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研究生:趙士傑
研究生(外文):Shih-Chieh Chao
論文名稱:變分法分析光波導及光纖之傳播特性
論文名稱(外文):Variational Analysis of Propagation Characteristics of Optical Fibers
指導教授:吳 慕 鄉
指導教授(外文):Mu-Shiang Wu
學位類別:博士
校院名稱:大同工學院
系所名稱:電機工程研究所
學門:工程學門
學類:電資工程學類
論文種類:學術論文
論文出版年:1994
畢業學年度:82
論文頁數:125
中文關鍵詞:變分法光波導光纖
外文關鍵詞:Variational methodOptical waveguidesOptical fibers
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變分法提供一個有效的方法分析許多無法獲得正確解的光波導問題。此外
,變分法可由簡單且基本的函數得到波導波導的模態特性,進而了解波導
的物理性質。本論文以變分法分析非均質平面光波導及光纖的傳播特性、
光纖方向耦合器與其在濾波器上之應用。本論文討論的主題如下:1 變
分法求固有值在分析光波導及光纖的應用。以一正確的嘗試函數運用此法
求得平面波導的傳播常數,其結果顯示變分法是相當有效的。2 變分法
與下降趨近法解析非均質平面光波導及光纖的純量方程式之比較。3 利
用變分法與一些新的嘗試函數求得單模非均質平面光波導的傳播特性與平
面光波導之間的模態耦合效率。4 利用擴展修正高斯法與延伸高斯法的
兩個新的嘗試函數分析光纖及耦合器。這些函數只使用一些簡單的基本函
數去近似基本模態場分佈且較現有的嘗試函數準確。5 實現由W式與步
階式光纖組成的方向耦合器達成窄頻與低旁波瓣之全光纖式濾波器。旁波
瓣的高度可以由適當調整元件的耦合強度而大幅降低。利用高斯函數加權
耦合係數,旁波瓣的高度可降低至-38 dB。此外,設計時所需的參數亦有
方法可循。

The thesis contains the following studies: 1. The
variational principle for eigenvalues in the analysis
of optical waveguides and fibers is presented. A correct
trial field is used to obtain the propagation constant of
the planar slab waveguide by this method. The results show
the validity of the variational method. 2. The solutions of the
scalar wave equation in the single- mode inhomogeneous
planar optical waveguides and fibers are considered
through the variational and steepest-descent
approximation techniques. A comparison of the numerical
results obtained by the two methods has been discussed. 3.
Some new trial fields are proposed for obtaining the
propagation characteristics of single-mode inhomogenous
planar waveguides and the modal coupling efficiency between two
graded- index waveguides, based on the scalar variational
principle. A comparison with other trial fields and the
exact numerical results has been discussed. 4. Two trial
functions which extend the modified Gaussian and the
generalized Gaussian method for the study of weakly- guiding
single-mode fibers and couplers have been demonstrated. These
functions use only simple elementary functions to
approximate the fundamental modal fields. The present
trial functions gives a significant improvement over the
existing trial functions. 5. Narrow-band and low-sidelobe all-
fiber spectral filter is achievable with directional
couplers constructed with a W- index and step-index fiber.
The sidelobe levels can be reduced significantly by properly
weighting the coupling strength along the device. With a
Gaussian function weighting, -38 dB transfer response
sidelobes have been obtained. Besides, some design rules
of the filter for the desired bandwidth and coupling
length are also given.

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