## 1. Introduction

[2] The integral equation method is one of the most popular techniques for modeling electromagnetic scattering from an indented screen or cavity structure. This important topic of research has attracted much attention over many years. The first and most widely used technique is the generalized network formulation (GNF) [*Harrington and Mautz*, 1976]. However, it suffers from the interior resonance problem at the frequencies corresponding to the resonant frequencies of the cavity formed by the closed metallic boundary. A variation of this approach, namely, the connection scheme, has been proposed by Wang and Ling to analyze electromagnetic scattering from cavities [*Wang and Ling*, 1991]. In the latter approach, the cavity is decomposed into subregions, each of which is treated via integral equations on the subregion boundaries. As such, it can be used to analyze a larger cavity problem. However, more singular frequencies will occur using this technique since resonances can occur not only for the whole cavity region but also for all subregions. Asvestas and Kleinman have developed a set of coupled integral equations using purely mathematical vector manipulation in conjunction with Maxwell's equations [*Asvestas and Kleinman*, 1994]. It has been claimed that the coupled integral equations are expected to be free of interior resonance, but it still remains to be shown. The same integral equations have been set up using a physical model based on image theory with a perfect magnetically conducting (PMC) ground plane and verified by simulating electromagnetic scattering from three-dimensional (3D) rectangular cavities in [*Xu et al.*, 2005]. *Wood and Wood* [1999] have applied these coupled integral equations to the two-dimensional (2D) cavity filled with a homogeneous material. For the 2D cavity problem, it has been numerically proved that the coupled integral equations are immune to the interior resonance problem. For the three-dimensional (3D) cavity problem, there is no proof to establish that the coupled integral equations are free from the interior resonance problem.

[3] In this paper, we first develop boundary integral equations for electromagnetic cavity problems using the symmetric equivalent current model based on image theory with a perfect electrically conducting (PEC) ground plane developed by *Reuster and Thiele* [1995]. In this equivalent model, the current on the cavity wall and its image form a continuous current across the rim of the cavity wall. This continuity of the current and its image will relatively simplify the numerical implementation of the proposed integral equations. By combining the integral equations over the aperture, we establish the proposed integral equations for the cavity problems. It is well known that only two kinds of resonance modes exist for cavity problems. One set of modes occurs when the open aperture is replaced by a PEC; these are the modes with zero tangential electrical fields over the open aperture. The other set of modes occur when the open aperture is replaced by a PMC; these are modes with zero tangential magnetic fields over the open aperture. It is proved that neither type of resonant mode can exist for the proposed integral equations if no excitation is present. In the numerical results section, some simulations for the scattering from standard cavity structures are given to verify the correctness of the proposed integral equations. Finally, to numerically verify the well posedness of the proposed integral equations, the condition numbers of matrices obtained from the GNF formulation and the proposed integral equations are analyzed versus frequencies and cavity depth. These condition numbers corroborate our analysis, indicating that the proposed integral equations are immune to the interior resonance problem for 3D cavities.