本論文主要以矽光子技術為平台之SOI (Silicon on Insulator)微環形共振腔元件為主軸，對其模擬及量測之結果進行分析，並建立理論模型，以了解並用於環形共振腔在應用上之設計。內文由環形共振腔之原理特性及設計做出發，並透過穩態及動態之分析對環形共振腔進行討論：
環形共振腔之原理與元件設計：
敘述環形共振腔在頻譜上的基本特性及原理，如推導波長之共振條件、自由頻譜範圍(FSR)之設計及各種參數與結構間之關係等，藉由其傳輸方程式了解環形共振腔在波長分波多工(WDM)應用上之設計。透過對環形共振腔頻譜進行最佳化，設計如多環(multi-ring)環形共振腔之元件，以用來滿足元件在光通訊頻寬上的需求，並藉由量測了解環形共振腔在不同結構設計中的參數特性。
環形共振腔之穩態分析：
透過單環之環形共振腔在量測上發現頻譜分裂的情形，探討並分析各種反射模態在環形共振腔中產生的原因。藉由模擬軟體(3D-FDTD)發現在高折射率差的情況下，環形共振腔在耦合區間上有折射率不連續的情形並產生反射模態。以此建立一套理論模型分析及討論在穩態下，反射模態對頻譜的影響。
環形共振腔之動態分析：
藉由此低同調干涉系統分析環形共振腔之干涉圖形，透過建立環形共振腔在不同圈數上之遞迴關係，建立環形共振腔在反射模態存在下之特徵矩陣，以了解頻譜在動態情況下的變化及趨勢，並預測反射隨著圈數的增加所帶來的影響，透過對量測及模擬的數據進行分析，擷取環形共振腔之參數及發現參數與波長間之關係，最後則藉由動態分析的方式探討環形共振腔在調變器上之應用。

In this thesis, the SOI micro-ring resonator based on Silicon photonics technology was discussed and analyzed with both simulation and experiment results. The novel theoretical model was proposed to explain the ring properties that can use in many applications. The contents depart in three topics:
The principle of the micro-ring resonator and devices design:
In this topic, the principle of the micro-ring resonator would be discussed. The resonant wavelength condition, free spectral range (FSR), and the relation between the ring parameters and the ring structure are explained. Through the transmittance function of the ring, one can optimize the transmittance spectrum of the ring to satisfy the bandwidth requirement in optical communication applications.
Analysis of the micro-ring resonator in steady-state:
In this topic, the double-dip resonance spectrum will be discussed. The double-dip resonance spectrum is generated by the reflection mode in the ring. Through the 3D-FDTD simulation, the coupling region of the ring illustrates the discontinuous index property that would generate the reflection mode. Thus, a novel theoretical model – a 4x4 scattering matrix is proposed to analyze the effect of the reflection mode.
Analysis of the micro-ring resonator in dynamic-state:
In this topic, the low coherent interferometry system will be discussed. Through the recursive relation of the ring, the interferogram on each round trip can be analyzed and extracted the parameters by Fourier transformation. Also, the interferogram can be used to predict the dynamic changes of the spectrum that is helpful for design of the ring modulator.

摘要 i
Abstract iii
目錄 iv
圖次 v
表次 xiv
第一章 緒論 1
1.1. 矽光子技術 3
1.2. 環形共振腔 5
1.3. 高密度波長分波多工技術之應用 6
1.4. 論文大綱 8
第二章 環形共振腔之原理與元件設計 10
2.1. 環形共振腔之原理 10
2.1.1. 全通式濾波器理論模型及模態耦合理論 11
2.1.2. 插入/抓取(add/drop)濾波器 15
2.1.3. 波長選擇性 17
2.1.4. 自由頻譜範圍(FSR) 17
2.1.5. 環形共振腔之失諧(detuning)現象 18
2.2. 環形共振腔之元件設計 20
2.2.1. 數位濾波器之型態及zero-pole分析 20
2.2.2. 頻寬之最佳化設計 23
2.3. SOI環形共振腔之設計、量測探討與分析 25
2.3.1. 環形共振腔元件之結構 26
2.3.2. 元件量測結果之探討 27
第三章 環形共振腔在穩態下之分析 32
3.1. 波長掃描之量測 32
3.2. 粗糙面(roughness)產生之反射模態 34
3.2.1. 粗糙面產生反射之機制 36
3.2.2. 人為操控反射模態之例：缺口(notch)之環形共振腔 39
3.2.3. 隨機分布之粗糙面產生反射之討論 40
3.3. 耦合區間產生之反射模態 40
3.3.1. 耦合區間產生反射之散射矩陣與理論模型 42
3.3.2. 單谷(single-dip)型頻譜之條件 44
3.3.3. 量測結果之分析與討論 46
第四章 環形共振腔在動態下之分析 50
4.1. 低同調干涉系統之分析方法 50
4.1.1. 低同調干涉系統之量測 51
4.1.2. 以低同調干涉量測系統分析環形共振腔 57
4.2. 環形共振腔反射特性之分析 69
4.2.1. 環形共振腔在耦合區間產生反射模態之特徵矩陣 72
4.2.2. 反射特性分析之結果與討論 75
4.3. 環形共振腔動態特性之分析 80
4.3.1. 環形共振腔之動態頻譜 82
4.3.2. 儲存於環形共振腔之能量 88
4.4. 環形共振腔在動態特性之應用 92
第五章 結論 98
參考文獻 100

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