臺灣博碩士論文加值系統

　　轉換光學理論為設計現代光學元件的一種新型方法，理想的控制電磁波之行進方向，決定轉換函數，進而經由理論計算得到轉換介值參數，再由自然界中材料，或由一些等效參數將理論參數實現。其設計方法有不受頻寬影響限制以及電磁波路徑決定多變之優點，但唯一的困難即材料參數可能含有非等向性或異常折射效果，自然界中不易取得。儘管如此，轉換光學有異於一般由因導果之設計方式，可以使一些與以往不同之新型元件，如隱形斗篷、隱形地毯，有機會問世。
　　我們先探討兩正交極化波之傳播特性，並利用轉換光學理論，設計出任意方向，任意光束大小之極化分波器。接著依照轉換光學設計的多變性，改變轉換函數，可設計出另一種偏移型式之極化分波器。由於本文所設計之函數形式，皆為最簡易之一次函數，其材料參數設計較為簡單，利用層狀堆疊之等效介質理論，可將理論參數用均質且等向性材料替換，並用數值模擬軟體COMSOL Multiphysics®分析，說明其可行性。另外由等效介質理論所衍生之概念，將一般金屬會反射電磁波之特性，結合層狀堆疊結構，設計出另一種極化分波器。
　　轉換光學是ㄧ種嶄新的概念，設計各種新舊型之光學元件。結合等效介質理論，可將轉換光學最難實現的材料參數化簡，即可提高設計之可行性。

Transformation optics is a powerful mathematical technique to control electromagnetic field. It can calculate material parameters by determining transformation function. The material parameters can be obtained by nature or composite medium designed by effective medium theory. We can operate a wide range of frequency and arbitrary control electromagnetic wave by transformation optics, but the material parameters usually have negative refraction and isotropic properties. Despite this fact, transformation optics which is different from previous design makes the new device appearance, such as invisible cloaking and invisible carpet.
We propose a new polarization splitter via transformation optics. Using the metamaterial to achieve polarization splitters, we can control the beam width, beam direction over a wide range of frequency. The metamaterial designed by stacking isotropic and homogeneous materials. Last, using finite element software COMSOL Multiphysics® demonstrates our design. In addition, from electromagnetic wave incident metal reflect, we design other polarization splitter by effective medium theory.
Transformation optics is a new concept used to design a variety of novel optical devices. The complex material parameters can be simplified and realized with effective medium theory, it makes device feasibility.

摘　要 I
Abstract II
致　謝 III
目　錄 IV
圖目錄 VI
符　號 VIII
第一章　緒論 1
1-1　前言 1
1-2　研究動機與目的 2
1-3　本文架構 4
第二章　文獻回顧 5
2-1　圓形的隱形斗篷 5
2-2　不同形式的隱形裝置 6
2-3　波導連接器 7
2-4　超穎材料 7
第三章　基本理論與分析 11
3-1　物理規律的協變形式 11
3-2　馬克斯威爾方程式的協變形式 13
3-2-1　四維的電流向量 13
3-2-2　電磁勢方程式與勞倫茲規範的協變形式 14
3-2-3　四維的電磁場張量 15
3-2-4　電磁場的對偶張量 16
3-2-5　馬克斯威爾方程式的協變形式 18
3-3　轉換介質的材料參數 20
3-4　等效介質理論[57] 22
3-5　元件設計 25
3-5-1　光集中器[9] 25
3-5-2　光旋轉器[6] 26
3-5-3　隱形地毯[26] 27
第四章　利用轉換光學設計新型極化分波器 32
4-1　任意大小且任意方向之極化分波器 32
4-1-1　相同光束大小且任意方向之極化分波器 34
4-1-2　改變光束大小且任意方向之極化分波器 35
4-3　一般金屬與等效介質理論所設計之極化分波器 38
第五章　結論與未來展望 47
5-1　綜合結論 47
5-2　未來展望 48
參考文獻 50

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