Dirichlet-to-Neumann 映射法應用於光子晶體能帶結構之計算

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姓名

張凱程(Zhang Kaicheng) 查詢紙本館藏

畢業系所

光電科學與工程學系

論文名稱

Dirichlet-to-Neumann 映射法應用於光子晶體能帶結構之計算

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摘要(中)

本論文採用數值分析方法Dirichlet-to-Neumannu映射(DtN map)來計算光子晶體的頻帶結構。由Dirichlet-to-Neumann映射的基本原理開始，探討DtN映射法在常見二維光子晶體結構：正方晶格、三角晶格、超晶格結構與蜂巢狀晶格中的應用。我們引入色散性介質，以DtN映射法模擬正方晶格頻帶結構，調配其參數使晶體具有雙負折射性質。在晶柱介質為Drude色散模型，背景介質為Lorentz色散模型的情況下，晶柱介質的電漿頻率( )為2.0，背景介質的無阻尼震盪頻率( )為0.38且填充率( )為0.56時，其雙負折射效應最為明顯。

摘要(英)

This thesis introduce a numerical analysis method,the Dirichlet-to-Neumann map(DtN map), to calculate the band structure of photonic crystals. From the basic principle of Dirichlet-to-Neumann map, we investgate the applications on general two-dimensional photonic crystal structures: such as square lattice, triangular lattice, super lattice and honey-comb lattice. We introduce dispersion material to simulate band structure of square lattice by DtN map, change the parameter that makes doule negative refractive medium. In Drude model cylinder and Lorentz model background crystal structure, the cylinder plasma frequency 2.0 and background non-damping resonant frequency 0.38 with filling rate 0.56 makes better double negative refractive medium.

關鍵字(中)

★ 光子晶體
★ DtN映射法
★ 正方晶格
★ 色散性介質

關鍵字(英)

★ photonic crystal
★ Dirichlet-to-Neumann map
★ square lattice
★ dispersion medium

論文目次

摘要 I
誌謝 III
目次 IV
圖目錄 V
第一章簡介 1
第一節研究背景 1
第二節研究目的 2
第二章 DTN映射法於波頻帶分析的應用 3
第一節波頻帶分析常見方法 3
第二節 DTN頻帶分析法與其應用 4
一、正方晶格頻帶分析 6
二、三角晶格頻帶分析 12
第三節 DTN頻帶分析法進階應用 17
一、超晶胞(super cell)頻帶分析 17
二、蜂巢狀晶格頻帶分析 22
第三章色散性金屬介質柱光子晶體頻帶特性 28
第一節低填充率色散金屬柱光子晶體等效模型 29
第二節 DTN映射法等效電漿模型驗證 31
第三節色散金屬柱光子晶體頻帶分析 36
第四章雙負折射介質光子晶體頻帶特性 39
第一節色散背景光子晶體頻帶分析 39
第二節雙負折射介質光子晶體頻帶分析 45
第三節雙負折射介質光子晶體準頻率曲線圖分析 47
第五章結論 48
第一節研究發現 48
第二節未來展望 49
參考文獻 50

參考文獻

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指導教授

欒丕綱

審核日期

2013-1-23

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