對於傳統光學而言，其成像的品質會受到繞射極限的影響，進而導致影像的解析度僅能達到約入射波長的一半，此限制源自於消逝波具有衰減特性而無法傳遞至遠場。針對繞射極限，科學家提出數種結構試圖解決此問題，超級透鏡首先被提出，其利用金屬薄膜產生的表面電漿子將消逝波的訊號加以放大藉以得到極佳的解析度，但此現象僅能在很窄的操作頻率中達到；另一方面，雙曲透鏡亦經科學家提出，此結構具有雙曲線型之等頻率曲線故能夠將消逝波轉換成傳遞波，然而此結構的彎曲形貌導致其無法被廣泛使用在各種應用中。
在本論文中，我們提出一個由銀奈米線及陽極氧化鋁基板所構成的平面型雙曲透鏡，預期此結構能夠展現出超越繞射極限的影像解析度。此平面型雙曲透鏡沿著不同軸向具有異號的介電常數，此特性對應到一個雙曲線型之等頻率曲線，使得其能夠將消逝波轉換成傳遞波。此外，我們亦採取了理論計算來設計此結構，藉由控制銀的體積佔有比率，我們能夠調控任意操作頻率下的等效介電常數。為了驗證理論計算之結果，次波長成像系統之模擬結果亦在本論文中呈現，模擬中所採用的入射波長為365奈米、532奈米以及633奈米。
為了實現此結構，我們將傳統的陽極氧化鋁製程加以修改而製備出毋需依靠支撐物之氧化鋁基板，此基板厚度約10微米且具有直徑約60奈米之奈米孔洞。利用電鍍製程，銀奈米線可以生長於氧化鋁基板的奈米孔洞中，形成此平面型雙曲透鏡。接著我們利用聚焦離子束蝕刻兩條狹縫，其間距設為120至400奈米，利用近場掃描式光學顯微鏡對兩條狹縫之量測，其結果顯示出次波長成像可以藉由提出的平面型雙曲透鏡而達成，影像的解析度可以到達入射波長的三分之一，此成果對於次波長之黃光微影系統的發展有相當程度之助益。

摘要 i
Abstract ii
Acknowledgements iv
Content v
List of Figures vii
List of Tables xii
Chapter 1 Introduction 1
1.1 Introduction to Imaging technology 1
1.2 Thesis Organization 3
Chapter 2 Literature Review 4
2.1 Perfect lens and Superlens 4
2.1.1 Perfect lens 4
2.1.2 Superlens 6
2.2 Hyperlens 11
2.2.1 Cylindrical-shaped hyperlens and its mechanism 11
2.2.2 Spherical-shaped hyperlens 21
2.3 Optical applications of indefinite materials 23
2.3.1 Negative refraction 23
2.3.2 Partial focusing 26
Chapter 3 Design, Calculation and Simulation 29
3.1 Motivation 29
3.2 Design of the flat hyperlens composed of silver nanowires in an anodic aluminum oxide (AAO) template 29
3.2.1 Hyperbolic iso-frequency contour 29
3.2.2 Indefinite materials 31
3.3 Theoretical calculation results 37
3.4 Numerical simulation results 43
3.5 Realization of the flat hyperlens by an anodic aluminum oxide template 49
Chapter 4 Experimental Procedures 51
4.1 Sample fabrication 51
4.1.1 Preparation of aluminum specimen 51
4.1.2 Fabrication of anodic aluminum oxide by a two-step anodization 51
4.1.3 Preparation for electroplating 59
4.2 Electroplating of silver nanowires 64
4.3 Focused ion beam (FIB) patterning 68
Chapter 5 Optical Measurement Results 72
5.1 Near-field scanning optical microscopy (NSOM) measurement setup 72
5.2 Near-field scanning optical microscopy (NSOM) measurement results 74
Chapter 6 Conclusions 84
References 86

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