臺灣博碩士論文加值系統

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.

摘要 I
SUMMARY II
誌謝 VIII
目錄 IX
表目錄 XII
圖目錄 XIII
符號說明 XVIII
第一章　緒論 1
1-1 前言 1
1-2 文獻回顧 3
1-2-1 光子晶體能隙 3
1-2-2 光子晶體共振腔與波導 4
1-2-3 光子晶體平面光波導元件 4
1-2-4 可調式光子晶體 6
1-3 本文架構 7
第二章　數值計算方法 10
2-1 前言 10
2-2 固態物理學中的晶格 11
2-2-1 真實空間與倒晶格空間 11
2-2-2 布洛赫定理(Bloch theorem) 12
2-3 平面波展開法 14
2-3-1 正方晶格( square lattice ) 15
2-3-2 三角晶格( triangular lattice ) 16
2-3-3 超晶胞與光子晶體共振腔 16
2-4 時域有限差分法 18
2-4-1 完美匹配吸收層( perfectly matched layer，PML) 19
2-5 共振腔品質因子 24
2-6 消光比與串訊干擾 25
2-7 感測器靈敏度 25
第三章　磁光材料與磁性光子晶體 31
3-1 磁光材料簡介 31
3-2 磁光材料特性 32
3-3平面波展開法計算含磁光材料光子晶體色散關係 34
3-4 外加磁場與共振頻率分離之關係 35
3-5 磁光材料與電磁波傳遞非互易性之關係 36
第四章　添加磁光材料缺陷之二維光子晶體元件 40
4-1 前言 40
4-2 含磁光材料之光子晶體共振腔 40
4-2-1 磁光材料缺陷半徑與約化耦合強度之關係 41
4-2-2 外加磁場強度與共振頻率分裂之關係 42
4-3 光子晶體高密度分波多工器 42
4-3-1 外加磁場及共振腔位置對單通道濾波器表現之關係 42
4-3-2 改變不同共振腔參數以調整擷取波長 43
4-3-3 雙邊與單邊的光子晶體高密度分波多工器表現 44
4-4 磁調控光子晶體光開關 47
4-5 光子晶體高解析度折射率感測器 48
4-5-1 共振腔旁空氣洞尺寸改變對Q值影響 48
4-5-2 外加磁場前後Q值與靈敏度改變之探討 48
4-5-3 感測器之感測極限 49
4-6 含磁光材料之光子晶體波導 49
4-6-1 波導參數對能量切換表現之探討 50
4-6-2 不同半徑線缺陷組合對能量切換表現之探討 51
4-7 含磁光材料線缺陷之非互易光子晶體耦合器 51
第五章　綜合結論與未來展望 100
5-1 綜合結論 100
5-2 未來展望 101
參考文獻 102

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