低同調干涉量測系統被使用來精確地量測光波導元件，此系統建立在一馬赫-詹德干涉儀基礎上。藉由低同調的光源，我們可以使光在波導裡的每一個獨立的光路徑產生干涉條紋，將這些干涉條紋做傅立葉轉換分析，可以獲得光在經過每一個路徑的振幅及相位響應，利用這些資訊我們即可以得到元件重要的參數。
然而，當使用此系統來測量環形共振腔時，干涉條紋彼此之間的距離和光在環形共振腔裡繞行一圈的長度有關。在有限的光源頻寬下量測小半徑的環形共振腔時，每個波包會與鄰近的波包產生嚴重的重疊，進而阻礙了我們去獨立地分析每一個光路徑。 因此，本論文提出了一種新的方法，透過訊號處理方法增加原本的光源頻寬，來克服光源頻寬限制下產生的干涉條紋重疊之問題，使我們可以成功地分析小半徑環形共振腔。又由於傳統的環形共振腔數學模型無法解釋環形共振腔頻譜分裂之現象，本論文使用的數學模型包含了環形共振腔耦合區域等效折射率變化產生之反射影響頻譜分裂。這些技術被使用在模擬以及實驗的分析上，使得估算出的參數誤差小於0.1%，此項成果將可讓人們未來在分析小半徑環型共振腔有更高的準確度。

Low coherence interferometric measurement has been used to investigate
optical waveguide devices with high accuracy. It is based on a Mach-Zehnder
interferometer system. By utilizing an incoherent light source, one can generate separate interferogram feature for each optical path. By analyzing each interferogram feature individually via Fourier transformation, the amplitude and phase information can be obtained. The information allows one to extract key parameters of the device. The distance between adjacent features of a ring resonator is related to ring length. With small ring radius, the interferogram spectrum exhibits severe cross interference between adjacent features that hinders one to analyze the optical path individually. This thesis proposes a novel technique to overcome the light source bandwidth limitation. By replacing the actual light source with a much broader virtual Gaussian light source via signal processing, which allows one to characterize small radius micro-ring resonator. In addition, the traditional ring model cannot have good explanation for the splitting of the measured spectrum. By utilizing our new model which contains the coupling region induced reflection effect, the fitted ring parameters can perform very well with measured spectrum. This technique has been applied to both numerical simulations and experimental data with significant improvement of the extracted ring parameters. The fitting errors are less than 0.1% in our method. The improvements allow one to better understand the wavelength dependency properties of small radius micro-ring resonators.

中文審定書 i
摘要 iii
Abstract v
1 Introduction 1
1.1 Silicon photonics technology . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Micro-ring resonator . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.3 Outline of this thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2 Principle of micro-ring resonator 9
2.1 Model and theory of micro-ring resonator . . . . . . . . . . . . . . . . . 9
2.1.1 All-pass type micro-ring resonator . . . . . . . . . . . . . . . . . 10
2.1.2 Add/drop type micro-ring resonator . . . . . . . . . . . . . . . . 13
2.2 Double-dip phenomenon . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.2.1 Single-dip condition . . . . . . . . . . . . . . . . . . . . . . . . 21
3 Characterization and analysis method 23
3.1 Wavelength scan method . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3.1.1 Experimental setup . . . . . . . . . . . . . . . . . . . . . . . . . 23
3.1.2 Disadvantage of WSM . . . . . . . . . . . . . . . . . . . . . . . 25
3.2 Low coherence interferometric measurement . . . . . . . . . . . . . . . 27
3.2.1 Experiment setup and analysis . . . . . . . . . . . . . . . . . . . 27
3.2.2 Characteristic matrix . . . . . . . . . . . . . . . . . . . . . . . . 31
3.2.3 Benefit and problem . . . . . . . . . . . . . . . . . . . . . . . . 35
4 Analysis of micro-ring resonator with small radius 37
4.1 Windowing method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
4.2 Reshaping method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
4.3 Simulation and experimental results . . . . . . . . . . . . . . . . . . . . 43
4.3.1 Simulation results . . . . . . . . . . . . . . . . . . . . . . . . . 43
4.3.2 Experimental results . . . . . . . . . . . . . . . . . . . . . . . . 46
4.4 Reshaping method optimization . . . . . . . . . . . . . . . . . . . . . . 55
5 Conclusion 59
Bibliography 61
Publications 67

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