SOI微環型共振器已經被廣泛應用在高密度整合積體光路之通訊系統中。然而，當微環型共振器的半徑縮減至數個微米之尺寸時，只要有些許製程誤差即會造成不理想的頻譜響應。而跑道式行進波共振器結構其傳輸波導與共振環間的強耦合能力，使彼此的耦合間隙能變寬可以增加製程容忍度。但由於小尺寸的SOI跑道式微環狀共振器其FSR較大，因此本論文利用在其中加入光柵輔助結構，產生順時針與逆時針方向傳播模態，達到共振分裂使通訊波段增加可操作的訊號傳輸通道以提升系統容量，期望能達到克服此限制的目標。
在本論文中，我們首先使用二維有限差分時域(2-D FDTD)法結合等效折射率法模擬SOI跑道式微環狀共振器，計算其長直傳輸波導與共振器間之耦合間隙從窄至寬的傳輸頻譜。接著利用時域模態耦合理論所推導的公式與二維有限差分時域法所模擬的傳輸頻譜作數值曲線擬合的分析，以得到共振器的品質因數與我們所需要的光學參數。接下來，模擬在SOI跑道式微環狀共振器中加入光柵輔助結構後對頻譜的影響。我們亦使用時域模態耦合理論推導共振器中加入光柵輔助結構後，產生的順時針與逆時針方向傳播模態導致的共振分裂之公式，再以同樣的步驟來探討此元件的特性。其中，我們討論了共振器中不同光柵結構與位置所產生的頻譜響應，包含不同長度下的對稱或單邊波導側壁光柵，以因應不同需求與應用來選擇適當的SOI跑道式光柵輔助微環狀共振器結構。最後，我們利用SOI波導的熱光效應，模擬SOI跑道式光柵輔助微環狀共振器在不同溫度下的共振位移情況，並計算其對溫度的敏感度為95.38 pm/°C，可提供熱光調制元件應用之參考。

Silicon-on-Insulator (SOI) micro-ring resonators (MRRs) are versatile elements in high-density integrated optics telecommunication systems. However, small inaccuracies in the fabrication process intensely deteriorate the response of SOI MRRs. By utilizing the racetrack resonator structures with strong coupling abilities, one can improve the fabrication tolerance. For the SOI racetrack resonators, the FSR is usually large. By introducing gratings into SOI racetrack resonators, the mutual mode coupling between the clockwise and counterclockwise modes can be induced and result in the resonance splitting. The grating-assisted SOI racetrack resonators can increase the operation wavelength and open up the possibility to overcome this limitation.
In this thesis, we first use the 2-D FDTD method with the effective index method (EIM) to obtain the transmission spectra of the SOI racetrack resonators. The transmission spectra are then fitted by using the time-domain coupled mode theory (CMT) to obtain the quality factor and optical parameters of the SOI racetrack resonators. Next, we demonstrate the characteristics of mode splitting resulted from the mutual mode coupling between the clockwise and counterclockwise modes in the grating-assisted racetrack resonators by utilizing both the CMT and the 2-D FDTD method with the EIM. By tuning the grating configurations, such as the length or the structure of sidewall gratings, one can obtain the desired transmission spectrum of the grating-assisted racetrack resonators. Finally, we numerically investigate the temperature-dependent spectral characterics of the grating-assisted SOI racetrack resonator by taking the thermal-optic responce of the SOI materials into account. The thermal sensitivity of this device is 95.38 pm/°C, and the calculted properties can help the further designs based on the grating-assisted SOI racetrack resonators.

第一章 緒論. . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1-1 SOI光波導介紹. . . . . . . . . . . . . . . . . . . . .1
1-2 微環型共振器介紹(Micro-ring Resonators, MRRs). . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1-3 研究動機. . . . . . . . . . . . . . . . . . . . . . . . . 4
1-3.1 元件結構與介紹. . . . . . . . . . . . . . . . . . . . . . . . 6
第二章 數值模擬分析方法. . . . . . . . . . . . . . . . . . . 7
2-1 光波導分析方法. . . . . . . . . . . . . . . . . . . .7
2-2 有效折射率法(Effective Index Method, EIM). . . . . . . . . . . . . . . . 7
2-3 波束傳播法(Beam Propagation Method, BPM). . . . . . . . . . . . . . 12
2-4 有限差分時域法(Finite-Difference Time-Domain, FDTD
Method) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
第三章 模態耦合理論(CMT)分析與模擬結果. . . . . . . . . . . . . . . . . .19
3-1 模態耦合理論. . . . . . . . . . . . . . . . . . . . 19
3-2 利用時域模態耦合理論分析SOI跑道式微環狀共振器. . . . . . .21
3-3 利用時域模態耦合理論分析SOI跑道式光柵輔助微環狀共振器.. . . . . . . . . . . . . . .. . . . . . . . . . . . . . 27
第四章 SOI光波導與跑道式微環狀共振器之數值模擬結果. . . . . .32
4-1 SOI光波導特性模擬. . . . . . . . . . . . . . . . .32
4-1.1 SOI單模光波導. . . . . . . . . . . . . . . . . . . .. . . . . 32
4-1.2 SOI定向耦合器(SOI Directional Coupler). . . . . . .38
4-2 SOI跑道式微環狀共振器. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .41
4-2.1 SOI跑道式微環狀共振器之耦合係數. . . . . . . . . 41
4-2.2 SOI跑道式微環狀共振器之傳輸頻譜模擬結果. . . .45
第五章 SOI跑道式光柵輔助微環狀共振器之數值模擬. . . . . . . . . .56
5-1 SOI跑道式光柵輔助微環狀共振器. . . . . . .56
5-2 SOI跑道式光柵輔助微環狀共振器的應用. . . . . . . . .75
第六章 結論與未來展望. . . . . . . . . . . .. . . . . . . . . . 79
參考文獻. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

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