平面光波導已逐漸成為未來光通訊不可或缺的元件，其是利用半
導體製程來大量製作功能複雜的積體光學元件的技術，可符合未來輕薄短小及低成本的趨勢，且其具有良好的穩定性、可量產，與可體積化的特性使其在光通訊產業中扮演著非常重要的角色。
當波導斜切角度等於零度時，其波導反射係數並不為零，但隨著
斜切角度增加其反射係數會逐漸降低，但其散射現象也會越來越明
顯；由於散射現象增加使得波導內會產生不想要的高階模態，所以如何在波導能量傳輸效率與散射現象中取得平衡點是我們目前所要分析的課題。為了分析上述的問題，我們在此利用模態來展開我們的反射係數與穿透係數。接著我們可利用解析連續法使兩邊的場型在介面上連續以及垂直微分連續。然後我們再發展出不完全積分方程來求解我們的反射及穿透係數。而不完全積分方程非常適用於小角度斜切角終端波導上。我們主要的分析對象為多模態一維光纖波導，一般波導斜切角度等於零度時其能量反射係數衰減約為-28dB，但當斜切角增至8 度時其能量衰減可提高至-60dB，因此我們可藉由解析連續法分析哪一個切割的斜角角度是最佳的，且其模擬結果與頻域有限差分法相符合。

Utilizing the semiconductor processing technology, a large number of optical components can be integrated into a small area. It is of low cost and high reliability and can be massively produced. The PLC(planar light circuit) has become an important component with the opto-communication industry.In this thesis, we aim to study dielectric waveguide termination witha slightly tilted facet. A waveguide with normal termination in the air will have non-zero reflection coefficients due to the impedance difference at the core-air junction. To reduce the reflection of the fundamental mode, it is custom to terminate the waveguide with a small tilted angle.
The angle is optimally chosen to avoid spurious scattering into high-order radiation modes.To analyze this problem, we employ the modal expansion method for both the reflected waves and the transmitted waves. We then
analytically extend the waves and join the two fields on the bordering line by matching the fields and their normal derivatives. An incomplete transverse-mode integral equation (TMIE) is derived for the reflection and transmission coefficients. The incomplete TMIE is good for
waveguide termination with small tilted angles. Our analysis show that for multi-mode 1-D slab waveguide (simulating the 1-D optical fiber), the fundamental mode reflection coefficient is about -28dB down. It gradually reduces to -60dB as we increase the tilt angle from around 8 degrees. The result agrees well with those calculate from
frequency-domain finite-difference method.

誌謝I
中文摘要II
英文摘要III
目錄IV
圖表目錄VI
第一章導論1
1-1：簡介1
1-2：研究動機2
1-3：解析連續法4
第二章三層介電質波導的理論推導5
2-1：三層介電質波導的模型5
2-2：三層介電質波導的模態分析7
2-2-1：二層介電質波導的模態分析(TE even mode) 9
2-2-2：二層介電質波導的模態分析(TE even mode) 12
2-2-3：二層介電質波導的模態分析(TE odd mode) 15
2-2-4：二層介電質波導的模態分析(TE odd mode) 18
2-2-5：二層介電質波導的模態分析(TM even mode) 21
2-2-6：二層介電質波導的模態分析(TM even mode) 24
2-2-7：二層介電質波導的模態分析(TM odd mode) 27
2-2-8：二層介電質波導的模態分析(TM odd mode) 30
2-3：二層結構轉為三層結構之步驟35
2-3-1：二層結構轉為三層結構(TE case，even mode) 36
2-3-2：二層結構轉為三層結構(TE case，odd mode) 38
2-3-3：二層結構轉為三層結構(TM case，even mode) 40
2-3-4：二層結構轉為三層結構(TM case，odd mode) 42
第三章模態匹配(mode matching) 44
3-1：TM case 45
3-2：TE case 51
第四章不完全積分方程(incomplete TMIE) 52
4-1：TM case 52
第五章波導場型模擬75
5-1：模擬結果76
第六章總結89
6-1：結果討論89
參考文獻
中英對照表

[1] 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,March 22, 2001
[2] Dietrich Marcuse ;”Reflection Loss of Laser Mode From Tilted End Mirror”,Journal of Lightwave Technology . Vol.7. NO.2, Feb-ruary 1989
[3] Peter Bienstman, E. Six, M. Roelens, M. Vanwolleghem, and Roel Baets, ”Calculation of Bending Losses in Dielectric Wave-guides Using Eigenmode Expansion and Perfectly Matched La-yers”, 2001
[4] Ishimaru,A.,”Electromagnetic Wave Propagation, Radiation ,and Scattering ,”Englewood Cliffs,N.J.:Prentice-Hall,1991
[5]施有彰You-Jang Shih ;”Analysis and Numerical Study of Recta-ngular Waveguide with Large Bending Angles”,國立中山大學光電工程研究所碩士畢業論文,June 2001
[6]游能忠Neng-Jung You ;”Application of coupled E/H field formula-tion to the design of multiple layer AR coating for large incident angles”,國立中山大學光電工程研究所碩士畢業論文,June 2001
[7]Tso-Lun Wu and Hung-Wen Chang,“Analysis of TE to x and TM to x Mode for Dielectric Slab Waveguides ”Optics and Photon-ics Taiwan ’01 Proceeding in Optical wavegudide Modeling,TB1-2 pp. 146-148, December 13-14, 2001.
[8] 許峻源Jiun-yuan Shiu ;”利用解析連續法分析小角度彎曲波導的反射係數與場型”,國立中山大學光電工程研究所碩士畢業論文
June 2004