金屬微帶光柵的模型化與在多層光柵問題上的應用

Abstract

轉換電磁場的分析成為電路的問題一直是電機工程中的重要課題。如此可以方便實際工程問題之分析與設計。本論文由元件的觀點出發，探討如何將金屬微帶光柵模擬成簡單的T網路模型，避免原本需要精細數值計算如mode-matching, spectral-domain method等的複雜程式，而以等效網路模型替代之。在分析的過程中，先用嚴格的mode-matching method計算得到單一光柵結構的散射參數S，再將散射參數轉為ABCD矩陣，則T模型的等效元件值即可算出。在此亦探討諸如光柵厚度，金屬傳導性，光柵視比，基層介電常數以及入射波之頻率和極化方向等參數變化與模型元件值之間的關係。最後，本論文提供系統性的數據，藉以驗證此簡單的元件模型應用在多層光柵結構，結果發現與嚴格計算甚為一致，充份展現此模型的便利性與實用性。

The modeling of an electromagnetic structure by an equivalent electric network has been the foundation of electrical engineering; it simplifies the analysis and design of electrical systems in general. The main purpose of this thesis is to develop equivalent networks for the class of metal gratings. Specifically, the scattering parameters of a single grating is calculated first by the rigorous method of mode matching, and the results are then transformed into the ABCD matrix from which the circuit elements of an equivalent network are obtained. The extensive numerical results are obtained, including the effects of the grating thickness, the metal conductivity, the aspect ratio, and the substrate. The networks so obtained are then utilized for the analysis of two or more gratings, and it is demonstrated that the network approach can be conveniently applied to the multi-grating case with ease.