Tamm表面電漿波是一種侷限於金屬與一維光子晶體界面的表面電漿波，其在任何入射角度下，以TM或TE極化偏振均可以產生表面波。
本論文藉由邊界連續之電磁波方程式與數值模擬分析，並使用Mathlab與嚴格耦合波分析(RCWA)之軟體，模擬金屬、液晶和多層膜結構所組成的元件，首先為了方便往後的計算，因此藉由電磁場邊界連續條件計算液晶層上下介面之反射、穿透係數，並利用界面矩陣與傳播矩陣計算此元件之總反射率，此為本論文之最重要的部分。在模擬中，調節液晶層中液晶分子的旋轉角度，分析其反射、能帶及場圖的現象，並且比較其反射率與表面波的關係，以及討論各層材料參數之影響，以此模擬來印證我們合作者(南交大光電鄭協昌老師)所做之實際液晶調控Tamm Plasmonic之元件，符合實驗結果與討論。

Tamm surface plasmon wave is a surface wave that is confined to the interface between a metal and a one-dimensional photonic crystal, it can be produced by both TM amd TE polarization at any incident angles.
In this paper, a device consisted of liquid crystal and distributed Bragg reflector is simulated by using Transfer Matrix Method. First, calculating reflection and transmission coefficient in liquid crystal layer by using electromagnetic boundary conditions. Second, calculating reflectivity by using interface and propagation matrix. Next, when liquid crystal is tuned angle, we analyze refleciotn, band gap and field diagram in simulation. Finally, we discuss the relationship that is between resonance wavelength and Tamm plasmon wave, furthermore, we change the thickness in other layers and discuss their influence to resonance wavelength. In conclusion, this research confirms Tamm Plasmonic device experiment result (NCTU, Dr. Jeng, Shie-Chang) and discuss them.

中文審定書 i
致謝 ii
摘要 iii
Abstract iv
圖次 viii
表次 xi
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 介紹 3
2.2 金屬的光學性質 4
2.3 金屬平面之表面電漿波模態 8
2.4 表面電漿共振激發架構 12
2.5 Tamm Plasmon 13
2.6 光子晶體 14
2.6.1 介紹 14
2.6.2 能隙 14
2.6.3 一維光子晶體 15
第三章 液晶 18
3.1 液晶的介紹 18
3.2 液晶的種類 18
3.3 液晶的物理特性 19
3.3.1 秩序參數 19
3.3.2 折射率異向性 20
3.4 光於各向異性材料之特徵電場 22
第四章 理論推導與計算 25
4.1 光軸在三維座標下液晶層之電場模態 25
4.2 座標轉換之電場 27
4.3 液晶層界面之反射與穿透係數 30
4.3.1 TM入射 32
4.3.2 TE入射 35
4.4 液晶層反射穿透矩陣 36
4.4.1 TM入射 36
4.4.2 TE入射 37
第五章 模擬與分析 39
5.1 電磁場矩陣式 39
5.2 模擬結果 40
5.2.1 液晶排列模擬 41
5.2.2 各向同性相液晶 44
5.3 調控各層材料參數 48
5.3.1 金膜厚度 48
5.3.2 液晶層厚度 49
5.3.3 Top TiO2厚度 51
5.4 材料層順序交換 51
第六章 結論 54
參考文獻 55

[1] R. Wood, "On a remarkable case of uneven distribution of light in a diffraction grating spectrum (from Philosophical Magazine 1902)," SPIE MILESTONE SERIES MS, vol. 83, pp. 287-287, 1993.
[2] U. Fano, "The theory of anomalous diffraction gratings and of quasi-stationary waves on metallic surfaces (Sommerfeld’s waves)," JOSA, vol. 31, pp. 213-222, 1941.
[3] E. Kretschmann and H. Raether, "Radiative decay of non radiative surface plasmons excited by light," Zeitschrift für Naturforschung A, vol. 23, pp. 2135-2136, 1968.
[4] W. L. Barnes, A. Dereux, and T. W. Ebbesen, "Surface plasmon subwavelength optics," nature, vol. 424, p. 824, 2003.
[5] M. Kaliteevski, I. Iorsh, S. Brand, R. Abram, J. Chamberlain, A. Kavokin, et al., "Tamm plasmon-polaritons: Possible electromagnetic states at the interface of a metal and a dielectric Bragg mirror," Physical Review B, vol. 76, p. 165415, 2007.
[6] O. Gazzano, S. M. de Vasconcellos, K. Gauthron, C. Symonds, J. Bloch, P. Voisin, et al., "Evidence for Confined Tamm Plasmon Modes under Metallic Microdisks and Application to the Control of Spontaneous Optical Emission," Physical Review Letters, vol. 107, p. 247402, 12/09/ 2011.
[7] J. Gessler, V. Baumann, M. Emmerling, M. Amthor, K. Winkler, S. Höfling, et al., "Electro optical tuning of Tamm-plasmon exciton-polaritons," Applied Physics Letters, vol. 105, p. 181107, 2014.
[8] C. Symonds, A. Lemaître, E. Homeyer, J. Plenet, and J. Bellessa, "Emission of Tamm plasmon/exciton polaritons," Applied Physics Letters, vol. 95, p. 151114, 2009.
[9] M. Kaliteevski, S. Brand, R. Abram, I. Iorsh, A. Kavokin, and I. Shelykh, "Hybrid states of Tamm plasmons and exciton polaritons," Applied Physics Letters, vol. 95, p. 251108, 2009.
[10] S. S.-U. Rahman, T. Klein, S. Klembt, J. Gutowski, D. Hommel, and K. Sebald, "Observation of a hybrid state of Tamm plasmons and microcavity exciton polaritons," Scientific reports, vol. 6, p. 34392, 2016.
[11] C. Little, R. Anufriev, I. Iorsh, M. Kaliteevski, R. Abram, and S. Brand, "Tamm plasmon polaritons in multilayered cylindrical structures," Physical Review B, vol. 86, p. 235425, 2012.
[12] X. Wang, P. Wang, J. Chen, Y. Lu, H. Ming, and Q. Zhan, "Theoretical and experimental studies of surface plasmons excited at metal-uniaxial dielectric interface," Applied Physics Letters, vol. 98, p. 021113, 2011.
[13] R. Luo, Y. Gu, X. Li, L. Wang, I.-C. Khoo, and Q. Gong, "Mode recombination and alternation of surface plasmons in anisotropic mediums," Applied Physics Letters, vol. 102, p. 011117, 2013.
[14] Y.-J. Hung, Y.-R. Yen, and I.-S. Lin, "Fresnel analysis of Kretschmann geometry with a uniaxial crystal layer on a three-layered film," AIP Advances, vol. 6, p. 045023, 2016.
[15] 顏吟叡, "金屬與各向異性材料介面之表面電漿波模態分析," 中山大學光電工程研究所學位論文, pp. 1-87, 2015.
[16] 鄭皓旂, "共振波長可調之 Tamm 電漿子元件之研究," 交通大學影像與生醫光電研究所學位論文, pp. 1-65, 2016.