## 1. Introduction

[2] The exact solution to a three-dimensional electromagnetic boundary value problem involving an oblate semispheroidal cavity with metallic walls flush-mounted under a metallic ground plane and coupled to the half-space above the plane via a circular hole is considered. The material above the ground plane is separated from the material inside the cavity by a diaphragm. All materials are isorefractive to each other.

[3] The primary source is an electric or a magnetic dipole located on the axis of symmetry of the structure and axially oriented. The analysis is performed in the frequency domain and the time dependence factor exp(−*iωt*) is omitted throughout. The exact solution is written in the form of series expansions involving oblate spheroidal wave functions. The expansion coefficients in the series are analytically determined by imposing the boundary conditions, thereby leading to a canonical solution of the boundary value problem. The notation for the spheroidal wave functions is that of *Flammer* [1957]. Preliminary results were presented by *Erricolo et al.* [2005d], obtained with a solution technique that extends the one used by *Berardi et al.* [2004]. This technique requires an isorefractive body [see *Uslenghi*, 1997a] and rotational symmetry. Rotational symmetry is required because in the oblate spheroidal coordinate system, the only known series expansion of an incident field is that of a dipole located along the axis of rotation, with the dipole oriented parallel to the axis [see *Bowman et al.*, 1987]. Therefore another usually simple form of the incident field, plane wave, is not considered because an analytical determination of the modal expansion coefficients cannot be obtained.

[4] This geometry models the penetration of electromagnetic radiation into a cavity or the radiation that escapes from a cavity. The diaphragm represents a mechanical cover that protects the cavity, similar to a radome for a radar antenna.

[5] This paper is organized as follows. The geometry of the problem is discussed in section 2. The analysis for the electric dipole excitation is given in section 3, while the analysis for the magnetic dipole is presented in section 4. In section 5, numerical results based on the evaluation of the series of oblate spheroidal functions are provided for the fields inside the cavity, inside the diaphragm and in the open space above the structure. Issues such as the evaluation of the fields and surface currents near the edge of the cavity, and the effect of the diaphragm presence are analyzed in detail. Conclusions are given in section 6.

[6] There are two main contributions from this paper. First, the exact solution of this complicated problem, which involves a sharp metallic edge, a cavity, and a curved surface separating different penetrable media is provided and it enriches the catalog of available canonical solutions. Second, the evaluation of this new solution provides a benchmark for the validation of frequency domain electromagnetic computational software.