本論文研究抗諧振反射光波導陣列波導光柵波長解多工器元件。不同於傳統的光波導技術，此設計可在矽基片上製作而適合於積體電路製造知技術。首先利用多層模理論和有效折射係數法來分析及設計抗諧振反射光波導結構，然後利用波束傳輸法 (Beam Propagation Method) 來模擬抗諧振反射光波導陣列波導光柵元件。利用這些分析工具設計了在矽基片上具有16個頻道、頻道間距為200 GHz、中心波長工作在1550.92 nm的抗諧振反射光波導陣列波導光柵波長解多工元件。此元件中心波長的損耗為2.83 dB，外圍波長的損耗為4.63dB，而3-dB 頻帶的寬度為0.74 nm，交互干擾的準位小於 —30dB。元件最小彎曲波導半徑為15mm，元件總尺寸為4×6 cm2。

In this thesis, the ARROW-based AWG device is designed. The design can be made of materials based on silicon substrates and is compatible to IC process technologies. First, we use the multilayer theory and Effective Index Method are used to analyze the ARROW structures. Then the Beam Propagation Method is used to simulate the performance of the ARROW-based AWG devices. Using these analyzing tools, we design a 16-channel ARROW-based AWG demultiplexer with 200-GHz spacing for 1550.92-nm operation on a Si substrate. The losses for the central and outer wavelengths are 2.83 and 4.63 dB, respectively. The 3-dB bandwidth is 0.74 nm. The crosstalk level is below —30 dB. The minimum radius of the bending waveguide in the device is 15 mm. The full device size is 4×6 cm2.

1 Introduction 1
2 Analytic Theories and Basic Structure for Antiresonant Re‡ ecting Optical
Waveguide Device 6
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.2 Multilayer Characteristic Matrix Method . . . . . . . . . . . . . . . . . . 6
2.3 E¤ective Index Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.4 Basic ARROW Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.5 Beam Propagation Method (BPM) . . . . . . . . . . . . . . . . . . . . . 11
3 Operating Principle and Design of Arrayed Waveguide Grating 12
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
3.2 Operating Principle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
3.3 Layout of AWG . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
3.4 Design Considerations of AWG Devices . . . . . . . . . . . . . . . . . . . 21
4 ARROW-based AWG Demultiplexer 26
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
4.2 Design of ARROW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
4.2.1 Design of ARROW by Multilayer Stack Theory . . . . . . . . . . 26
4.2.2 E¤ective Index Method for Channel ARROW Waveguides . . . . 30
4.3 Design of ARROW-based Arrayed-Waveguide Grating . . . . . . . . . . . 35
i
4.3.1 AWG Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
4.3.2 Performance of Designed AWG Devices . . . . . . . . . . . . . . . 37
4.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
5 Conclusion 45

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