Asymptotic Analysis of Scattering for Finite Periodic Reflectarray/Transmitarray Antennas in the Near- Zone Focused Radiations Shih-Chung Tuan 1 and Hsi-Tseng Chou 2 1 Dept. of Communication Eng., Oriental Institute of Technology , Pan-Chiao ,Taiwan 2 Dept. of Communication Eng., Yuan Ze University, Chung-Li , Taiwan Abstract - This paper presents the asymptotic formulation of ray fields in the decomposition of electromagnetic (EM) scattering mechanisms from a one-dimensional, semi-infinite and periodic array when it is illuminated by a line source. This technique can be applied to analyze the passive FSS (frequency selective surface) type periodic structure with identical elements, or the reflectarray and transmitarray type antennas that are phased to radiate EM fields focused in the near zone of the array aperture. The solutions are built up based on the Floquet mode expansion of the scattering fields, and are obtained by asymptotically evaluating the resulted integrals to express the fields in terms of reflected/transmitted and edge diffracted fields as previously addressed in the framework of uniform geometrical theory of diffraction (UTD). Index Terms —Reflectarray Antennas, Transmitting Array Antennas, Floquet mode expansion. I. INTRODUCTION The analysis of electromagnetic (EM) scattering from periodic array structures is very important in the designs of frequency selective surface (FSS), metamaterials and reflectarray/transmitarray antennas [1]-[4]. These types of applications employ periodic structures to enhance the performance of antenna radiation by enforcing the waves propagating through the structures. To well characterize these phenomena, an effective analysis approach with the capability to interpret the scattering mechanisms is very crucial to achieve the design goals. In the past development, most techniques suffer from the limitation of computational resources, and have to assume periodic arrays with identical elements. Plane wave illuminations were generally assumed in order to reduce the analysis to be over a unit cell of element. Numerical methods, such as method of moment (MoM), finite element method (FEM) and modal expansion method, are widely applied to analyze the scattering field within this unit cell. Array factors are afterward multiplied to account for the total contribution from every element of a finite array. In contrast to the time-cumbersome element-by- element computation for the scattering fields, which are also short of physical phenomenon interpretation, the effective formulation based on the asymptotic evaluation becomes more attractive because it may accelerate the computation by decomposing the scattering fields in terms of the components in the diffraction ray theory including reflected/transmitted and edge diffracted ray components. The computational efficiency is based on a fact that only a few rays are sufficient to provide accurate results. Nevertheless, this ray type solution provides good mechanisms to interpret the scattering phenomena. II. A 2-D FINITE ARRAY RADIATION PROBLEM (A) Composition of 2-D Radiation from a 1-D Array The semi-infinite, linear array of line sources is illustrated in Figure 1, whose elements are indexed by ~ n N = -∞ and located at ' ( ,0) n x r nd = on the x-axis with a period x d . The line source is located at ) , ( f f f z x = ρ and radiates fields by | | 0 4 / ) 2 ( 0 0 | | 2 4 |) | ( 4 1 ) ( f jk f j f f e k I e k H I j u ρ ρ π ρ ρ π ρ ρ ρ - - - - 2245 - = (1) which will excite the reflecting or transmitting elements in Figure 1(a) and (b), respectively. In (1), 2 / k π λ = is the wave number with λ being the wavelength in free space, and 0 I is used as the reference amplitude of line source. The fields scattered from the array can be found from the radiation of equivalent current, ) ' ( ρ I , on the closed surface enclosing the array structure as illustrated in Figure 1. To the degree of accuracy in the Kirchhoff approximation, the induced current is assumed to be found from the infinite array structure illuminated by the same incident field. Thus it can be approximately expressed as ) ' ( ) ' ( ) ( ) ' ( ρ φ ρ ρ ρ j i f e Q u I = (2) where i ρ and ' ρ are the position vectors on the closed surface. The function, Q , is related to the reflection and transmission coefficients for the cases of Figure 1, with φ being the phase. In the current investigation, one is interested in the scattering field in the z + space, thus only the current on t S is considered with the others omitted for simplification. The scattering field can be expressed as where -∞ → a x and x b Nd x = in the current development. WE3B_01 WE3B_01 WE3B_01 WE3B_01 Proceedings of ISAP 2014, Kaohsiung, Taiwan, Dec. 2-5, 2014 117