具非對稱週期耦合微環共振器光傳輸特性

Abstract

本論文主要研究非對稱週期結構耦合微環共振器之特性，首先運用馬克士威電磁波理論與轉移矩陣法，分析電磁波於非對稱週期結構之耦合微環共振器中之傳輸性質。接著使用能帶圖與反射相位及札克相位之對應來設計結構參數，並藉由調控微環結構半徑、不同耦合係數、相異能帶匹配等方式，來分析光於拓樸邊緣態與邊緣態的傳輸特性。特別的是當兩種結構長度一致也就是相同能帶匹配下，共軛條件附近會產生最高的穿透率與品質因數，且共振峰值位置可以維持無因次化頻率固定不會改變。而相異能帶匹配的情況會使品質因數更進一步的提升，但拓樸邊緣態範圍會縮小。相同能帶匹配下擁有最廣的拓樸邊緣態範圍，其優點為具有強健性與拓樸保護的特性。研究結果指出，反射相位為正時，札克相位相異的區域，穿透率最大值發生處與品質因數最大值發生處會很接近；札克相位相同的區域，穿透率最大值發生處與品質因數最大值發生處會一致，所有能帶匹配情況皆有此現象。

This thesis mainly studies the characteristics of the coupled microring resonators with asymmetric periodic strutures. Firstly, Maxwell's electromagnetic wave theory and transfer matrix method are used to analyze the transmission properties of electromagnetic waves in the coupled microring resonators with asymmetric periodic strutures. The structural pa-rameters are designed by using the correspondence between the energy band gap and the reflection phase and the Zak phase, and by adjusting the micro-ring structure radius, dif-ferent coupling coefficients, and differences band matching and other methods can be used to analyze the transmission characteristics of the optical topological edge state and the edge state. In particular, when the two structures have the same length, that is, the same energy band gap is matched, the highest transmittance and quality factor will be generated near the conjugate condition, and the position of the resonance peak can be maintained and the dimensionless frequency is fixed and will not change. The matching of different energy band gaps will further improve the quality factor, but the range of top-ological edge states will be reduced. In the condition of the same energy band gaps matching, it has the widest range of topological edge states, and its advantages include the characteristics of robustness and topological protection. The research results indicate that when the reflection phase is positive, the area where the Zak phase is different, the place where the maximum transmission occurs and the place where the maximum quality factor occurs will be very close; the area where the Zak phase is the same, the place where the maximum transmission occurs will be consistent with the place where the maximum qual-ity factor occurs. This phenomenon occurs in all band gaps matching situations.