analyze and optimize the waveguide designs. BPM can not calculate wide angle optical traffic due to its intrinsic paraxial limitation. Both FD-TD, FD-FD handle wide-angle bi-directional traffic but both demand tremendous computational resources. In this thesis, we develop a new formulation called full eigen-mode expansion technique (FEMET) that considers only forward propagating but all wide-angle traffic. It is a simplified version of our existing bidirectional, coupled transverse-mode integral-equation (CTMIE) formulation. FEMET includes all forward propagating, high-order mode field but neglects reflection at the dielectric discontinuities. Since FEMET uses no matrix equations, it is much faster than CTMIE. To verify the accuracy of FEMET we consider the titled straight waveguide (TSR) as our test example. TSR has an exact solution in its natural coordinate system which allows us to study computational characteristics of FEMET. The two FEMET computational control parameters are the total number of waveguide sections and the number of modes used in each section. Together they control the speed and accuracy of FEMET. We use FEMET to analyze radiation and mode interference of both S-bend waveguides and two-corner bends. These results compare well with result computed by other methods. |
目次 Table of Contents |
第一章 導論 1 1.1 簡介 1 第二章 FEMET理論分析傾斜式直線波導 5 2.1 FEMET理論基本觀念 5 2.2 傾斜式直線波導座標系統轉換 8 2.3 FEMET分析傾斜式直線波導 9 2.4 傾斜式直線波導數值模擬結果 11 第三章 FEMET理論分析S型彎曲波導 34 3.1 TE入射FEMET理論架構與推導 34 3.2 S型彎曲波導切區設計和數值模擬結果 40 第四章 FEMET理論分析兩段式彎曲波導 59 4.1 兩段式彎曲波導數值模擬結果 59 4.2 彎曲波導能量分析 69 4.3 彎曲波導的驗正 75 第五章 結論與未來工作 83 參考文獻 84 中英文對照表 86 |
參考文獻 References |
[1] F.J.Mustieles, E.Ballesteros, and P. Baquero, " Theoretical S-Bend Profile for Optimization of Optical Waveguide Radiation Losses, "IEEE Photonics technology letters, Vol. 5, no.5, pp.551~553, May 1993. [2] Tsutomu Kitoh, Norio Takato, Mitsuho Yasu, and Masao Kawachi "Bending loss Reduction in Silica-Based Waveguides by Using Lateral Offsets "IEEE Journal of lightwave technology. Vol. 13, 4,pp.55~562, April 1995 [3] Paolo Monguzzi, Raffaella Costa, and Mario Martinelli, "Design of curved waveguides: the matched bend, "J. Opt. Soc. Am.A/Vol. 20, No. 1/,130-137January 2003. [4] L.D.Hutcheson, Ian A. White and James J. Burke, " Comparison of bending losses in integrated optical circuits, " Optics Letters,276-278, 1980. [5] Stuart N. Radcliffe and Terence P. Young" New Low-Loss Bend Structures for High-Density Integrated Optical Switch Arrays "IEEE Journal on selected areas in communications.Vol. 6. No. 7.pp.1169~1177,August 1988. [6] Junji Yamauchi "Propagating Beam Analysis of Optical Waveguides" Hosei University, Tokyo, Japan 2003. [7] Yasuhide Tsuji, Masanori Koshiba, and Tomohide Tanabe, "A Wide-angle Beam Propagation Method Based on a Finite Element Scheme, " IEEE Transactions on magnetics .vol. 33, no. 2, pp. 1544~1547, March 1997. [8] 黎聯群, "多模干涉器的場理論及元件物理," 碩士論文, 國立中山大學光電工程研究所,(2006). [9] 周逸軒, "雙向多模解析法分析二維環型共振腔結構," 碩士論文,國立中山大學光電工程研究所, 2003. [10] A. Ishimaru, "Electromagnetic Wave Propagation, Radiation, and Scattering, " Prentice-Hall ,Seattle, pp. 104-105, 1991. |
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