Study of Direction Patterns of Narrow-Strip, Sparsely Filled Pre-Fractal Gratings

Characteristics of E-polarized wave scattering by systems of absolutely thin and conductive flat impedance strips, arranged according to the laws of construction of a perfect set with variable fractional dimension, have been investigated. The scattering problem statement is classically rigorous under certain assumptions. In this case, several classical methods, namely the method of integral equations and Lord Rayleigh’s asymptotic method, along with their modifications, have been used. Considerable attention is paid to two generalizations of the classical nowhere dense perfect set with dimension ln2/ln3, which significantly expand the possibilities for practical applications of such sets. A detailed mathematical analysis of the process of creating two different classes of nowhere dense perfect sets with variable fractional dimension is proposed. This analysis forms the basis for the creation of correct mathematical models of the scattering of plane electromagnetic waves by using strip systems. A simple asymptotic model of scattering of an E-polarized wave by narrow-strip sparsely filled gratings, ordered according to the laws of construction of perfect sets with variable fractional dimensions ln2/lnc (c > 2) and ln3/lnc (c > 3), has been developed. This model forms the basis for developing algorithms to calculate the direction patterns of certain classes of strip gratings ordered according to new mathematical laws. The study and modeling performed by the author can be useful for improving the performance quality of electronic devices that use antenna gratings.