Mathematical Models of E-Polarized Electromagnetic Plane Wave Scattering From Pre-Fractal Conducting Strip Gratings

Subject and Purpose. The scattering of an E-polarized electromagnetic plane wave by pre-fractal conducting impedance strip gratings is addressed. To order strip systems mathematically, the simplest class of self-similar perfect sets with variable fractional dimension is introduced. The considered asymptotic model of sparse-filling strip gratings considerably simplifies the scattering problem and enables effective investigation of basic characteristics of E-polarized wave scattering by conducting strip gratings, including radiation patterns. Methods and Methodology. Mathematical models of the E-polarized plane wave scattering from conducting strip gratings are derived using classical approaches (the integral equation technique and Rayleigh’s method) and their modifications. The basic full-wave mathematical model of E-polarized electromagnetic plane-wave scattering by conducting strip gratings reduces to a first-kind integral equation system that is solved numerically. The scattered far field is explored and yields essential integral characteristics of strip-grating scattering. Results. Mathematical models have been developed to study the scattering of an E-polarized electromagnetic plane wave from pre-fractal sparse strip gratings. These asymptotic models have proven effective for both determining output variables and examining key scattering characteristics. Important integral characteristics, such as radiation patterns, have been obtained and permit examining the fractal attributes of prefractal conducting impedance strip gratings. Conclusions. The presented mathematical models of the E-polarized electromagnetic plane wave scattering from pre-fractal strip gratings are efficient for determining output variables and examining fundamental scattering characteristics, such as radiation patterns, thereby laying the foundation for extensive investigation into the fractal attributes of key scattering characteristics of pre-fractal impedance strip gratings interrogated by a plane E-polarized wave.