A fast solution of TM wave scattering by a coated 2D partially filled rectangular crack

Abstract

An analytical technique of kobayashi potential (KP) method is applied to study the TM plane wave scattering by a coated 2D partially filled rectangular crack in a ground plane. Initially, by expanding a summation of waveguide modal eigenfunctions, the electric field inside the coating layer is found. Then, the crack contribution is taken into account by addition of the Bessel eigenfunctions in both the coating layer and the semi-infinite half space. By applying the KP method and utilizing the Weber–Schafheitlin discontinuous integrals, the governing equations of an infinite summations with unknown coefficients are derived. Then, by imposing the boundary conditions, the unknown coefficients are determined. The proposed method is validated by comparisons made with the finite element method results. Finally, the effect of a progressively filling crack and the dielectric layer height increase on the far-field scattered field is investigated. The permittivities and permeabilities of the coating and the filling dielectric could be lossy or lossless. The proposed method is applicable to both narrow and wide cracks and is accurate and computationally efficient.

Keywords:

• 2D partially filled crack
• coated rectangular crack
• dielectric layer
• Weber–Schafheitlin integrals
• Kobayashi potential method
• TM plane wave scattering

Acknowledgments

The authors express their sincere appreciation to Prof. H. Shirai at Chuo University, Prof. H. Serizawa at Numazu National College of Technology and Dr B. Alavikia at waterloo University for their valuable comments.