Analyzing The Electromagnetic Characteristics Of Frequency Selective Surface By Three-Dimensional Spectral Method

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.