張家歐臺灣大學:應用力學研究所鄭家福Cheng, Chia-FuChia-FuCheng2010-06-022018-06-292010-06-022018-06-292008U0001-1610200808462400http://ntur.lib.ntu.edu.tw//handle/246246/184721本文模擬磁性材料於空間中週期性排列特性，進而得知其光學特性，以期之後相關後續研究發展。 文中所模擬的磁性光子晶體，其主要磁性層為亞鐵磁性材料(ferromagnetic material)的滲入鉍之釔鐵石鎦石(Yttrium Iron Garnet, YIG, )，而等向性介質則採用 、GaAs等材料，其分別具有不同的相對介電常數。本文將各別就材料性質、晶格結構、排列方式等對其帶隙之影響進行模擬討論。 第二章中運用傳遞矩陣法分析一維層狀磁性光子晶體，在無限週期的假設下，計算出其頻帶關係。再則於有限層狀結構下，對於不同結構參數下的磁性光子晶體，分析磁性光子晶體其特有的法拉第旋轉效應，並由此設計出法拉第光學旋轉器。 第三章主要以三角元素向量之有限元素法進行磁性光子晶體的模態分析，分別對正方及三角晶格結構之磁性光子晶體作頻帶關係之數值模擬，再則運用磁性光子晶體的非互易對稱性質(non-reciprocal symmetry)，於二維的假設下設計出具有光學隔離效果之光子波導。 最後經過以上的數值模擬，進行分析作出下列結論：. 磁性光子晶體在能隙中的導通模態有顯著的法拉第效應。. 能隙受外加磁場變化影響。. 經由特別的結構的設計出現非互易對稱性。. 磁性光子晶體與一般非磁性光子晶體的差異主要為磁光效應的增強、非互易性質等。This thesis focuses on the performances of MPCs (magnetic photonic crystals). Accordingly, the optical property of MPCs will be demonstrated and then it can be used well in following research. The article considers that the magnetic material layer of MPCs is bismuth-substituted yttrium iron garnet (Bi-YIG) which is ferromagnetic material, and the isotropic material layers are GGG, GaAs, SiO2, etc. Those materials have different relative permittivities. The influence of the material property, the lattice structure, and the arrangement on the bandgap is simulated and discussed. In the chapter 2, 1-D layer MPCs with the transfer matrix method (TMM) is analyzed and its band structure under the infinite period assumption is obtained. Secondly, consider various MPCs, and analyze the Faraday rotation effect in the finite layers. Consequently, the Faraday rotator can be carried out. The mode analysis of various MPCs by the full-vectorial finite element method is demonstrated in the chapter 3. Using the non-reciprocal symmetry of MPC, the photonic waveguide which isolates the EMW with the specific frequency in 2D assumption can be devised. Finally, the following conclusions are made：. MPCs with the defect mode have the obvious Faraday rotation effect.. The bandgap is slightly influenced by the applied external magnetic field.. Non-reciprocity only appears in the MPCs with specific arrangement.. The main differences between general PCs (photonic crystals) and MPCs are the enhancement of the magnetic-optic effect, non-reciprocity, etc.口試委員會審定書...........................................I謝......................................................II文摘要.................................................III文摘要..................................................IV錄.......................................................V目錄.................................................. VII目錄....................................................XI一章 導論............................................1.1 前言.............................................1.2 磁性光子晶體簡介.................................1.3 文獻回顧.........................................3.4 本文目的與內容...................................4二章 一維層狀磁性光子晶體模擬........................5.1 傳遞矩陣法(TMM)…................................5.1.1 非等向性均勻介質4x4矩陣..........................5.1.2 非磁性材料的傳播及界面矩陣......................12.1.3 特定磁化方向的傳播及界面矩陣....................13.1.4 色散公式........................................19.2 無限週期模擬....................................21.2.1 x磁化方向.......................................22.2.2 y磁化方向.......................................23.2.3 z磁化方向.......................................24.3 有限層模擬......................................15.3.1 垂直xy平面入射(ky=0)............................24.3.2 穿透率及法拉第旋轉公式..........................26.3.3 無缺陷層狀結構模擬..............................30.3.4 具缺陷層狀結構模擬..............................31.3.5 法拉第旋轉器設計................................33.4 模擬問題及討論..................................34.5 模擬結果........................................36.5.1 無限週期層模擬結果..............................36.5.2 有限週期層模擬結果..............................48三章 有限元素法之理論與光子晶體分析..................57.1 有限元素法......................................57.1.1 二維有限元素法區域離散..........................57.1.2 有限元素法應用於光子晶體計算....................58.1.3 完美匹配層......................................59.2 二維磁性光子晶體模擬擬..........................62.2.1 不同晶格下磁性光子晶體頻帶模擬..................62.2.2 非互易對稱磁性光子波導模擬......................64.3 模擬問題及討論..................................67.4 模擬結果........................................68.4.1 不同晶格下磁性光子晶體頻帶模擬結果..............62.4.2 非互易對稱性磁性光子波導模擬結果................73四章 結論與未來展望..................................82.1 結論............................................82.2 未來工作........................................82考文獻.................................................83application/pdf2940674 bytesapplication/pdfen-US磁性光子晶體傳遞矩陣法法拉第旋轉效應有限元素法非互易對稱性質光學旋轉器Magnetic Photonic CrystalTransfer Matrix MethodFaraday Rotation EffectFinite Element MethodNon-reciprocal SymmetryFaraday Rotatorthesishttp://ntur.lib.ntu.edu.tw/bitstream/246246/184721/1/ntu-97-R95543010-1.pdf