一維光子晶體缺陷模態分析

PROPERTIES OF DEFECT MODES IN ONE-DIMENSIONAL PHOTONIC CRYSTALS

王政輝(Z.-H. Wang)

指導教授 ： 吳謙讓

國立臺灣師範大學/理學院/光電科技研究所/碩士(2010年)

摘要

在此篇論文中，涵蓋了三個主題。第一是研究缺陷模態垂直入射到對稱和反對稱多層窄頻濾波器的簡單例子。藉由轉換矩陣的方式來計算出波長和透射率關係圖。在反對稱濾波器，只有一個缺陷模態存在光子能隙中缺陷模態的位置隨著設計波長而改變。在對稱結構的濾波器，發現到會有兩個缺陷模態。使用Bloch waveapproximation 方法，這兩個缺陷模態分別是缺陷層在對稱和反對稱結構中場的解答。第二主題是延伸第一主題的相同結構但改變入射傾斜角。藉由對TE 和TM 波計算波長和透射率關係做缺陷模態的研究。缺陷模態和入射角的關係也被圖解之。此外,也觀察到缺陷層的厚度也會影響缺陷模態的數目。第三部份是研究在一維超導光子晶體中角度,厚度和光子能帶結構的關係。這是研究permittivity 為0 超導材料的臨界頻率。能帶結構可視為由兩個超導和介電材料所組成的厚度解析方程。在角度和能帶關係中，在TM 偏振，會存在一個強大局部疊置能帶近似於臨界頻率。當角度增加所顯示出的能帶也會增強。

關鍵字

光子晶體 ； 缺陷 ； 光子能隙 ； 濾波器 ； 共振器

並列摘要

In this thesis, we have three topics. The first one is to study the defect modes in the asymmetric and symmetric multilayer narrowband transmission filters in the simple case of normal incidence. It is based on the wavelength-dependent transmittance calculated by making use of the transfer matrix method. In an asymmetric filter, there exists only one defect mode within the photonic band gap and its position can be changed when the design wavelength is varied. In a symmetric filter, it is found that there are two defect modes. Using Bloch wave approximation, these two defect modes respectively correspond to the symmetric and the asymmetric field solutions in the defect layer.
　　The second part is to extend the first part to the oblique incidence for the same structures. The defect modes are investigated by the calculated wavelength-dependent transmittance for both TE and TM waves. The dependences of defect modes on the angle of incidence are illustrated. Additionally, the effect of defect thickness on the number of defect modes is also examined.
　　The third part is to study the angle- and thickness-dependent photonic band structures in a one-dimensional superconducting photonic crystal. It is studied near and below the threshold frequency at which the superconducting material has a zero permittivity. The gap structure is analyzed as a function of the thicknesses of the two constituent superconducting and dielectric materials. In the angular dependence of the band structure, in TM-polarization, there exists a strongly localized superpolariton gap approximately the threshold frequency. This gap is shown to be enhanced as the angle increases.

並列關鍵字

photonic crystals ； defect ； photonic band gap ； filters ； resonator ； Fabry-Perot

參考文獻

1. E. Yablonovitch, “Photonic band-gap structures,” J. Opt. Soc. Am. B 10, 283-295 (1993).

2. J. D. Joannopoulos, R. Meade, and J. Winn, Photonic Crystals (Princeton University Press, Princeton, 1995).

3. C. M. Soukoulis, Photonic Band Gap Materials (Kluwer Academic, Dordrecht, 1996).

4. P. Yeh, Optical Waves in Layered Media (John Wiley & Sons, New York, 1998).

5. S. J. Orfanidis, Electromagnetic Waves and Antennas (Rutgers University, 2008), ww.ece.rutgers.edu/~orfanidi/ewa.