A fundamental approach: E-polarized electromagnetic wave diffraction by two dimensional arbitrary-shaped objects with impedance boundary condition

Abstract

In the present study, a new methodology in computational electromagnetics is developed for two-dimensional arbitrarily-shaped objects with impedance boundary conditions. The proposed approach investigates the E-polarized electromagnetic diffraction by a two-dimensional object with the Leontovich boundary condition. The scattered electric and magnetic fields are expressed as the convolution integral of the corresponding Green’s function and the current induced on the obstacle surface. After obtaining integral equations by applying the boundary condition, the integral equations are solved as in the case of the method of auxiliary sources (MAS) which is a well-known method in computational electrodynamics. The results are compared with first, different methods such as the method of moments (MoM), orthogonal polynomials (OP), and second, different boundary conditions such as Dirichlet, Neumann, and fractional boundary conditions. Some results are also obtained for the different shape scatterers at some values of the surface impedance.

Pulse diffraction by a circular dielectric cylinder

“…This approach eliminates the singularity problems in radiation integrals. In the regularized form of MAS, Hankel's function (Green's function in 2D problems) is regularized and singularity problems are solved by regularizing the kernel of the radiation integrals (Hankel's function) [19]. For smooth surfaces, MAS gives better results, whereas the regularized form of MAS is also suitable for discontinuous or complex surfaces.…”

“…In Table 1, dimensions regarding the geometry of the problem are provided. The electric field outside the object can be expressed as ( 7) [18,19]:…”

“…The methodology was first proposed by Georgian mathematician Viktor Kupradze and then, Revaz Zaridze utilized the approach in electromagnetic scattering [16,17]. Since then, the method is not only been used for the direct problem but also, for 2D and 3D inverse problems that are solved and validated by the other methods [18,19]. In [18], the characterization of the electrical properties of the dielectric objects is investigated by employing the method of auxiliary sources.…”

“…In [18], the characterization of the electrical properties of the dielectric objects is investigated by employing the method of auxiliary sources. In [19], mathematical analysis of the electromagnetic scattering field is investigated and the approaches are promising in employing the determination of the electrical properties of the objects. In this article, the method of auxiliary sources is validated by the experimental outcomes.…”

Electromagnetic scattering of H‐polarised cylindrical wave by a double‐sided impedance circular strip

“…In this study, a circular strip geometry excited by a cylindrical wave is investigated, with different impedance values on the outer and inner surfaces. The research examines resonant phenomena not observed in previous literature, demonstrating the influence of impedance values and location dependencies on the resonator structure's Q‐factor [26–28].…”