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| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 邱奕鵬(Yih-Peng Chiou) | |
| dc.contributor.author | Cheng-Han Du | en |
| dc.contributor.author | 杜承翰 | zh_TW |
| dc.date.accessioned | 2021-06-16T08:29:09Z | - |
| dc.date.available | 2019-01-27 | |
| dc.date.copyright | 2014-01-27 | |
| dc.date.issued | 2014 | |
| dc.date.submitted | 2014-01-09 | |
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| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/58753 | - |
| dc.description.abstract | 本研究中我們開發出數種基於高階有限差分法的光學模擬工具。波導模擬為開發主軸，然而調整後的沿平面傳播之有限差分頻域分析可以模擬更一般性的問題。我們推導出一般化結構斷面上的任意階場型微分之連續關係式，結合泰勒級數展開應用於高階有限差分法並計算數種波導結構。數值評估顯示高階有限差分法帶來更高階誤差收斂。這個現象讓我們得以在模擬問題中使用更稀疏的格點切割，降低計算
資源需求而維持模擬準確度，甚至進一步精準。我們也研發出此方法在光束傳播法及沿平面傳播之有限差分頻域分析的應用，亦顯示高階有限差分法為這些模擬方法帶來更高的數值精確度及模擬效率。而泰勒級數展開及介面連續關係的概念也被應用於彎曲波導模態分析，其中我們由嚴謹計算式出發並得以準確模擬光電元件中的劇烈彎曲，而模擬工具的開發仍然非常簡單。 我們也利用已開發的數值模擬工具研究具備表面電漿極化子現象之波導。基本結構的模擬結果與已知理論吻合，也驗證我們的模擬工具能夠有效分析此類問題。在混合電漿波導模擬中，我們提出並分析一系列垂直指向耦合元件結構的新設計，而這些結構可相容於絕緣上矽的製程。為此我們分析金屬/絕緣體/金屬（MIM）與絕緣體/金屬/絕緣體（IMI）架構。平板結構分析顯示MIM 式指向耦合器的性能較好， 並可達到次微米的耦合長度。在三維結構模擬中，MIM 式設定亦顯示其次微米耦合的特性。其中耦合長度可縮短至0.496 微米，此乃約真空波長之三分之一，且耦合後之能量損耗可低於5%。在些微降低結構緊湊度的結構中，耦合長度仍然維持次微米，但能量損耗可更進一步降至3%。藉由光束傳播法分析，我們展示MIM 式垂直指向耦合器可在0.496 微米達成耦合，也驗證了我們提出的設計可大幅縮小元件。 | zh_TW |
| dc.description.abstract | In this study, several photonic simulation tools based on higher-order finite-difference method are developed. Waveguide mode analysis is the main development, while modification to in-plane finite-difference frequency-domain
analysis allows more general device simulation. We derive generalized continuity relations of arbitrary-order field derivatives across an abrupt interface, which will be combined with Taylor series expansion and applied in higherorder finite-difference analysis of several waveguide structures. Numerical assessment shows higher error convergence order when using higher-order finite-difference scheme. It allows coarser discretization of problem and decreases computation resource demand while accuracy is still maintained or even improved. Applications in beam propagation method and in-plane finite-difference frequency-domain method are also investigated and developed, and accuracy and efficiency of these techniques are also enhanced by higher-order finite-difference scheme. The concept of Taylor series expansion and interface continuity relations are also applied in bent waveguide mode analysis, where rigorous formulation allows accurate modeling of modern devices with sharp bends and its implementation is very simple. Waveguides with surface plasmon polariton effect are investigated using developed simulation tools. Simulation results of fundamental waveguides agree with known theory and effectiveness of the tools are verified. In simulation of hybrid plasmonic waveguides, we propose and analyze a series of vertical directional couplers based on SOI-compatible hybrid plasmonic waveguides. Metal-insulator-metal (MIM) and insulator-metal-insulator (IMI) configurations are investigated. Slab waveguide analysis shows that MIM directional couplers have better directional coupling performance with submicron coupling capability. Three-dimensional analysis also shows submicron directional coupling of MIM directional couplers. When the power loss is lower than 5%, the coupling length can be as short as 0.496 micron (about one third of the wavelength 1.55 micron). Slightly less compact design still yields sub-micron coupling length, when normalized power loss is less than 3%. By using beam propagation analysis, we demonstrate and verify a compact design that guided mode coupling along vertical direction can be achieved in 0.496 micron using our proposed MIM design. | en |
| dc.description.provenance | Made available in DSpace on 2021-06-16T08:29:09Z (GMT). No. of bitstreams: 1 ntu-103-D98941004-1.pdf: 4299602 bytes, checksum: e7826808e179693a05b816242ee8013e (MD5) Previous issue date: 2014 | en |
| dc.description.tableofcontents | 摘要i
