Evalauation of the periodic Green's function near Wood's anomaly and application to the array scanning method

Abstract

Our research concentrates on the numerical study of electromagnetic scattering or radiation from doubly periodic infinite structures by the method of moments (MoM), which find applications in phased arrays and metamaterials [1]. The range of inter-element phase shifts of our interest extends from 0 to 2π if we use the array scanning method (ASM) [2] in post processing to compute the scattered or radiated fields in case of non-periodic excitations. When the inter-element phase shifts range from 0 to 2π, one of the anomalies we may encounter in computing the scattered or radiated fields is the so-called Rayleigh-Wood's anomaly that occurs when one of the space harmonics becomes grazing or mathematically, when ψ = ±βd + 2π p, p = 0,1,2,… where ψ and d are the inter-element phase shifts and spacings of the periodic structure, respectively, and β is the propagation constant [3]–[4]. Therefore, we need to evaluate the periodic Green's function near Rayleigh-Wood's anomaly to apply the ASM properly.