A Semi-analytical Method for TE Scattering from Arbitrary Shaped Radially Inhomogeneous Cylindrical Shells at Normal Incidence

Abstract

Radially inhomogeneous cylindrical shells, whose electrical properties vary contin-uously along the radial direction only, are encountered in various engineering applications. In some of these applications, circular radially inhomogeneous shells can be deformed with notches or grooves or can be used for shielding noncircular cores. Previously, we proposed a fast meshless method to compute the electromagnetic field that is scattered from such arbitrary shaped radi-ally inhomogeneous cylindrical shells when they are normally illuminated by $\text{TM}_z$ plane waves. Here, we adapt this method to the $\text{TM}_z$ illumination case. In this method, the longitudinal field component ($E_{z}$ for the $\text{TM}_z$ case, $H_{z}$ for the $\text{TM}_{z}$ case) is represented as a series of special functions, which is the general solution of a governing differential equation, at each layer (the core, the shell, and the outermost medium). In the inhomogeneous shell, the governing differential equations and their general solutions are different for the $\text{TM}_{z}$ and ‘ $\text{TM}_{z}$ cases as well as for different inhomogeneity profiles. In order to determine the unknown coefficients of the series rep-resentations of the fields, the boundary conditions are imposed and a procedure based on Fourier series expansion of the fields on boundaries and the orthogonality of complex exponentials is applied. In the $\text{TM}_{z}$ case, differently from the $\text{TM}_{z}$ case, the boundary condition related to the transverse field components includes complex discontinuity terms, necessitating a modification in the procedure. Numerical results show that the proposed method is accurate and effective also for the $\text{TM}_z$ illumination case.