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研究生:呂錦任
研究生(外文):Jin-Renn Leu
論文名稱:幾何光學分析微機電陣列光學元件之積體化研究
論文名稱(外文):Study of the Integrated Optical MEMS Switch Array Element by Ray Theory
指導教授:柯正浩
學位類別:碩士
校院名稱:元智大學
系所名稱:電機工程學系
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:2006
畢業學年度:94
語文別:英文
論文頁數:117
中文關鍵詞:高斯光束干涉反射比
外文關鍵詞:Gaussian BeamInterferenceReflectance
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在本篇論文中,我們以理論推導的方式,提出了一種考慮讓微機電光學開關陣列體積最適化的簡單公式,我們分別考量高斯光束的傳播特性、反射鏡面的傾斜轉動角度、鏡面擺放在光開關光路中的位置、鏡面的干涉效應,以及系統所使用的光波波長等因素來研究使得光學開關陣列體積得以縮小的方法。經由這些公式,我們可以將反射鏡面擺放在光路中任意位置,透過定義最佳高斯光束的腹腰值方法,而來確定最小需求反射鏡面寬度,或透過定義建設性干涉極大來確認最佳反射鏡面厚度。對於鏡面干涉效應的處理,我們建立一種三條入射光束的模式用來計算鏡面反射光之光輻射密度。三條光束法使得整個分析更趨近於高斯光學,或者說用簡單的幾何光學來模擬複雜的高斯光束,尤其是在光束極小而其光分歧角度達45°以上。我們將三條光束干涉效應與單一入射光束干涉效應作比較,特別是反射鏡面越作越小的同時,哪些才是主要關鍵因素。總合我們的推導結果,設計一種4×4縱橫矩陣式光學開關陣列,對此陣列的體積大小及16個光路的反射光輻射密度均勻性作一分析說明。
In this thesis, we propose a theoretical model for minimizing the physical size of optical switch matrix, the authors have designed and analyzed a simplified formulation of determining the size of MEMS mirror by using simple geometrical analysis. The beam waist radius, mirror tilted angle, propagation wavelength, location of mirror and interference are considered for deriving the optimum mirror size. The theoretical results shown that it is possible to define an optimum beam waist radius of Gaussian to obtain the minimum required mirror length and a maximum construct interference to obtain the optimum required thickness of mirror while the mirror is deposited on a particular location. A three-rays interference model is established to substitute for the conventions light beam interference analytical method, this model allows more exact to approximate the Gaussian mode to evaluate the flux densities of reflected beams. A comparison between three-rays interference and light beam interference are made with the phenomenon of fast beam divergence. In addition, a 4×4 crossbars optical switch is investigated, the minimum switch matrix size and the uniformity of encountered reflectance of mirror plate is reported.
Chinese Abstract ………………………………………………i
English Abstract ………………………………………………ii
Acknowledgment …………………………………………………iii
Contents …………………………………………………………iv
List of Figures ………………………………………………viii
List of Tables …………………………………………………xiv

Chapter 1 Introduction ……………………………………………1

Chapter 2 Theoretical model of integrated MEMS Optical Switch Arrays…………………………………………………………7

2-1 Introduction ……………………………………………………7

2-2 Analysis of adaptive mirror length with theoretical Gaussian mode by an approach of geometrical optics ………8

2-2-1 Theory of Gaussian mode distribution and propagation parameters……………………………………………………………9

2-2-2 Theoretical derivation of mirror length based on Gaussian hyperbola approximation beam for an angle tilted crystalline silicon mirrors of cross-connect switches……11

2-3 Determines the optimum mirror length by differentiating the deriving result with Gaussian
propagation parameters ……………………………………………20

2-3-1 Determines the optimum mirror length by way of differentiating the Gaussian propagation parameter- mirror location ……………………………………………………………21

2-3-2 Determines the optimum mirror length by way of differentiating the Gaussian propagation parameter- waist …………………………………………………………………………23

2-3-3 Optimum mirror length determination corresponding to the mirror tilted angle …………………………………………27

2-4 Summary …………………………………………………………29


Chapter 3 Investigation of the thickness of angle-turned mirror elements with three geometrical rays approach instead of Gaussian method………………………………………43


3-1 Introduction……………………………………………………44

3-2 Introduction of the model of three geometrical rays tracking substitute for Gaussian beam ………………………45

3-2-1 Determining the amplitude or intensity distribution of Gaussian beam with three geometric rays which spreading from beam waist ……………………………………………………47

3-2-2 Deriving the incident angle of x ray, y ray and z ray when a reconstruct Gaussian model applied onto the boundary of mirror plate…………………………………………48
3-3 The multi-beam interference among the three geometry tracing reflected rays with silicon substances mirror plate …………………………………………………………………53

3-3-1 The general expressions of the fractional amplitude reflection and transmission coefficient, scalar amplitude and flux densities of higher-order Gaussian reflected beams for the mirror plate with an arbitrary angle of incidence……………………………………………………………54

3-3-2 Set up a model of three rays interference to substitute for the Gaussian beam ……………………………61

3-4 Definition of the optimal thickness of MEMS mirror elements to make the reflectance to maximum………………65

3-5 The comparison of reflected flux densities and required optimum thickness of mirror by using light beam and three-rays model ……………………………………………69

3-6 Summary…………………………………………………………71

Chapter 4 Design of the integrated MEMS mirror Optical switching matrix …………………………………………………83

4-1 The optimized design of 1×2 MEMS minimum size cross-connect with the alignment of mirrors and lenses ………84

4-1-1The smallest final beam radius for switching system design ………………………………………………………………84

4-1-2 The focus length of lenses and the focus distance from fiber to lenses ……………………………………………87

4-1-3 The designing of 1×2 MEMS minimum size cross-connect with the optimized alignment of mirrors and lenses……………………………………………………………… 88

4-2 The optimized designing of 4×4 MEMS fiber coupling cross-connect with the alignment of mirrors and lenses
………………………………………………………………………89

4-3 The reflectance uniformity amount all the channels of 4×4 MEMS mirror arrays……………………………………………93

4-4 Summary…………………………………………………………95


Chapter 5 Conclusions……………………………………………106

References …………………………………………………………110

Publication List …………………………………………………xv
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