石墨烯與介電多層結構之光傳輸特性

Abstract

本論文主要目的在於研究石墨烯與介電多層結構的光傳輸特性以及能帶結構。本文首先介紹了石墨烯的光學特性以及基本的電磁波傳遞原理，接著藉由改變介電層的折射率、厚度以及入射光的角度，探討單層、雙層以及多層石墨稀與介電結構之TE極化以及TM極化入射下的反射率、穿透率以及吸收等特性。接著以轉移矩陣法結合布洛赫定理分析入射光在正向入射時，石墨烯與四分之一波長堆疊系統的能帶結構。研究結果顯示石墨烯與介電多層結構的能帶特性有別於傳統四分之一波長的結構，除了原有的禁帶頻段產生藍移之外，當介電層的厚度符合半波長的條件時，布里淵區的中心處會裂開產生窄頻的禁帶。

The main purpose of this thesis is to study the propagation of light and the bandstructure in graphene-dielectric multilayers. At first, the optical properties of graphene and the basic principle of electromagnetic wave is introduced. Next, the properties of light propagation such as reflection, transmission and absorption in TE mode and TM mode for single, double and multi-layer graphene-dielectric structures are studied by changing the angle of the incident light, the refractive index and the thickness of the dielectric layers. Using the transfer matrix and the Bloch’s theorem, the band structure for normal incidence of the graphene-embedded quarter-wave stack can be analyzed, which is different from the ones in traditional quarter-wave stack. The forbidden gaps at the zone boundary are shifted toward high frequency compared with the traditional quarter-wave stack. Moreover, the center of the Brillouin zone in graphene-embedded quarter-wave stack will split to mini gaps.