光學微球型共振腔因具有高品質因子與小模場體積等特點，被廣泛地運用在光通訊、非線性光學、染料雷射和生物感測等領域。光在球型共振腔的共振模態WGM(Whispering-gallery Modes)一般是透過耦光元件消逝場耦合(Evanescent field coupling)而激發，如何調控共振腔與耦光元件之間的耦合距離是極為重要的課題。
本研究將微流體系統與光學系統加以整合，提出了一個可調式光學共振腔的構想，利用投影機的光誘發光介電泳力(optically-induced dielectrophoresis)操控微米球共振腔，微調共振腔與單模脊狀波導之間的距離。我們在光電泳晶片內滴入混有聚苯乙烯球(n=1.571)的蔗糖水溶液(n=1.399)，並以SU-8負光阻(n=1.569)製作波導結構於晶片上。經由實驗測試發現，我們可以操控聚苯乙烯球並控制與光波導維持一穩定的距離；經量測光波導的穿透頻譜，藉由頻譜上峰值的深度與半高寬，可將聚苯乙烯球與光波導操作在過耦合(over-coupling)，近臨界耦合(near critical-coupling)，和弱耦合(under-coupling condition)等三種情況。
本研究成功地利用光介電泳晶片操控聚苯乙烯微米球，作為一可調式的光學共振腔，此元件最顯著的特點為可藉由一低功率的投影機，控制光學共振腔的耦合條件。

Optical microsphere resonators are widely applied in various fields including, optical communications, researches on nonlinear optical effect, dye lasers, and label free detection for biosensing , due to the high quality factor and small mode volume. However, to effectively excite the microsphere resonator is challenging since the external light should be coupled to the resonant modes, or called whispering gallery modes (WGM), with a precisely controlled distance.
In this study, a new integrated microsphere resonator optofluidic device is presented. The microsphere resonators are manipulated by optically-induced dielectrophoresis(ODEP) for precisely tuning the coupling distance between the resonator and a single mode rib waveguide. We fabricate single mode rib waveguide structure made by SU-8(n=1.569) on the ODEP device, with polystyrene beads(PSB, n=1.571) of 100-μm diameter were suspended in a liquid chamber with high-density sucrose solution (n=1.397). We have manipulated PSB which is pushed away and keeps a stable distance from the waveguide. Through measuring transmittance spectra at different coupling distance, PSB is operated at the over-coupling, near critical-coupling and under-coupling condition, respectively, by examining the transmission dips of the spectra.
We have successfully realized a compact optofluidic platform for studying tunable microsphere optical resonators in an aqueous medium. Asalient feature of this platform is that the microsphere can be freely operated in any of the coupling conditions via a low-power image
projector.

