此篇論文主要以轉移矩陣法(Transfer Matrix Method, TMM)來模擬石墨烯層狀結構在THz下的光學性質。

在第一個主題中，我們將由TMM來模擬Si和SiO2所形成的光子晶體在THz下不同入射角度的光子能隙的變化。

在第二個主題中，我們將單層的石墨烯參雜在由Si和SiO2所形成的光子晶體的不同位置中，並藉由改變石墨烯的化學勢以及電磁波在TE和TM的不同入射角度，來探導其對光子能隙的變化。

在第三個主題，則是將石墨烯放在每一層的Si和SiO2中，同樣改變石墨烯的化學勢以及電磁波在TE和TM的不同的入射角度，來探導其對光子能隙的變化。在低頻的範圍與出現了第一個主題中的沒有出現的截止頻率，在不同角度的TE波變化趨勢也與前三種結構的變化略有不同。

In this thesis, we shall study the optical properties in graphene layered structures. There are two topics to be studied. In the first topic, we used transfer matrix method (TMM) to investigate photonic crystal used by Si and SiO2 and a layer of graphene. In these structures, we could find the photonic band gap (PBG) will be shifted as the angle of incident increase. And PBG will increase as the TE wave angle of incident increase, but TM wave is opposite. In the second topic, we also used the same method to investigate photonic crystal used by (Si/SiO2/graphene). In the structure, we could find the cutoff frequency and PBG will be shifted as the chemical potential increase or angle of incident increase. And PBG will increase as the TE and TM wave angle of incident increase.

[1] Nair R R, Blake P, Grigorenko A N, Novoselov K S,Booth T J, Stauber T, Peres N M R and Geim A K 2008 Science 320 1308
[2] Stauber T, Peres N M R and Geim A K 2008 Phys. Rev. B 78 085432
[3] Mak K F, Sfeir M Y, Wu Y, Lui C H, Misewich J A and Heinz T F 2008 Phys. Rev. Lett. 101 196405
[4] Wang F, Zhang Y, Tian C, Girit C, Zettl A, Crommie M and Shen Y R 2008 Science 320 206
[5] Li Z Q, Henriksen E A, Jiang Z, Hao Z, Martin M C, Kim P, Stormer H L and Basov D N 2008 Nature Phys. 4 532
[6] https://zh.wikipedia.org/wiki
[7] Marco Fiorillo, Andrea F. Verre, Maria Iliut; etc. Graphene oxide selectively targets cancer stem cells, across multiple tumor types: Implications for non-toxic cancer treatment, via 「differentiation-based nano-therapy」. Oncotarget. 2015
[8] pochi yeh optical waves in layered media
[9] Hanson, G. W., “Dyadic Green’s functions and guided surface waves for a surface conductivity model of graphene,” Journal of Applied Physics, Vol. 103, No. 6, 064302, 2008.
[10] Lixia Yang ,Lingling Li ,and Lunjin Chen ,Electromagnetic Characteristics of 1D Grapheme Photonic Crystal by Using SBC-FDTD Method of Oblique Incidence in THz
[11] S. Robinson and R. Nakkeeran Photonic Crystal Ring Resonator Based Optical Filters
[12] E. Yablonovitch, “Photonic crystals: semiconductor of light,” Scientific American December, 47 (2001)
[13] C.-J.Wu,H.-C Lin, Investigation of Photonic Band Gap in a Semicondoctor-Organic Photonic Crystal in Ultraviolet Region, OPTICAL REVIEW Vol. 18 No.4(2001)
[14] Deng Xin-Hua Yuan Ji-Ren Liu Jiang-Tao Wang Tong-Biao, Tunable terahertz photonic crystal structures containing graphene
[15] Zhengren Zhang, Transport properties of photon and electron in one-dimensional multilayered functional materials
[16] Qiao Wen-Tao Gong Jian Zhang Li-Wei Wang Qin Wang Guo-Dong Lian Shu-Peng Chen Peng-Hui Meng Wei-Wei, Propagation properties of the graphene surface plasmon in comb-like waveguide
[17] Sheng Shi-Wei Li Kang Kong Fan-Min Yue Qing-Yang Zhuang Hua-Wei Zhao Jia,Tooth-shaped plasmonic filter based on graphene nanoribbon
[18] Liu Haoran, Study of the propagation characteristics of surface plasmon polariton wave in single layer Graphene
[19] Tianrong Zhan, Xi Shi, Yunyun Dai, Xiaohan Liu and Jian Zi, Transfer matrix method for optics in graphene layers
[20] Gong Jian Zhang Li-Wei Chen Liang Qiao Wen-Tao Wang Jian, Negative refraction and bulk polariton properties of the graphene-based hyperbolic metamaterials
[21] Deng Xin-Hua Liu Jiang-Tao Yuan Ji-Ren Wang Tong-Biao, A new characteristics matrix method based on conductivity and its application in the optical properties of graphene in THz frequency range