左手材料光波導

Abstract

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.