臺灣博碩士論文加值系統

光子晶體是一門新發展中的領域，可運用於光子晶體光纖及光子晶體雷射等方面。有關二維光子晶體完全帶隙的研究，本文以數值模擬方法，利用平面波展開法針對二維光子晶體正方晶格砷化鎵（GaAs）介質圓柱以正方格子狀結構之介質連結，發現正方格子狀介質之寬度與介質柱半徑的大小影響帶隙變化至鉅，經由參數之最佳化選擇後，發現能有效增加光子晶體完全帶隙的寬度，當格子寬度為31 nm時，介質柱半徑為305 nm時，帶隙寬度可達Δω=0.08216(2πc/a)。此結果大於文獻 [22]中所提出之Δω=0.0685 (2πc/a)，帶隙寬度明顯提昇約20%。若針對二維光子晶體正方晶格介質圓柱以交差格子狀結構連結，此結構經由參數之最佳化選擇後，發現亦能有效增加光子晶體完全帶隙的寬度，當格子寬度為65nm時，介質柱半徑為295.3nm時，帶隙寬度可達Δω=0.10664 (2πc/a)。此結果又比文獻 [22]所提出之Δω，帶隙寬度明顯提昇約40%。本論文最後一章以時域有限差分法探討二維三角晶格圓柱之傳輸特性，而進一步用不同的數值模擬方法了解光子晶體之帶隙特性。

Optimal design of a two-dimensional photonic crystal with a square lattice of dielectric rods with veins in GaAs is investigated numerically using plane wave expansion method. It is shown that how a maximum complete two-dimensional band gap is obtained by optimally connecting the dielectric rods with cubic shape veins. The complete two-dimensional photonic bandgap of our optimal design reaches Δω= 0.08216 (2πc/a) (where a is the lattice constant, c is the light speed in vacuum) when the radius of dielectric rod is 305 nm and the half width of vein is 31 nm. In additions, a maximum complete two-dimensional band gap is obtained by optimally connecting the dielectric rods with cross shape veins, which bandgap reaches Δω= 0.10664 (2πc/a) when the radius of dielectric rod is 295.3 nm and the half width of vein is 65 nm.. This analysis provides a new design method in bandgap engineering and gives a guideline for practical fabrication. In the last chapter of this thesis, we use the other simulation method, finite different time domain method, to explore the transmission characteristic of a two-dimensional Photonic crystal with square lattice dielectric rods.

中文摘要………………………………………………………………………………… i
英文摘要………………………………………………………………………………… ii
誌謝……………………………………………………………………………………… iii
目錄……………………………………………………………………………………… iv
圖目錄…………………………………………………………………………………… vi
第一章 前言…………………………………………………………………………… 1
1.1 光子晶體簡介……………………………………………………………… 1
1.2文獻回顧…………………………………………………………………… 4
1.3研究動機…………………………………………………………………… 7
1.4論文章節概要……………………………………………………………… 7
第二章 模擬方法-平面波展開法與時域有限差分法 ……………………………… 9
2.1 前言……………………………………………………………………… 9
2.2 平面波展開法…………………………………………………………… 9
2.3 時域有限差分法………………………………………………………… 12
第三章 提昇二維光子晶體完全帶隙之寬度設計-以正方格子連接介質柱………… 14
3.1 前言……………………………………………………………………… 14
3.2 數值模型………………………………………………………………… 14
3.3結果與討論……………………………………………………………… 19
3.4結論……………………………………………………………………… 22
第四章 提昇二維光子晶體完全帶隙之寬度設計-以交叉格子連接介質柱………… 23
4.1 前言……………………………………………………………………… 23
4.2 數值模型………………………………………………………………… 23
4.3結果與討論……………………………………………………………… 24
4.4結論……………………………………………………………………… 28
第五章 以時域有限差分法研究三角晶格光子晶體之傳輸效率與能帶特性……… 29
5.1 前言……………………………………………………………………… 29
5.2 數值模型………………………………………………………………… 29
5.3結果與討論……………………………………………………………… 30
5.4結論……………………………………………………………………… 31
第六章 結論…………………………………………………………………………… 33
參考文獻………………………………………………………………………………… 35
簡歷……………………………………………………………………………………… 38

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