奈米平凹透鏡之成像特性研究

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姓名

何治樺(Chih-Hua Ho) 查詢紙本館藏

畢業系所

光電科學與工程學系

論文名稱

奈米平凹透鏡之成像特性研究
(Study on the imaging properties of some plano-concave nanolenses)

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摘要(中)

傳統上，要將平行光聚焦於一個小光點，需要使用一個凸透鏡。近年來關於光子晶體的研究提供了另一種途徑：選擇光子晶體的負折射頻帶為工作頻帶，則以此光子晶體做成的凹透鏡就可以將光聚焦。已有大量的論文研究過光子晶體的負折射特性，此外也已經有幾篇關於光子晶體凹透鏡的研究被發表。這類透鏡做為一類奈米光學元件，具有短焦距以及能進行次波長成像的優點。然而這類透鏡的設計與實作還是顯得複雜，因此本論文提出空氣透鏡的概念以取代並簡化相關設計，並探討其成像特性。
　　本論文首先探討二維光子晶體奈米平凹透鏡的負折射行為與成像特性，接著將二維光子晶體以一維光子晶體取代，最後提出空氣透鏡的概念，以期不必使用光子晶體的複雜結構，亦能達到於奈米尺度之環境中有效將入射光聚焦的目標。
　　我們在介電質背景中置入一空氣平凹透鏡，其中之凹面為圓柱面，並選取背景介電係數與透鏡介電係數相差甚大的參數進行模擬。當光從背景介質傳播進入凹透鏡形狀的凹洞中(由光密介質進入光疏介質)再回到背景介質中，光線會產生與玻璃凸透鏡一樣的匯聚行為，達到聚焦的效果。為了找出較好的聚焦特性，我們對空氣平凹透鏡做非球面的處理，將凹面以幾種圓錐曲面取代，並比較在各種圓錐曲面下，以時域有限差分法（以 Maxwell 方程組為基礎的波動光學）與光線追跡法（幾何光學）進行聚焦位置的預測及成像點大小的分析比較。
　　在我們的分析中，以橫橢圓2的成像品質最佳(幾何光學預測與波動光學現象吻合度最高)。作為一個應用的例子，我們將空氣透鏡與光子晶體波導組合在一起，形成光學耦合器，並展示其有效將光強集中導入波導的結果。我們相信，適當設計的奈米級空氣透鏡元件將能在未來的奈米光子學中獲得普遍應用。

摘要(英)

Traditionally, to focus a beam of light into a tiny spot, we need a convex lens. Recently, alternative approach based on the researches of the propagating waves in photonic crystals (PhC) has been proposed: by choosing a negative-refraction (NR) photonic pass-band as operating band, a plano-concave lens of PhC makes a beam of incident light converge. Up to now, a huge amount of research papers discussing the features of NR in PhC together with a few papers studying the focusing ability of concave lenses of PhC have been published. As a kind of nano-optical component, a concave lens of PhC has the advantage of shortening the focal length and focusing the incident light beam into a spot of sub-wavelength size. However, the design and fabrication of a PhC lens are still too complicated. We therefore propose in this thesis the new idea of ‘air lens’ to simplify the previous designs. In addition, we investigate thoroughly the focusing characteristics of this device.
　In the thesis, we begin with the investigation of the NR phenomenon and imaging characteristics of plano-concave nanolens in a 2D PhC. We then replace the 2D PhC structure with a 1D PhC and explore if the same work can still be done. Finally, the idea of air lens is proposed. We hope to avoid such a complicated structure like PhC but achieve the same goal of making light converged effectively in the nanoscale environment.
　We first create a plano-concave air lens in a dielectric medium, whose concave surface is cylindrical. As one of the simulation parameters, a large dielectric constant of the background medium is assumed in order to focus the incident light effectively. When light propagates from a denser medium into a less dense one and back to the denser medium, the concave air lens converges light like the convex glass lens does in air. To find better converging characteristics, we then make the concave surface non-cylindrical. We replace the cylindrical surface with several conic surfaces. Moreover, we use FDTD (the wave optics based on Maxwell equations) method as well as the ray-tracing (geometrical optics) method to simulate and predict the locations of the focal points. In addition, we compare the spot sizes and focus locations for different surfaces.
　In our analysis, the second type of oblate elliptical surface has the best imaging performance, in which the geometrical prediction matches the wave phenomenon very well. As an example of application, we assemble an optical coupler of concave air lens and a photonic-crystal waveguide (PCW) and show how efficiently the light beam can be coupled into the PCW. We believe that appropriately designed air nanolens will become a commonly used component in the nanophotonics in the future.

關鍵字(中)

★ 成像
★ 光子晶體
★ 負折射
★ 繞射極限
★ 透鏡
★ 奈米

關鍵字(英)

★ negative refraction
★ photonic crystals
★ imaging
★ lens
★ nano
★ diffraction limit

論文目次

中文摘要 I
Abstract II
誌謝 III
目錄 IV
圖索引 V
表目錄 VII
第一章　緒論 1
　　1.1光子晶體簡介與發展 1
　　1.2光子晶體基本特性 3
　　1.2.1帶隙 4
　　　1.2.2異常折射效應 5
　　1.3研究動機 6
　　1.4論文架構 7
第二章　理論基礎 8
　　2.1馬克斯威爾方程式 8
　　2.2布洛赫定理 10
　　2.3布里淵區與頻帶結構 11
第三章　數值模擬方法 13
　　3.1平面波展開法 13
　　3.2時域有限差分法 14
　　3.2.1基本理論 14
　　3.2.2吸收邊界條件 16
　　3.3多重散射法 19
第四章　奈米平凹透鏡之成像特性 24
　　4.1二維光子晶體平凹透鏡文獻回顧 25
　　4.1.1階梯狀─介電質平板挖空氣柱 25
　　4.1.2圓柱面─介電質平板挖空氣柱 28
　　4.1.3圓柱面─背景空氣排介電質柱 29
　　4.2一維光子晶體平凹透鏡文獻回顧 32
　　4.3空氣平凹透鏡 34
　　4.3.1圓柱面 36
　　4.3.2直橢圓面 38
　　4.3.3橫橢圓面 40
　　4.3.4拋物面 42
　　4.3.5雙曲面 44
第五章結論與未來展望 48
參考資料 50

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指導教授

欒丕綱(Pi-Gang Luan)

審核日期

2012-7-27

推文