光子在其波長尺度下的周期排列晶體中，存在著光子晶體能隙，這樣的結構被稱為光子晶體。由於光子晶體能隙具有隔絕光波傳遞的效果，可以藉此用來調整光波的傳播方向進而在數個波長的尺寸下設計各式光學元件。本文提出並設計各種利用填充磁光材料缺陷的可調式二維光子晶體元件，包括高密度分波多工器、光開關、折射率感測器及光二極體等，其結構是由矽的背景與空氣洞組成，並添加磁光材料形成點缺陷或線缺陷之後，外加磁場來調變光學性質。當外加磁場施於垂直光子晶體排列的方向時，會造成點缺陷形成的共振腔之退化共振模態產生頻率分裂與模態旋轉的現象，並使外加磁場前後共振腔中光場分佈改變以達到能量切換的效果；此外，分裂後的共振模態品質因子會大幅提升，使共振腔對頻率的選擇性更高，並可藉此達到高密度分波與提升感測器解析度的目的。當垂直光子晶體排列方向的磁場加於添加磁光材料形成的光子晶體線缺陷後，將使特定頻段的可傳遞模態消失，並達到阻擋能量的效果；而若將兩排磁光材料線缺陷並排形成耦合器並分別施加相反方向的磁場，將使正反兩方向的耦合長度不同，經過設計後便可使光波傳播後無法反向傳遞，並形成一光二極體。本文將利用平面波展開法計算並分析光子晶體的能帶結構及缺陷模態，並利用時域有限差分法來模擬電磁波在結構中傳遞的情形及驗證光子晶體元件的可行性。

In this research a series of tunable photonic crystal (PhC) devices are proposed. The magneto-optical (MO) materials are infiltrated into the PhC structure to become point or line defects. With out-of-plane magnetization, the degenerate resonant modes splits into two counter-rotating modes at different frequencies. Furthermore, the quality factor of two splitting modes significantly increases to about 4000, which is suitable for applications of dense wavelength-division-multiplexing (DWDM) systems and refractive index sensors. When the out-of-plane magnetization is applied to the MO line defects in the PhCs, the fundamental waveguide mode vanishes in specific frequency region. This phenomenon causes the fundamental mode waves blocked by the PhC structure. Based on the effect, the power can be switched by applying external magnetic fields. When two MO line defects are put side by side in the PhC structure with opposite direction of magnetization, the time-reversal and space inversion symmetries breaks, which causes the difference of the dispersion curves for opposite propagating directions. Using this effect a PhC diode can be achieved. Computations are performed using plane wave expansion (PWE) and finite difference time domain (FDTD) method.

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