Abstract iii 1 Introduction 1 1.1 Interface Boundary Condition and Higher-Order Finite-Difference Guided Wave Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2 Plasmonic and Hybrid Plasmonic Waveguides and Directional Couplers . 4 1.3 Overview of the Dissertation . . . . . . . . . . . . . . . . . . . . . . . . 7 1.4 Contributions of the Present Work . . . . . . . . . . . . . . . . . . . . . 8 2 Higher-Order Finite-Difference Waveguide Analysis 11 2.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.2 High-Order Finite-Difference Method . . . . . . . . . . . . . . . . . . . 12 2.3 Perfectly-Matched Layers . . . . . . . . . . . . . . . . . . . . . . . . . . 14 2.4 Maxwell’s Equations and Vector Helmholtz Equation . . . . . . . . . . . 16 2.5 One-Dimensional Finite-Difference Waveguide Mode Analysis . . . . . . 18 2.5.1 Graded-Index Approximation and Index Averaging (IA) . . . . . 18 2.5.2 Interface Continuity Relations . . . . . . . . . . . . . . . . . . . 19 2.5.3 High-Order Finite-Difference for One-Dimensional Problem . . . 22 2.6 Two-Dimensional Full-Vectorial Finite-Difference Mode Analysis . . . . 26 2.6.1 Arbitrary-order Planar Interface Continuity Relations . . . . . . . 27 2.6.2 Arbitrary-order Cylindrical Interface Continuity Relations . . . . 30 2.6.3 Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 2.7 Waveguide Mode with Circular Symmetry . . . . . . . . . . . . . . . . . 39 2.8 Beam Propagation Method . . . . . . . . . . . . . . . . . . . . . . . . . 41 2.9 Two-Dimensional In-Plane Finite-Difference Frequency-Domain Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 2.10 Full-Vectorial Bent Waveguide Mode Analysis . . . . . . . . . . . . . . 45 3 Simulation Results: Higher-Order Finite-Difference Waveguide Analysis 51 3.1 One-Dimensional Waveguide . . . . . . . . . . . . . . . . . . . . . . . . 51 3.1.1 Step-Index Waveguide . . . . . . . . . . . . . . . . . . . . . . . 51 3.1.2 Multiple-Quantum-Well Waveguide . . . . . . . . . . . . . . . . 54 3.2 Full-Vectorial Two-Dimensional Waveguide Mode Analysis . . . . . . . 58 3.2.1 Optical Fiber . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 3.2.2 Photonic Crystal Fiber . . . . . . . . . . . . . . . . . . . . . . . 61 3.2.3 Dual-Core Photonic Crystal Fiber Coupler . . . . . . . . . . . . . 63 3.2.4 Terahertz Pipe Waveguide . . . . . . . . . . . . . . . . . . . . . 65 3.3 Circularly Symmetric Waveguide Mode Analysis . . . . . . . . . . . . . 68 3.3.1 Step-Index Fiber: Reprise . . . . . . . . . . . . . . . . . . . . . 68 3.3.2 Terahertz Pipe Waveguide: Reprise . . . . . . . . . . . . . . . . 69 3.3.3 Index-Anti-Guided Waveguide . . . . . . . . . . . . . . . . . . . 70 3.4 Beam Propagation Method . . . . . . . . . . . . . . . . . . . . . . . . . 71 3.5 In-Plane Finite-Difference Frequency-Domain Analysis . . . . . . . . . . 74 3.6 Bent Waveguide Mode . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 4 Simulation Results: Plasmonic and Hybrid Plasmonic Waveguide 81 4.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 4.2 One-Dimensional Plasmonic and Hybrid Plasmonic Waveguides . . . . . 82 4.2.1 Single Surface SPP, MIM, and IMI . . . . . . . . . . . . . . . . 82 4.2.2 Hybrid Plasmonic Waveguides and Directional Coupler Design . 87 4.3 Two Dimensional Hybrid Plasmonic Waveguides and Directional Coupler 92 5 Conclusion 101 Bibliography 103 Publications of Cheng-Han Du 115 | |
| dc.language.iso | en | |
| dc.subject | 有限差分法 | zh_TW |
| dc.subject | 混和表面電漿波導 | zh_TW |
| dc.subject | 光波導 | zh_TW |
| dc.subject | Hybrid plasmonic waveguides | en |
| dc.subject | finite-difference method | en |
| dc.subject | Optical Waveguides | en |
| dc.title | 準確有限差分導波分析及其應用 | zh_TW |
| dc.title | Accurate Finite-Difference Analysis of Guided Waves and Its Applications | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 102-1 | |
| dc.description.degree | 博士 | |
| dc.contributor.oralexamcommittee | 張宏鈞(Hung-Chun Chang),黃鼎偉(Ding-Wei Huang),賴志賢(Chih-Hsien Lai),王子建(Tzyy-Jiann Wang),林晃巖(Hoang Yan Lin) | |
| dc.subject.keyword | 有限差分法,光波導,混和表面電漿波導, | zh_TW |
| dc.subject.keyword | finite-difference method,Optical Waveguides,Hybrid plasmonic waveguides, | en |
| dc.relation.page | 117 | |
| dc.rights.note | 有償授權 | |
| dc.date.accepted | 2014-01-10 | |
| dc.contributor.author-college | 電機資訊學院 | zh_TW |
| dc.contributor.author-dept | 光電工程學研究所 | zh_TW |
| 顯示於系所單位： | 光電工程學研究所 | |
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