目 錄
摘 要………………………………………………………………………………Ⅰ
Abstract……………………………………………………………………………Ⅱ
目 錄…………………………………………………………………………………Ⅲ
圖 目 錄……………………………………………………………………………Ⅴ
表 目 錄…………………………………………………………………………Ⅶ
第一章、緒論 1
1.1前言 1
1.2研究動機與目的 3
1.3論文架構 3
第二章、理論背景 4
2.1微球型光學共振腔模態 4
2.1.1耳語廊模態 4
2.1.2自由光譜範圍 6
2.1.3品質因子 7
2.2光波導理論 10
2.2.1平板波導 10
2.2.2脊狀波導 15
2.2.3單模脊狀波導 18
2.3共振腔與光波導的模態耦合 20
2.3.1耦合模態理論 20
2.3.2耦合因子 22
2.4光介電泳原理 24
2.4.1介電泳效應 24
2.4.2光介電泳原理 26
第三章、元件設計模擬與製作流程 27
3.1球型共振腔模擬 29
3.1.1有限元素法 29
3.1.2 WGM模擬結果 30
3.2脊狀波導模擬 33
3.2.1單模脊狀波導條件 33
3.2.2介電層厚度 35
3.3介電泳模擬 37
3.4元件設計與製程 43
3.4.1元件製作流程 44
3.4.2元件製作流程詳細說明 45
第四章、實驗量測與分析 48
4.1光介電泳操控系統 48
4.1.1操控系統架構 48
4.1.2光介電泳測試 49
4.2光學量測系統 50
4.2.1光學量測系統架構 50
4.2.2光學量測分析 53
第五章、實驗結果與討論 59
參 考 文 獻 61
圖目錄
圖1.1.1 球型共振腔應用於拉曼雷射示意圖 1
圖1.1.2 以稜鏡耦合激發WGM示意圖 1
圖1.1.3 以錐狀光纖激發WGM示意圖 1
圖2.1.1 自由空間中的球形共振腔內部光場傳遞示意圖 4
圖2.1.2 共振腔內徑向與極座標方向場分佈示意圖 6
圖2.1.3 自由光譜範圍FSR示意圖 7
圖2.2.1 光於光波導中傳遞滿足全反射條件－n_1>n_2 〖>n〗_3 10
圖2.2.2 步階平板波導示意圖 10
圖2.2.3 對稱型模態分佈 13
圖2.2.4 非對稱型模態分佈 14
圖2.2.5 導波模態之傳播常數範圍 14
圖2.2.6 等效折射率法基本概念 16
圖2.2.7 等效折射率法分析脊狀波導範例圖 17
圖2.2.8 脊狀波導結構圖 18
圖2.3.1 相位匹配示意圖 21
圖2.3.2 模場重疊示意圖 21
圖2.3.3 光波導與共振腔耦合示意圖 22
圖2.4.1 在非均勻電場中，(a) 粒子的極化能力高於周圍溶液，受到正介電泳力
作用，粒子會往強電場區移動。(b) 粒子的極化能力低於周圍溶液，受
到負介電泳力作用，粒子會往弱電場區移動。 25
圖2.4.2 光誘發介電泳示意圖 26
圖3.1.2 元件模擬流程圖 27
圖3.2.1 實驗設計概要圖 28
圖3.1.1 聚苯乙烯球之WGM光場模擬結構 32
圖3.1.2 模擬聚苯乙烯球之TEn=1,l=621 WGM 光場分布 32
圖3.1.3 模擬聚苯乙烯球之TEn=1,l=307 WGM 光場分布 32
圖3.2.1 模擬單模脊狀波導結構圖 34
圖3.2.2 單模脊狀波導模擬圖，利用Rsoft 軟體的BPM所模擬，其中λ=1550
nm，模場為TM模態。 35
圖3.2.3 模擬介電層厚度結構與材料參數圖 36
圖3.2.4 不同介電層厚度波導能量的損耗；(a) SiO2厚度為0.5 μm，(b)
SiO2厚度為1 μm 。 36
圖3.3.1 模擬介電泳操縱頻率結構圖 37
圖3.3.2 實部f_cm因子隨頻率變化圖 38
圖3.3.3 (a)光介電泳之∇E_^2場圖，(b)當y=188.9 μm時，不同x位置時的
∇E_^2值 40
圖3.3.4(a)因脊狀波導產生之∇E_^2場圖，(b)當y=188.9 μm時，不同x位置時
的∇E_^2值 40
圖3.3.5 脊狀波導與光介電泳所造成的∇E_^2之場圖 42
圖3.3.6 y=188.9 μm與頻率為(a)120K Hz 、(b) 70K Hz時的∇E_^2值
42
圖3.3.7 位置為x=176 μm，y=188.9 μm時，其所受到脊狀波導與光介電泳兩者
造成的∇E_^2隨頻率的變化 42
圖3.4.1 元件設計圖 43
圖3.4.2 元件製作流程圖 44
圖3.4.3 脊狀波導俯視圖 47
圖3.4.4 元件上下板俯視圖 47
圖3.4.5 元件完成圖；(a)元件橫截面示意圖，(b)元件實際圖。 47
圖4.1.1 光介電泳操控系統架構示意圖 49
圖4.1.2 對100 μm聚苯乙烯球進行操控，如圖(a)~(c)利用光所誘發之負介電泳
力可移動聚苯乙烯球，改變其與波導之間的距離。 49
圖4.2.1 光學量測系統示意圖 51
圖4.2.2 元件量測架設實際圖 52
圖4.2.3 光學量測步驟圖 52
圖4.2.4 聚苯乙烯球與波導在不同耦合長度下的光譜圖 53
圖4.2.5 聚苯乙烯球與波導在不同耦合長度下的FSR分析圖 55
圖4.2.6 中心波長約為1561.5 nm峰值歸一化之穿透頻譜 56
圖4.2.7 聚苯乙烯球與波導在不同耦合長度下的Q值分析圖 58
表3.1.1 元件的材料特性 28
表3.1.1 解析WGM特徵方程式參數設定 31
表3.1.2 解析WGM特徵方程式所得共振腔之光學特性 31
表3.2.1 單模脊狀波導模擬參數 34
表3.2.2 計算當脊高b改變時，對應的脊寬a要小於多少才能滿足單模條件之結
果 34
表3.3.1 CM factor 模擬參數 38
表3.3.2 模擬脊狀波導與光介電泳之∇E_^2之參數 39
表3.4.1 元件製作之材料來源 43

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