以頻域動差法分析多層頻率選擇表面之反射及穿透係數

Abstract

頻率選擇表面 (frequency selective surfaces, FSS) 是在空間中，呈週期排列之二維金屬結構。由於其濾波之特性，使其極具研究價值。FSS可分為金屬貼片型單元(patches) 與金屬屏隙孔型單元 (apertures)。在頻率響應上，貼片型FSS有帶斥 (bandstop)，隙孔型有帶通(bandpass)之特性。在實際設計上，同常會將FSS嵌入介電層中或多層不同形狀之FSS之排列堆疊，而達到特定之頻率響應。 FSS之應用相當廣泛。在微波頻段中，可作為天線系統之反射器、濾波器、雷達罩、波導控制器等。在紅外光頻段中，可作為極化器、增加雷射效率等。其他如射頻辨識系統(RFID)等，皆是利用此週期結構所特有之濾波特性。 近年來，一般自然界並不存在之超穎物質 (metamaterial)，擁有傳統材料所沒有的電磁特性，例如磁導體，左手物質。而使用特殊金屬幾何圖案之週期結構可達到人工磁導體 (artificial magnetic conductor)與特殊的磁反應。 FSS之物理機制如下：當入射場通過FSS之金屬表面時，金屬表面會產生感應電流；而感應電流會產生散射場。另一方面，入射場通過不同介電層界面時，也會有反射波與透射波產生。而在空間中，任意位置之總場便是由感應電流與介電質之界面造成之反射與透射場之總和。再來，我們藉由金屬表面之邊界條件，可獲得電場積分方程式 (electric field integral equation)。由於FSS之週期排列特性，可引用Floquet理論，將電流用富立葉級數展開，而將積分方程式離散化。而聯繫電場與電流之格林函數 (Green’s function)則用由1980年，Itoh所提出之頻域阻抗法 (spectral immitance approach)解得。我們使用動差法(moment method)，將未知的感應電流用基底函數 (basis function) 展開，再將統御方程式與測試函數 (testing function) 作內積，求解相應之未知感應電流係數。為了加快收斂速度，我們使用快速富立葉轉換 (fast Fouruier transform) 減少運算時間。此外，未知數隨格點增加而愈加龐大，我們必須使用共軛梯度法 (conjugate gradient method)求解。我們使用有了感應電流，便可算出反射和透射場，進而求出反射係數和透射係數。 FSS之主要設計參數有：單元金屬之幾何圖案、面積、金屬與金屬間之空隙、介電質之介電常數、介電質之厚度、 Wood 變異現象 (Wood’s anomalies)、介電層與FSS之層數，本文都將加以討論。

Frequency selective surfaces (FSSs) have inspired great interest because of its filtering property. In general, FSSs comprise periodically arranged metallic patch elements or aperture elements within a metallic screen. The patches exhibit total reflection while the apertures exhibit total transmission in the resonant region. FSSs have widespread applications over much of electromagnetic spectrum. In the microwave region, FSSs can be utilized in reflector antennas, radome design, microwave monolithic circuit (MMIC) and beam controller. In the infrared region, the FSS is used as polarizers, beam splitters, laser and multiband IR filter. RFID tags, tunable filters, dichroic sub-reflectors, waveguide controlled coupling, reflective lens arrays, and single- and multi-mode array antennas are can be made by FSSs. Recently, metamaterials such as artificial magnetic conductors or left-handed materials also can be realized by periodic structures. The formulation is described as follows. When incident field propagate through an FSS, and this causes a surface current to be induced on the conducting screens, which in turn, radiate scatter field. Applying boundary condition, we can obtain electric field integral equation (EFIE). Because of periodicity of FSSs, we can utilize Floquet’s theorem to discretize integral equation. We use moment method to solve the induced current. We apply conjugate gradient method and fast Fourier transform for more computational efficiency. Finally, the reflection and transmission coefficient can be obtained from total reflected field and transmitted field, respectively.