Sound and Electromagnetic Wave Scattering by a Compact Circular Pore With a Finite Depth

Abstract

The three dimensional wave scattering of an oblique wave incident on a flanged circular compact pore of finite depth is solved analytically by the method of matched asymptotic expansion. We assume smallness of the product of the incident wave number and the pore radius and divide the scattering field into an inner region and an outer radiation region. For the wave system, the physical variables, e.g. sound pressure, electric/magnetic fields, satisfy the Laplace equation in the inner region. For the circular shaped pores, they can be solved by the method developed by Fabrikant. Then via the matching processes, the wave radiation in the outer field is determined. The theory is developed first for sound wave scattering. Both rigid and pressure-release boundary conditions are investigated. For a pore with a finite depth, the leading radiation terms for both conditions are at the same order of magnitude. They contain one monopole and one dipole for the former and one dipole for the latter. Quadrupoles and an octupole are found in the next higher order. Subsequently, the theory is applied to the electromagnetic wave scattering. The problems are formulated based on the duality property of the source-free Maxwell equations. A multipole expansion for the scattering wave similar to the acoustic counterpart is obtained. A few residue multipoles arising from the higher order inner region are found. The leading dipoles and their orientation are demonstrated.