介電質與石墨烯超晶格結構之光學特性

Optical Properties of Dielectric and Graphene Superlattices

鄭宇翔(Yu-Hsiang Cheng)

指導教授 ： 薛文証

國立臺灣大學/工學院/工程科學及海洋工程學研究所/博士(2016年)

https://doi.org/10.6342/NTU201610495

摘要

本文中探討光在一維準週期介電質結構以及石墨烯介電質複合結構中之傳輸特性。研究中發現，當光在這些結構中傳輸時，會展現出異於傳統光子晶體結構之特性。本文中首先對雙周期準晶作研究。研究中發現這種準晶類型會擁有與傳統光子晶體中的布拉格條件類似的三條準布拉格條件，這三條準布拉格條件與圖厄-莫爾斯和斐波納契結構的準布拉格條件並不相同。並且，當電磁波處於準布拉格條件時，會經歷極大的反射。接著，本文提出了可以藉由圖厄-莫爾斯結構來製造出窄頻寬的共振。透過圖厄-莫爾斯結構原本的結構而不需要加任何變化，即刻產生出分散在頻譜上的窄頻寬的共振。並且這些共振點無論是數量還是品質因子都可以透過增加準週期階數來強化。最後，透過建立對稱性的斐波納契介電質結構的方式，本文中發現了類似法布里-珀羅共振的共振形式。而這些共振點擁有著與傳統的週期性缺陷結構不同的性質。關於光在對稱性的斐波納契介電質結構中的傳輸與中隔層距離的關係也將在本文中探討。
石墨烯與介電質複合材料在可見光與兆赫電磁波中的性質也將在本文中探討。本文發現在可見光下石墨烯與介電質複合材料的吸收會在周期數增加時有著不規律的變化。若是週期數增加，吸收在特定條件可能反而下降，而這與同長而言會規律變化的吸收材料不同。此外，本文發現這種變化還可以由化學位能控制。本文也發現兆赫電磁波中石墨烯與雙介電質複合材料擁有異於準晶體和光子晶體之準布拉格條件。這種準布拉格條件和光子帶隙同時與材料參數與石墨烯的化學位能有關。一旦施加在石墨烯上的化學位能改變，準布拉格條件也會跟著改變，此外，最大帶隙可以在異於半波長或四分之一波長的堆疊上找到。

關鍵字

光子能隙結構 ； 布拉格反射 ； 準週期 ； 共振現象 ； 石墨烯 ； 吸收

並列摘要

The propagation of electromagnetic waves in one-dimensional quasi-periodic dielectric and graphene-dielectric superlattices are studied in this thesis. It is found there are interesting properties in these structures, which differ from traditional photonic crystals. For double-period dielectric superlattices, there are three quasi-Bragg conditions with extreme reflectance which is analogous to the Bragg condition in traditional photonic crystals. Moreover, both the condition and number of the quasi-Bragg condition in double-period superlattices differ from those in other quasi-periodic superlattices, such as Fibonacci and Thue-Morse superlattices. In addition, sharp resonance peaks from Thue-Morse dielectric superlattices are proposed in this thesis. It is found with the original Thue-Morse structure, resonances with sparse dispersion in the frequency range can be produced. Moreover, both the number and quality factor of these peaks increase when the generation order increases. Symmetric Fibonacci dielectric superlattices are also discussed in this thesis. It is discovered with a symmetric Fibonacci structure, Fabry-Pérot-like resonances can be found. These resonances have different properties from traditional defected bilayer superlattices.
The effect of the space layer in the structure on its transmission spectra is also studied in this thesis. Graphene-dielectric superlattices in visible light and graphene-double-dielectric superlattices in the terahertz range are analyzed in this study. It is found the graphene-dielectric superlattices in visible light display a non-monotonic absorption behavior when the period number increases. When the period of the structure increases, the absorption of the structure may decrease under certain conditions. Such a phenomenon differs from the traditional absorptive materials that behave in a monotonic way. Moreover, the unusual absorption behavior can be controlled using chemical potential. Quasi-Bragg conditions in the graphene-double-dielectric superlattices in the terahertz range, which differ from the Bragg condition in traditional photonic crystals and the quasi-Bragg condition in quasi-periodic superlattices, are proposed. It is found the quasi-Bragg condition and photonic bandgap in graphene-double-dielectric superlattices depend on both the structure parameters and the chemical potential of the graphene. When the chemical potential applied to the graphene sheets is changed, the quasi-Bragg condition in the structure is changed. Moreover, the maximum gap can be found with the layer thicknesses of the dielectric layers that differ from traditional quarter-wave or half-wave thickness.

並列關鍵字

Photonic bandgap materials ； Bragg reflectors ； Quasicrystal ； Resonator ； Graphene ； Absorption

參考文獻

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