Spherical-Multipole Analysis of the Scalar Diffraction by a Circular Aperture in a Plane Screen

Abstract. The paper deals with a new spherical-multipole solution for the scattering of an arbitrary incident wave by a circular aperture in an acoustically soft or hard plane. The boundary-value problem is formulated as a three-domain problem. In each of the domains the field is expanded by means of a complete spherical-multipole expansion, which automatically satisfies the soft or hard boundary condition on the plane, if applicable. The multipole amplitudes of the incident field in the presence of the soft or hard plane are supposed to be given and explicitly derived for a plane wave and for a uniform Complex-Source Beam (CSB). The unknown multipole amplitudes are found from the conditions of continuity of the field and its normal derivative at the boundaries between the domains, leading to a quadratic system of linear equations. All coupling integrals are solved completely analytically. Possible and expected zeros and singularities of the field values or their derivatives at the rim of the aperture develop in the course of an increasing number of multipoles, while at the other locations a finite number of multipoles is sufficient to represent the field. The numerical evaluation validates and improves numerical results found in the literature for the geometrically complementary case of acoustically hard and soft circular discs. Further numerical results for the near- and far field exemplarily prove the robustness and convergence of the proposed method.