金屬光柵散射與導波特性之研究

Abstract

金屬光柵係由週期性的金屬帶所構成,已被廣泛應用於微波及光學系統 中,比如極化轉換器,分波器,濾波器,以及漏波天線. 其理論分析與實驗量 測,數十年來屢見發表於文獻上. 本論文考慮金屬光柵的實際情況,就金 屬導電係數及金屬帶厚度的影響.以嚴謹的態度發展出一套全新的分析方 法. 如此, 對金屬光柵的基本特性建立精確可靠的數據, 以所得的結果作 為各種不同分析方法之驗證標尺. 本論文所發展的新方法中, 最主要的部 分在於將金屬的導電係數併入其介電常數之虛部,因此金屬光柵可等同介 質光柵來處理. 本研究中最基本的發現是金屬光柵層內的本徵函數 (或模 式) 可分為兩組, 其中一組為眾所周知的空氣模式組, 另一組則是鮮為人 知的金屬模式組. 這兩組模式的並存可以描述金屬光柵內的微觀電磁場分 佈. 依據模式的特徵, 金屬光柵的相關物理現象, 如金屬帶上的電流分 佈, 可以容易, 清楚的給于解釋. 金屬光柵的應用環境一般為多層介質結 構, 本論文採用嚴格的模式匹配法來分析, 該方法已被廣泛運用在介質光 柵的問題上. 文中分為兩大部分, 首先討論單層光柵的應用,包括分波器, 極化轉換器, 以及漏波天線, 其次再研究雙層光柵在電磁屏蔽上的應用. 根據嚴格的理論分析, 所得的結果將提供各應用設計所需的數據. 第一部 分中, 經分析得知金屬帶厚度在分波器及極化轉換器的設計上為一重要參 數, 它與最佳化入射角之間的關係彼此相依, 而非如文獻上所言是彼此獨 立. 另外在設計級化轉換器時, 當入射角偏離 0 或 90, 會有兩組最佳化 入射角的產生. 在金屬光柵的導波特性方面, 厚的金屬帶光柵對反向輻射 波的漏波常數有加強作用, 同時也會窄化阻波帶的頻寬. 然而, 導電係數 除了改變導波的衰減常數外, 對漏波常數並沒有太大的影響. 另一值得注 意的參數是空氣區與金屬帶間的比值, 它會影響輻射波的射出角度. 在 本論文的第二部分中, 有系統地分析任意交錯的雙層光柵結構做為電磁屏 蔽的應用. 文中針對結構內的諸多參數及入射角, 討論其對屏蔽效率的影 響. 經由分析得知垂直交錯的雙層光柵結構屏蔽效果最好, 另外, 入射波 的能量有一部分會被導入該結構中的介質層, 而金屬帶厚度則會相當程度 地影響屏蔽特性. Metallic grating made of rectangular shape metal strips are widely used in themicrowave and optical systems, such as the polarization converter, beam splitter, filter, and leaky wave antenna. Both the theoretical analysis and measurement data have been published in the literature in the past decade. This thesis presents a new approach for the analysis of metallic gratings by considering the practical finite metal ocnductivity and strip thickness. The metal conductivity is incorporated into the complex dielectric constant of the metal medium, thus the metallic grating can be regarded as a dielectric one. In this approach, the fundamental discovery is that there are two sets of eigen-mode exist in the metal grating region, one is the air modes and the other one is the metal mode. It is shown that the two sets of mode are responsible for the fields' distribution in the grating region. The induced current distributions in the metal strips can be explained appropriately and clearly on the physical basis of these guided modes. It is then compared with the mathematical basis functions as often encountered in the transmission line problem.The metal-strip grating structure is a multilayered configuration. Rigorous mode matching method developed for the dielectric grating problem has been applied in the analysis of metallic grating one. The applications of gratingstructure studied in this thesis can be divided into two parts. The first partdiscusses the single grating problem that includes the applications of beam splitter, the polarization twister, and the leaky wave antenna. Subsequently,double gratings' structure used for the electromagnetic shielding applicationis analyzed in the second part. It is shown that the thickness of grating playsan important role on the design of all the applications. However, the finite conductivity only affects on the power dissipation in the imperfect metal-grating structure.In the design of polarization twister, the film thickness is correlated with the optimum incident conditions instead of independent as reported in the literature. In addition, as the polarization angle deviates from 0 and 90, there are two sets of optimum conditions exist. For the guidance characteristics, the thick metal strip can enhance the leakage rate of the backward radiation wave and reduce the width of stopband. While for the effect of metal conductivity, it does not affect the leakage rate despite the large influence on the attenuation constant. On the other hand, the aspect ratio cancritically change the radiation angle. For the application of double gratings'structure, the shielding performance is investigated by verifing the structuralparameters and the incident angles. It is shown that the perpendicularly crossed metal-strip gratings has the optimum shielding performance. Besides, part of the incident wave power can be guided into the dielectric layer sandwiched between the two gratings.