薛文証臺灣大學：工程科學及海洋工程學研究所張家榮Chang, Chia-JungChia-JungChang2007-11-262018-06-282007-11-262018-06-282007http://ntur.lib.ntu.edu.tw//handle/246246/51059本論文將從介紹左手材料開始，接著由馬克斯威爾方程式出發並配合轉移矩陣法推導出左手材料光波導的波導理論，並對三層左手材料平板光波導的特性做一番探討，最後歸納出左手材料光波導與傳統光波導不同的特性。另外在週期性結構部份，我們會從週期性結構中的布洛赫定理出發並配合轉移矩陣法推導出其能帶邊緣方程與能帶結構關係式，藉由改變其結構參數，針對能帶結構的變化與左手材料獨有的性質來討論。由分析結果顯示在左手材料之導模態與表面模態的特性與傳統材料有明顯的不同，在導模態中特徵模態會消失而且一階模態會單獨存在，表面模態中在對稱結構下會產生模態簡併現象而且電磁波能量會集中在介面上，在雙層週期性結構中布魯斯特線是可以被控制的，而且其能帶結構圖比傳統材料複雜許多。In this thesis, optical waveguide with the left-handed material (LHM) is investigated. Maxwell’s equations and translation matrix method (TMM) are used to develop the waveguide theory for optical waveguide with left-handed materials. Then the characteristics of three-layer planar waveguides with left-handed materials are studied. Consequently, some different characteristics in optical waveguides between left-handed materials and conventional materials are compared. Furthermore, in the part of periodic structures, Bloch theory and translation matrix method are used to develop the band-edge equations and the relations of band structures, and then discuss the characteristics of band structures by changing the parameters of periodic structures. The analytical results show some characteristics of guided mode and surface mode in left-handed materials which is different in conventional materials. In guided modes, the fundamental mode disappears in any case, and the first order mode may appear in some particular parameters. In surface modes, mode degeneracy appears in a symmetric structure, and the energy of electromagnetic wave is focused on the interface. In two-layer periodic structure, the Brewster line is controllable, and the band structures are more complicated in left-handed materials than conventional materials.目錄 中文摘要…………………………………………………………………i 英文摘要…………………………………………………………………ii 目錄……………………………………………………………………iii 表目錄……………………………………………………………………v 圖目錄……………………………………………………………………vi 符號表…………………………………………………………………viii 第一章 導論………………………………………………………………1 1.1 背景與研究動機……………………………………………………1 1.2 文獻回顧……………………………………………………………2 1.3 論文架構……………………………………………………………3 第二章 左手材料之波導理論……………………………………………4 2.1 左手材料特性………………………………………………………4 2.2 平板波導理論………………………………………………………6 2.3 三層平板波導分析…………………………………………………9 第三章 週期性波導之能帶……………………………………………21 3.1 週期性光波導理論………………………………………………21 3.2 雙層結構之能帶…………………………………………………22 第四章 數值分析………………………………………………………27 4.1 三層左手材料光波導之特性……………………………………27 4.1.1 導模態………………………………………………………27 4.1.2 表面模態……………………………………………………28 4.2 週期性左手光波導的特性分析…………………………………35 4.2.1 週期性左手光波導之能帶邊緣與能帶結構特性…………35 4.2.2 導磁係數比值對能帶結構圖的影響………………………38 4.2.3 負折射率對能帶結構圖的影響……………………………39 4.2.4 左手材料層厚度對能帶結構圖的影響……………………39 第五章 結論與未來展望………………………………………………70 5.1 結論……………………………………………………………70 5.2 未來展望………………………………………………………71 參考文獻………………………………………………………………72688794 bytesapplication/pdfen-US左手材料負折射率負導磁係數負介電常數光波導left-handed materialnegative refractive indexnegative permeabilitynegative permittivityoptical waveguidethesishttp://ntur.lib.ntu.edu.tw/bitstream/246246/51059/1/ntu-96-R94525049-1.pdf