Stability for the Electromagnetic Scattering from Large Cavities

Consider the scattering of electromagnetic waves from a large rectangular cavity embedded in the infinite ground plane. There are two fundamental polarizations for the scattering problem in two dimensions: TM (transverse magnetic) and TE (transverse electric). In this paper, new stability results for the cavity problems are established for large rectangular shape cavities in both polarizations. For the TM cavity problem, an asymptotic property of the solution and a stability estimate with an improved dependence on the high wavenumber are derived. In the TE case, the first stability result is established with an explicit dependence on the wave number.