利用漸進皺褶邊界條件分析皺褶結構於桿狀表面之快速表面波

Abstract

在現代科技中，我們憑藉著能夠產生表面等離子化現象之結構，將『場』束縛與限制在該結構表面上，而本篇論文探討之皺褶結構於桿狀表面也扮演著重要的角色，例如應用於奈米聚焦（nano-focusing）、生物感測（bio-sensing）、光譜學與檢測儀器等相關技術上都可以發現其蹤跡。先不論我們在工程上使用之目標，此結構簡單且在理論上容易分析、能快速與準確預測，直接影響了設計上的難易程度與品質。此論文中，吾人對於皺褶結構橫向於桿狀金屬之表面且其皺摺之凹槽間填充著介電材料之結構，提出了一個新穎的分析方法。基於漸進皺褶邊界條件（ACBC）的分析方程式能夠合適且簡潔的描述此架構，使其提供了此架構快速表面波之精準預測與解析解。而此方法不僅能表示頻率與電磁波速之色散關係，還提供了嚴謹的方程式描述『場』之特性。在此論文中，吾人也透過獨立的商用全波電磁模擬軟體來驗證－由此方法產生之色散模態與場的空間分部之結果。除此之外，也進行了關於表面波特性如何隨幾何和材料性質變化的參數研究，以及對導體損耗和表面場約束的方面的研究。

By virtue of the surface plasmons that it can support and thus the ability to confine fields on its surface, the corrugated rod plays an important role in various areas of modern technologies, finding applications such as nano-focusing, bio-sensing, spectroscopy, and detection. Regardless of the engineering goal, the ease, speed, and accuracy of the theoretical treatment of this structure directly affect the quality of the designs. In this thesis, we present a novel analytical method for treating transverse corrugated metallic rods with generally dielectric-filled grooves which offers highly rapid surface-wave modal solutions with good precision. Based on the ACBC- the asymptotic corrugations boundary condition, the formulation is amenable and elegant. Not only does it produce the dispersion relationship between the frequency and wavenumber, the approach also provides the rigorous functional forms of the fields. Results of modal dispersion and field distributions generated by our method are validated with those simulated by an independent full-wave solver. In addition, parametric studies on how the surface wave characteristics vary with geometrical and material properties have been conducted, along with investigations into the aspects of conductor losses and surface field confinement.