為了達成高密度整合系統的目標及擁有較大的FSR值來容納更多信號通道，現今製作之微環型共振器都會縮減至數個微米尺寸。然而當微環型共振器尺寸縮小時，彎曲損耗會大幅地增加，加上環型共振器其傳輸波導與共振腔之間只有點耦合區域，使得整體光學耦合能力低、臨界耦合間隙小，因此製程只要有些許誤差即會造成不理想的頻譜響應。而跑道式微環型共振器結構，可以藉由增加耦合區域長度，使得耦合能力增加，以拉大臨界耦合間隙及增加製程容忍度，但是跑道式微環型共振器之共振腔長直波導與彎曲波導間存在著模態不匹配的問題，這會造成過多的損耗。因此本論文設計錐狀結合錯位結構於共振腔長直波導與彎曲波導間，並適當地增加彎曲波導寬度，以降低模態轉換損耗及輻射損耗，提供更高品質因數之跑道式微環型共振器，並可以拉大臨界耦合間隙。
在本論文中，我們首先使用二維有限差分時域法結合等效折射率法模擬SOI 跑道式微環型共振器，計算其長直傳輸波導與共振腔間之耦合間隙從窄至寬的傳輸頻譜，再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，以求得共振器所需之光學參數。接著，我們模擬在SOI跑道式微環型共振器中分別加入錐狀結構後對元件的影響，可得知臨界耦合間隙可以拉遠0.025 μm，而品質因數可以提高近2倍。最後，結合兩改善結構的優點，模擬錐狀結合錯位之跑道式微環型共振器且將傳輸波導也改為與共振腔相同的結構，使得耦合區域相位匹配，進而可以再提高光學耦合能力與共振腔之品質因數。我們所設計之對稱錐狀結合錯位跑道式微環型共振器與傳統型相比，其臨界耦合間隙拉遠0.15 μm，而品質因數則提高了6倍。

In order to achieve high-density integration and large free spectral range (FSR), the size of the microring resonators (MRRs) should be reduced. However, the bending loss raises as the microring resonators are too small. In addition, the gap between the straight waveguide and the ring waveguide in MRR structures must be very small to achieve the critical coupling condition due to the weak coupling coefficient. By utilizing the micro-racetrack resonator structures with strong coupling abilities, we can enlarge the critical gap and improve the fabrication tolerance. However, the micro-racetrack resonators may suffer higher losses resulted from the mode conversion between the straight and bent waveguides. In this paper, we widen the bent waveguide and adopt taper with offset structure to reduce the radiation loss and mode conversion loss of micro-racetrack resonators.
In this thesis, we first use the 2-D finite-difference time-domin (FDTD) method with the effective index method (EIM) to obtain the transmission spectra of the SOI micro-racetrack resonators. The transmission spectra are then fitted by using the time-domain coupled mode theory (CMT) to obtain the quality factors of the SOI micro-racetrack resonators. We have demonstrated that the taper structure for the SOI micro-racetrack resonators can enlarge the critical gap by 0.025 μm and enhance twice the total quality factor. Finally, we employ a taper with offset structure between the bent and straight waveguides. In addition, the transmission waveguide is designed of the same structure to form symmetric SOI micro-racetrack resonators. The critical gap is shown to be increased by 0.15 μm, and the total quality factor is enhanced by six times.

誌謝………………………………………………………………………... i
中文摘要. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . ii
英文摘要. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . …….. . . . . . . . .iii
目錄. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv
圖目錄 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . .vi
表目錄 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . x
第一章 緒論. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1
1-1 Silicon On Insulator光波導. . . . . . . . . . . . . . . . . . . . . .1
1-2 微環型共振器結構及原理(Microring Resonators, MRRs). . . . . . . .2
1-3 研究動機. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .6
第二章 數值模擬分析方法. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .9
2-1 波束傳播法(Beam Propagation Method, BPM). . . . . . . . . . . . . . . . .9
2-2 有限差分時域法(Finite-Difference Time-Domain, FDTD
Method). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .12
2-3 等效折射率法(Effective Index Method, EIM). . . . . . . . . . . . . . . . .16
第三章 跑道式微環型共振器之光學特性. . . . . . . . . . . . . . . . . . . . . . .21
3-1 光波導之單模條件. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .21
3-2 基本跑道式微環型共振器. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .26
第四章 改善之跑道式微環型共振器. . . . . . . . . . . . . . . . . . . . . . . . . . .36
4-1 錐狀跑道式微環型共振器. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .36
4-2 錯位跑道式微環型共振器. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .43
4-3 錐狀結合錯位跑道式微環型共振器. . . . . . . . . . . . . . . . . . . . . . . .48
第五章 結論與未來展望. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .55
參考文獻. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .56

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