表面電漿波為金屬與介質介面之本徵模態，其為二維平面波，一般在均勻介質/金屬之表面電漿波色散關係為k_spp=k_0*√(ε_o*ε_e/(ε_e+ε_o ))，此公式是由馬克斯威爾方程式與電磁場邊界條件連續求得。在各向異性材料(如單光軸液晶)中，將不同方向之相對介電常數(relative permittivity)引入馬克斯威爾方程會在波數向量空間得到一k space之複雜曲面，而對於單軸晶體/金屬的表面電漿波問題，則色散曲線更為複雜。本論文利用介電係數張量ɛ_ij或k曲面方程式與電磁場邊界條件修正一般色散關係(上述)，對單光軸晶體而言可表達為解析解k_spp=k_0*√((ɛ_m(ɛ_m (ɛ_e*sin^2(θ)+ɛ_o*cos^2(θ))-ɛ_e*ɛ_o))/(ɛ_m^2-" " ɛ_e*ɛ_o ))(光軸與表面電漿波kspp、界面法線同平面)或數值解(光軸於其他方向旋轉)，再進一步導證三層結構(liquid crystal/Au/glass)之色散關係，及驗證前人之實驗結果-波克萊舒曼(Kretschmann)結構之反射率，實驗與數值計算相符。

Surface plasmon mode is an eigenmode on the interface between the metal and the dielectric, it’s the two-dimensional plane wave, the usual surface plasmon dispersion relation on the dielectric/metal is k_spp=k_0*√(ε_o*ε_e/(ε_e+ε_o )) , the formula is derivative from the Maxwell’s equations and boundary conditions. In the anisotropic material, such as the uniaxial liquid crystal, we can get an complicated surface in the K-space by substituting the relative permittivity from different axial into the Maxwell’s equations, moreover, the dispersion relative curve is more complicated for the surface plasmon problem on the uniaxial crystal/metal interface. This aim of this paper is to amend the dispersion relation which is mentioned above by using the permittivity tensor、K space equations and the electromagnetic field boundary condition. That can be expressed as an analytical solution which optical axis is in the same plane with the wave vector of surface plasmon and the normal line of the interface k_spp=k_0*√((ɛ_m(ɛ_m (ɛ_e*sin^2(θ)+ɛ_o*cos^2(θ))-ɛ_e*ɛ_o))/(ɛ_m^2-" " ɛ_e*ɛ_o )) or a numerical solution which optical axis rotate in other directions for the uniaxial crystals. Furthermore, we derives the dispersion relation of three layer structure(LC/Au/glass) and verify the previous results that the calculating reflectivity of Kretschmann structure is corresponded with the experiment.

中文審定書 i
英文審定書 ii
摘 要 iii
Abstract iv
目 錄 iv
圖 次 vii
表 次 ix
第一章 序論 1
1.1 前言 1
1.2 文獻回顧與研究動機 1
1.3 論文架構 2
第二章 表面電漿波 3
2.1 金屬的光學性質 3
2.2 金屬平面表面電漿波模態 6
2.3 表面電漿共振激發架構 10
2.4 三層結構反射率之理論 13
第三章 液晶的簡介 16
3.1 液晶種類 16
3.2 液晶的秩序參數 17
3.3 折射率異向性 18
3.4 光於各項異性材料 20
3.5 光於單光軸材料 24
第四章 液晶之表面電漿波 26
4.1 光軸在XZ平面雙層結構下之表面電漿波 26
4.2 光軸在XY平面雙層結構下之表面電漿波 30
4.3 光軸在YZ平面雙層結構下之表面電漿波 37
4.4 光軸在XZ平面三層結構下之表面電漿波 41
4.5 光軸在XY、YZ平面三層結構下之表面電漿波 46
4.6 Kretschmann組態之反射率 52
4.6-1 光軸在XZ平面三層結構下之反射率 52
4.6-2 光軸在XY平面三層結構下之反射率 58
4.6-3 光軸在YZ平面三層結構下之反射率 68
第五章 結論 74
參考文獻 75

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