雙週期表面阻抗波導及散射之特性研究

Abstract

我們用一個在一維方向上有兩個不同週期變化的阻抗表面來研究波的波導及散射特性,其中因為兩個不同週期間的交互作用所產生不同於一般以往的單週期結構物理現象是主要的研究部分.我們用一種嚴格的分析方法,考慮三維空間的邊界條件,可以準確的用來解釋這些物理現象.在此,假設我們所探討的結構沿著x方向有兩個週期的變化,在y方向則無窮延伸沒有變化,藉由索引[1][2][5]中已經有的單週期結構研究,本論文可視為架構其上的延伸探討,由於兩個週期間的交互作用,可得到一些新的波導特性,進而形成一寬頻元件.本論文中,我們以橫向極化電波(TE wave)及橫向極化磁波(TM wave)來分析平面波的方法加以研究雙週期表面阻抗一般的傳播特性[1].漸進地,我們也探討如週期性及非週期性的雙週期結構,週期相近的雙週期結構,及調變深度的影響,如此,雙週期表面阻抗一般的波導及散射特性變得以呈現.

We present here a study of wave phenomena associated with a doubly periodic impedance surface, e.g., an impedance surface that is modulated by two periodic functions of different periods in the same direction. Our main interest is in the interaction between the two different periods to explore new physical phenomena that cannot be taken place in the singly periodic case. Such a structure permits a rigorous formulation as a three-dimensional boundary value problem, so that any new physical phenomenon can be identified with confidence. Here, the periodic impedance surface consists of two different periods in the x direction and no variations in the y direction. The studies of singly periodic structure can be found in the literature [1][2][5], and this paper can be viewed as an extension based on the knowledge of these studies. Due to the interactions between the two periods, we find some new guiding characteristics in this doubly periodic structure. With these additional characteristics, they can be utilized as several broad band elements. In the study, we investigate the general dispersion characteristics of such a structure using a useful method by presenting both TE- and TM-polarized plane waves in the uniform medium [1]. And gradually, we observe our experiments on the following cases, such as: the differences between commensurate and non-commensurate ones; two closely separated periods; modulation indices' effects on the attenuation constants; etc. Thus, the scattering and guiding characteristics are generally presented.