Asymptotic models of electromagnetic wave scattering from a sparsely filled grating of electrically narrow strips

Several mathematical models of the plane linear polarized electromagnetic wave scattering from electrically conductive zero-thickness impedance strip and gratings are observed and discussed systematically. The full-wave mathematical model of E-polarized wave scattering is presented as a system of log-singular integral equations. The second full-wave mathematical model is presented as a system of the Cauchy type integral equations with two sets of spatial conditions. It deals with H-polarized wave scattering from an impedance strip grating. Both mathematical models are used to construct correct asymptotical models of wave scattering from sparsely filled gratings of electrically narrow strips. The simplest case of wave scattering from a flat single impedance strip is studied in detail. The key scattering problems are completely solved for the asymptotic model of an electrically narrow strip. The main approximations of the output variables and their first corrections are found and examined. Computer experiments based on approximate analytical formulas were made for both wave polarizations. The model of E-polarized wave scattering is simplified and applied to a sparsely filled grating of electrically narrow strips. Two different classes of self-similar perfect sets are used to arrange strips in flat pre-fractal gratings. Simplified solutions of the scattering from some of the simplest pre-fractal sparsely filled gratings are examined.This article is part of the theme issue 'Analytically grounded full-wave methods for advances in computational electromagnetics'.