利用漸近邊界條件分析表面波於皺褶結構之色散

Abstract

電磁能隙(Electromagnetic Bandgap, EBG)結構在近年來被廣泛的研究與應用，而皺褶性結構是其代表之一。在探討EBG結構時，色散圖(Dispersion diagram)和反射相位(Reflection phase)是兩個最重要的特性。在此篇論文中，我們將研究如何準確及快速地獲得皺褶性結構的色散圖，藉由近似法和邊界條件，從基本向量勢與電磁場的關係中推導出其特徵方程式，從方程式進而得到完整的色散圖。接著我們會與傳統獲取色散圖的方法: 橫向共振技術 (Transverse Resonance Technique, TRT)以及模擬軟體來做比較，藉此來評估其準確性及快速性。我們最後也實際建造了一個皺褶性結構，藉由散射參數來間接證明此特徵方程式所得的色散圖。

傳統上研究皺褶性結構時，會著重當波行進方向為在皺褶結構表面上0度或者90度時的情況，也就是所謂的軟和硬表面(Soft/Hard surfaces)。此篇論文會進一步探討波斜向入射時的情況。藉由觀察皺褶性結構的色散圖，我們將會發現其與一般週期性結構不一樣的地方，故我們亦會研究此特性對於不同方向的表面波在皺褶性結構上行進時會有何影響。

在量測階段時，通常無法直接獲取色散圖，而必須透過散射參數來間接說明，然而我們希望能夠透過量測還原出色散圖。因此在此篇論文，我們探討散射參數與波數之間的關係，期許可以將量測的散射參數有效地還原成色散圖。目前我們已經可以將模擬的散射參數數據還原成色散圖，期許將來可以應用在實際地量測數據。

Electromagnetic bandgap (EBG) structures had been widely investigated in literature in recent years, and the planar corrugated surface is one of them. In studying such structures, the dispersion and reflection phase diagrams are two of the most important characteristics. In this thesis, we will study how to retrieve the dispersion diagram of the corrugations accurately and rapidly. By an asymptotic method and the use of classical vector potentials, we can derive the characteristic equation, thereby obtaining the surface-wave dispersion diagram. To demonstrate its accuracy and quickness, the method we proposed will be compared to a full wave simulator and the transverse resonance technique (TRT), the latter being a traditional method for getting the dispersion diagram. Finally, we fabricated a corrugation, and measure its scattering parameters to indirectly verify the dispersion diagram obtained by the method we proposed. In traditional studies of corrugations, surface-wave propagations along only the two principal directions are considered, pertaining to the so-called soft and hard surfaces. In this thesis, we will further explore the situation whereby the wave propagates obliquely on the surface. By observing the dispersion diagram of the corrugations, we will notice its difference compared to normal periodic structures, and then explain the wave propagation properties on the corrugation surface. At the measurement stage, it is difficult to get the dispersion diagram directly, and usually the scattering parameters are used to explain the width and position in the frequency spectrum of the bandgaps. In the thesis, the relationship of the scattering parameters and wavenumbers are discussed, so that the measured scattering parameters can be transformed to the dispersion diagram effectively. So far we succeed in transforming the simulated scattering parameters to the dispersion diagram, and we hope this method can be applied to measured data in the future.