Abstract

The electromagnetic scattering problem of normal incident waves on an elliptic chiral cylinder is considered. The cylinder is assumed to be homogeneous and isotropic and extends infinitely long in the z direction. An exact boundary value solution for the scattering problem of the TM wave by the elliptic chiral cylinder is analyzed and presented. The solution is based on the separation of variable technique in the elliptic cylinder coordinates system, and expressed in terms of Mathieu and modified Mathieu functions. The incident, transmitted and scattered electromagnetic waves are expressed in terms of an infinite series of wave functions. The matrix forms of the expansion coefficients are found by applying the boundary conditions and orthogonality of the Mathieu functions. The expression of the radar cross section (RCS) per unit length or echo width of electromagnetic wave scattering by elliptic chiral cylinder for co- and cross-polarized waves are derived by using the asymptotic expansions for modified Mathieu functions. Validation of the developed formulation and computer program are investigated by considering many limiting cases such as circular dielectric, circular perfect conducting, and circular chiral cylinders, as well as elliptic dielectric and elliptic perfect conducting cylinders. Numerical results of the forward and back scattered echo widths for both co- and cross-polarized waves for various cases are presented and discussed. The numerical results show the co- and cross-polarized bistatic and monostatic echo widths depend on the frequency and incidence angle of the incident wave, constitutive parameters and geometry of the elliptic chiral cylinder. In general, the echo widths decrease by increasing the chirality admittance, and increase by increasing the axes of the elliptic chiral cylinder.