Wave radiation by a sphere with a circular hole

Abstract

A method was described and developed in [ 1,2] for solving the problem of plane electromagnetic wave diffraction at an ideally conducting hollow sphere with a circular hole, for the case of normal incidence to the plane of the hole. In the present paper we use the same method to solve the problem of wave radiation by a similar structure, excited by an a~symmetric electric dipole inside the structure. The present problem cannot be reduced to the one studied in [ 1,2] , except in the case when the dipole is at infinity on the axis of symmetry of the sphere, while the dipole moment is oriented parallel to the plane of the hole. Just as in the case of normal incidence of a plane wave on the plane of the hole, if the dipole moment is oriented along the axis of symmetry of the sphere the three-dimensional problem can be reduced to a two-dimensional problem, Depending on whether the dipole is inside the sphere, and in particular, at its centre, or is outside the sphere, we have to consider three independent problems. The difference between the problems can be seen throu~out the course of the solution. The main reason for the difference Lies in the fact that we arrive at infinite systems of linear algebraic equations with different properties.