臺灣博碩士論文加值系統

本論文研究二維光子晶體波導中的多模干涉效應(Multimode Interference，MMI)及其自生成像原理(Self-Imaging)。首先，利用有限差分時域法(Finite-Difference Time-domain，FDTD)來觀察二維光子晶體多模波導中的成像現象和成像位置。發現到其成像位置與模態傳輸分析(Modal Propagation Analysis，MPA)所得到的成像位置一致。利用以上兩種方法(FDTD、MPA)在各個不同的光子晶體多模波導作驗證，都可以得到相符的結果。證明傳多模波導的成像原則與分析方式可以套用在光子晶體多模波導上。本研究並應用光子晶體多模干涉現象設計了一個一分為二的波長分波器(Wavelength-Division-Demultiplexer)，分波對象為1.480微米及1.625微米。有限差分時域法模擬得到其效率為:在1.480微米有0.33dB的插入損耗(Insertion Loss)及15.4dB的對比(Contrast)，在1.625微米有0.33dB的插入損耗及12.9dB的對比。

In this study, the multimode interference (MMI) effect and its principle (self-imaging) in 2-D photonic crystal waveguides (PCWs) are investigated. By using the finite-difference time-domain (FDTD) computation performed on a multimode photonic crystal line-defect waveguide, the self-imaging phenomenon and the imaging positions along the propagation axis are observed, and it is found that the results are in good agreement with those derived from the modal propagation analysis (MPA). This mean that the analytic methods for MMI in conventional multimode waveguides still can be applied in 2-D line-defect PCWs. We take several multimode PCWs for examples to confirm this idea. Moreover, we design a photonic crystal 1-to-2 1.480/1.625μm wavelength-division-demultiplexer based on MMI in PCWs. Its performance in numerically simulated by FDTD computation. The results show that the insertion loss is about 0.33 (dB) for the wavelength 1.480μm, and 0.33 (dB) for 1.625μm. The contrast is about 15.45 (dB) for the wavelength 1.480μm, and 12.9 (dB) for 1.625μm, respectively.

1. Introduction 1
2. Analytic Theories and Methods for Photonic Crystals 4
2.1 Introduction 4
2.2 Plane-Wave Expansion Method 5
2.3 Two-Dimensional Photonic Crystals 8
2.4 FDTD Method 13
2.5 Band Diagrams Calculation 16
3. Modal Propagation Analysis for Multimode Interference 22
3.1 Introduction 22
3.2 The Self-Imaging Principle 22
3.3 Modal Propagation Analysis 25
4. Self-Imaging Phenomena in Multimode PCWs 29
4.1 Introduction 29
4.2 Three-line-defects Multimode PCWs 30
4.3 Four-line-defects Multimode PCWs 36
4.4 Five-line-defects Multimode PCWs 42
5. Design of a PC Wavelength-Division-Demultiplexer 47
5.1 Introduction 47
5.2 Design of a 1-to-2 1.480/1.625 um
Wavelength-Division-Demultiplexer 48
6. Conclusion 55

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