矽波導製作於絕緣體上矽晶片已大量應用於積體化光子電路，各式元件如光子晶體共振腔已被實現。在光學量子計算中，量子位元是以光的偏振方向來定義，需使用偏振旋轉器控制量子位元的狀況，或形成邏輯閘。 本研究提出一個新型光子晶體結構，製作於絕緣體上矽波導，可形成偏振旋轉器，並由於其光子能隙的作用，具有反射的效果。我們在此結構中設計一個共振腔，可達到具有偏振旋轉，又有濾波功能的積體化光波導元件。 本研究將透過有限時域差分法、有限元素法、特徵模態展開法，這三種方法來分析各個結構。一開始從仿一維光子晶體結構下手，發現單純的仿光子晶體結構無法形成偏振旋轉的效果，進而往已知L型波導結構搭配光子晶體結構的這個方向著手。 經研究發現，在圓洞結構中在特定波長下，設計出的結構會有低反射且穿透面的偏振有旋轉的現象，因此具穿透式偏振旋轉器的潛力。若設計為蝕刻圓洞波導具空腔結構時，在輸入光為特定波長時，可成為一反射式可控輸出偏振比例的濾波器。 我們也提出方洞之光子晶體結構，相較於圓洞的結果，不管是在偏振旋轉、濾波器上品質因子表現，皆是蝕刻方洞的結構較好。在蝕刻方洞結構上，我們估計使用70個週期洞結構，可以推測出元件達到反射率接近100%。這樣的高反射率的反射鏡可用在在品質因子的共振腔中。 本研究發現，當增加蝕刻洞數時，不但可以增加品質因子，也可以調整輸出的偏振比例；當改變空腔長度時，即可調整輸出的尖峰波長位置；當調整占空比、洞的寬度與深度、 兩洞中心距離，便可做到控制輸出偏振比例的情況，這些情況在濾波器與雷射共振腔同時適用。可讓我們設計出在特定波長，特定偏振輸出與特定Q值的濾波器與雷射。 ;Silicon waveguides are fabricated on insulators of silicon wafers that have been widely used in integrated photonic circuits. Various components such as photonic crystal resonators have been realized. In optical quantum computing, qubits are defined by the polarization state of light. Therefore, the polarization rotators are necessary to be used to control the state of qubits or to form logic gates. In this study, we propose a novel photonic-crystal structure on SOI waveguides. The photonic crystal structure is shifted to the center of the waveguide to form a reflective polarization convertor. A resonant cavity is designed in the polarization convertor. The transmission and the reflection and the cavity modes are investigated. Three methods, Finite-Difference Time-Domain, Finite-Element Method, Eigenmode expansion method are adopted. The rotation of polarization is demonstrated in the photonic crystal structure with shifted circular air holes. The rotation of the polarization depends on the diameter, the shift, the number of the air holes. With a cavity in the structure, the cavity modes can be observed in the transmission and the reflection spectra. The polarization state of the transmission and reflection of the devices can be designed by varying the diameter, the shift, the number of the air holes. The photonic crystal structure with shifted rectangular holes is also investigated. The reflectivity close to 100% could be achieved for the photonic crystal structure with 100 shifted rectangular holes. A cavity is positioned in the structure to study the transmission and the reflection spectra as well as the cavity modes. The results show that the photonic crystal structure with shifted rectangular air holes can be used to form the transmissive and the reflective filters with a rotation of polarization. The wavelength of the cavity mode and the transmissive and reflective filter can be tuned by modifying the cavity length. By varying the number of etched rectangular air holes , the duty cycle, the width and the depth of the etched rectangular air holes, the polarization of the output light can be adjusted to a specific state. In this study, the waveguide is designed in silicon. The photonic crystal structure with shifted air holes can also be designed in other active materials to design a laser with specific polarization state.
