We consider a plane E-polarized wave scattering from an infinite flat grating of slots cut in a perfect electrically conducting plane, backed with a dielectric slab. At first, we reduce this problem to a dual series equation for the complex amplitudes of the Floquet spatial harmonics. Then we perform its analytical regularization, based on the inversion of the main part with the aid of the Riemann-Hilbert Problem. This yields a Fredholm second-kind infinite matrix equation, numerical solution of which has a guaranteed convergence. We perform numerical experiments demonstrating how the rate of convergence depends on the thickness and dielectric permittivity of the slab. Our computations demonstrate the Fano-shape resonances on the so-called lattice modes, responsible for the phased array blindness. Their frequencies lay near to the Rayleigh anomalies and, if the slots or strips are narrow and the slab is thin, may have ultrahigh Q-factors.

我们考虑了平面E极化波的散射，该散射是从在理想的导电平面中切割并带有电介质板的狭缝的无限平坦光栅中散射出来的。首先，我们将这个问题简化为 Floquet 空间谐波复振幅的对偶级数方程。然后我们在黎曼-希尔伯特问题的帮助下基于主要部分的反演执行其解析正则化。这产生了 Fredholm 第二类无限矩阵方程，其数值解具有保证收敛性。我们进行数值实验，证明收敛速度如何取决于平板的厚度和介电常数。我们的计算证明了所谓的晶格模式上的 Fano 形状共振，这是造成相控阵失明的原因。