【作者】 孟凡计；

【导师】 杨儒贵；

【作者基本信息】 西南交通大学 ， 电磁场与微波技术， 2008， 博士

【摘要】 频率选择表面(Frequency selective surface,简称FSS)是由无源谐振单元(金属贴片或孔径)按一定的排列方式组成的单层或多层周期性阵列结构。FSS的频率选择性源于其周期性结构与电磁波的相互作用。当入射波的频率接近贴片或孔径的谐振频率点时,FSS表现出全反射或全透射特性。正是这种对入射波全反射或全透射的特性,使得FSS在微波和光学领域得了广泛的应用。零厚度阵单元组成的FSS的带宽较窄。为了能在较宽的频带内获得良好的频率选择性能,通常采用多层零厚度阵单元组成的FSS层叠在一起,每层之间具有一定的间隔,并填充介质。介质加载多层FSS的结构虽然可以实现宽频带特性,但多层周期阵列的层叠导致结构复杂,而且还会丧失周期阵列剖面低的优点,不利于与其它器件合成。此外,介质加载多层零厚度FSS形成的结构的机械性能也差。与零厚度阵单元组成的FSS相比,具有一定厚度的阵单元组成的FSS的频带较宽,近年来引起越来越多的研究者们关注。在某些场合,这种非零厚度阵单元组成的FSS完全可以代替多层零厚度的FSS。本文是采用三维谱域法分析FSS。三维谱域法是用矩量法进行求解的,因此,文中首先论述矩量法的一般步骤,以及基函数和测试函数的选取原则。在矩量法中,格林函数的奇异性是一个无法回避的问题。为此,文中给出几种用于消除格林函数奇异性的方法。此外,针对矩量法不易计算大量未知数的情况,列举一些用于矩量法的加速技术。本论文还分析了FSS具有频率选择性的机理,并给出由不同阵单元组成的FSS的等效电路模型。FSS的频率选择性与很多因素有关,例如,阵单元的形状、间距、排列方式,以及入射波的角度和极化特性等。此外,还讨论了介质加载对FSS的性能影响。对于具有一定厚度的阵单元,原有的用于分析零厚度周期阵列的二维谱域方法不再适用。本文从傅里叶变换出发,基于Floquet定理给出分析自由空间中由任意形状的理想导电体阵单元组成的FSS的三维谱域公式。对于自由空间中的三维谱域公式进行了适当地修改,使其不仅可以分析自由空间中由非理想导电体阵单元组成的FSS,同时也适用于介质加载的FSS。针对不同形状的阵单元,本文还讨论了三维谱域法中无穷级数的截断准则。并采用传输线方法分析了FSS的反射系数和传输系数。最后,使用三维谱域公式分析一维和二维周期排列的零厚度阵单元组成的FSS以及介质加载的零厚度阵单元组成的FSS的频率特性。对于非零厚度阵单元组成的FSS,也分为一维和二维排列方式进行了讨论。由于阵单元的厚度不为零,导致阵单元棱边上产生的感应电流不再间断。本文给出了如何在棱边上设置基函数以保证电流连续性的方法。对于分析FSS常用到的Rooftop电流基函数和Razor-Blade测试函数也给予详细的说明。用本文提出的三维谱域法可以对于任意形状阵单元按一维或二维周期排列组成的FSS进行非常有效地分析,为分析这种类型的FSS的电磁特性提供了一种新的途径。更多还原

【Abstract】 Frequency selective surface (or called FSS) is a single layer or multi-layer structure, which is periodically comprised of many passive resonant elements (such as patches or apertures). The frequency selectivity relies on the interaction between periodic structure and electromagnetic wave, which behaves as the total reflection (for patches) or transmission (using apertures) in the neighborhood of the element resonant frequency. The FSS is applied widely in microwave and optical fields due to their properties of total reflection or transmission on the incident wave.The bandwidth of FSS comprised of the unit cells with zero thickness is very narrow. To obtain excellent frequency selectivity in a wide bandwidth, we can cascade multi-layer screens, and there is a space filled with dielectric between two neighbor screens. However, it will increase the complexity and damage the low profile of the configuration, and it is not easy to integrate with other parts. Furthermore, the structure comprised of multi-layer screens with loading dielectric is considerable weak in mechanistic capability.Comparing to FSS with zero thickness, FSS comprised of unit cells with some thickness has wider bandwidth. Therefore, it has been attended extensively by more researchers. This structure can replace completely the cascading multi-layer screens in many cases due to the wide bandwidth.In this thesis, FSS is analyzed by using three-dimensional spectral domain method based on method of moment. General method of moment will be introduced first, and then the choices of basis functions and test functions are discussed. For method of moment, the singularity of Green’s function is not to be ignored. Therefore, several techniques to eliminate the singularity are presented. Furthermore, a few accelerating approaches for method of moment are introduced in order to compute the problem with large unknowns.The mechanism of selectivity and the equivalent circuit of FSS are analyzed. The frequency selectivity of FSS is related to many factors, including the shape and size of cell, the distance between cells, and the direction and polarization of incident wave. In addition, the effect of loading dielectric on FSS is discussed also.For the unit cells with some thickness, the original two-dimensional spectral method is available no longer, and it is suitable only to the unit cells with zero thickness.Based on Fourier transform and Floquet theorem, a three-dimensional spectral domain method is presented for the FSS comprised of perfect electric conductors with any shapes in free space. Taking some modification, this formula can also be used to analyze FSS with imperfect conductors or perfect conductors with loading dielectric of arbitrary shape. For different unit cells, the truncation criterion of infinite series is discussed. The reflection and transmission coefficients of FSS are defined by using transmission line theory.At last, the FSS comprised of different cells is analyzed by using the three-dimensional spectral domain method, and these unit cells have zero thickness and some thickness arranged periodically in one-dimensional or two-dimensional free or dielectric spaces. For the unit cells with non-zero thickness, the induced current is continuous at the edges. A suitable basis function needs to be constructed in order to ensure the continuity of the induced current at the edges. The Rooftop current basis functions and Razor-Blade test functions will be described in detail to analyze FSS.The three-dimensional spectral domain method is very efficient to analyze FSS comprised of the cells with arbitrary shapes arranged periodically in one-dimensional or two-dimensional space, and this is a new approach to solve the electromagnetic scattering from FSS.更多还原