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博碩士論文 etd-0705112-214404 詳細資訊
Title page for etd-0705112-214404
論文名稱
Title
多層光波導特徵模態之通用表示式分析
General Forms of Eigen-Mode Analysis for Multilayer Optical Waveguides
系所名稱
Department
畢業學年期
Year, semester
語文別
Language
學位類別
Degree
頁數
Number of pages
142
研究生
Author
指導教授
Advisor
召集委員
Convenor
口試委員
Advisory Committee
口試日期
Date of Exam
2012-06-25
繳交日期
Date of Submission
2012-07-05
關鍵字
Keywords
模態分析、超穎介質、非線性光波導、導波、多層光波導
Multilayer Waveguide, Mode Analysis, Metamaterial, Nonlinear Waveguide, Guided Wave
統計
Statistics
本論文已被瀏覽 5741 次,被下載 315
The thesis/dissertation has been browsed 5741 times, has been downloaded 315 times.
中文摘要
在本論文對於平面多層光波導中之傳播模態提出了一系列的探討。非線性光波導是指光波導結構中含有折射率會隨電場強度改變的介質。針對此種介質本研究利用模態定理提出了一種通用性的模態解法。此方法可有效含蓋多種結構之多層非線性平面光波導。對於同時具有負介電係數與負導磁率之超穎介質多層平面光波導,本論文也提出了一種通用性的模態解法。本研究對於具有超穎導波層之三層波導中所存有的禁止區提出了解釋與計算。並提了一個完整的模態集合。本論文所提之通用表示式可求得在多層光波導中的模態傳播行為與橫向電場的分佈,這些光波導之介質材料可以是線性、非線性或超穎介質。最後,本論文利用前述之方法設計一個線性之全光式模態轉換器。嚴密的推導與數值分析的結果證明本論文所提之多層光波導特徵模態通用表示式是正確的方法。
Abstract
In this thesis, we proposed general forms of eigen-mode analysis for multilayer optical waveguides. This study discussed the periodic structure in transverse direction and used the slowly varying envelope approximation to approximate the wave function. Firstly, we presented a general method for analyzing the multilayer nonlinear optical waveguide structure by using modal theory. The nonlinear optical waveguide is a medium whose refractive index changes with the electric field intensity. The general method can also be degenerated into some other special cases for analyzing multilayer nonlinear optical waveguide. Secondly, a general method for analyzing the multilayer optical waveguides with photonic metamaterials characterized by simultaneously negative dielectric permittivity and magnetic permeability was studied. The research pointed out explicitly that the three-layer planar waveguide with photonic metamaterials could support forbidden regions. The complete set of modes of all possible solutions for the TE wave in photonic metamaterials optical waveguide was found. The transverse electric field distributions and dispersion relations in multilayer optical waveguides can be obtained by using these general forms. Finally, we used the general forms to design an all-optical mode converter which composed of a pair of multibranch optical waveguides. The analytical and numerical results show excellent agreement.
目次 Table of Contents
Acknowledgement i
Abstract iii
Contents v
List of Figures vii
List of Tables x
List of Symbols xi
Chapter 1 Introduction 1
Chapter 2 Basic Theory and Numerical Method 5
2.1 Modes of the Three-Layer Planar Waveguide 5
2.2 Third-Order Nonlinear Effect 8
2.3 Material Classifications 10
2.4 Beam Propagation Method 12
Figures 17
Chapter 3 Analyzing Multilayer Optical Waveguide with All Nonlinear Layers Nonlinear Waveguide Structure 21
3.1 Introduction 21
3.2 Method and Analysis 23
3.2.1 Analytic Formulation 23
3.2.2 Degenerated Description 28
3.3 Numerical Results 30
3.4 Summary 34
Figures 36
Chapter 4 Analysis and Calculations of Forbidden Regions for TE Guided Waves in the Three-Layer Planar Waveguide with Photonic Metamaterial 61
4.1 Introduction 61
4.2 Method and Analysis 62
4.2.1 Analytic Formulation 62
4.2.2 Transverse Modes in DNG Planar Waveguide 65
4.3 Numerical Results 68
4.4 Summary 69
Figures 71
Chapter 5 Analyzing the Multilayer Optical Planar Waveguides with Double-Negative Metamaterial 79
5.1 Introduction 79
5.2 Analytic Formulation 80
5.3 Numerical Results 83
5.4 Summary 84
Figures 86
Chapter 6 A General Rule for Designing Multibranch High-Order Mode Converter 93
6.1 Introduction 93
6.2 The Formulation of General Rules 94
6.3 Numerical Results 97
6.4 Summary 98
Figures 100
Chapter 7 Conclusion and Future Work 109
Appendix 111
I:Degenerated into the multilayer optical waveguides with nonlinear cladding and nonlinear substrate 111
II Degenerated into the multilayer nonlinear optical waveguides with a localized arbitrary nonlinear guiding film 111
III Degenerated into the multilayer optical waveguides with all nonlinear guiding film 112
Ⅳ The dispersion equations in DNG waveguides 113
References 120
Publication List 127
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