UNIQUENESS OF THE SOLUTION OF ELECTROMAGNETIC BOUNDARY-VALUE-PROBLEMSIN THE PRESENCE OF LOSSY AND PIECEWISE HOMOGENEOUS LOSSLESS DIELECTRICS

In this paper, the uniqueness of the solution of electromagnetic bound ary-value problems is investigated and, in some cases, proven. The bou ndary-value problems considered are always defined in limited regions containing linear dielectric materials that are neither lossy nor loss less everywhere. The boundary conditions are given by specifying over the closed boundaries either the tangential components of the electric field or the tangential components of the magnetic field (or possibly by specifying the tangential components of the electric held over par t of the boundaries and the tangential components of the magnetic fiel d over the rest of the boundaries). In particular, the solution is pro ven to be unique in the case of linear dielectric materials which are piecewise homogeneous and lossless, except for some linear and lossy s ubregions that may be inhomogeneous. As a byproduct of this analysis, one can conclude that a cavity resonator, loaded with linear and lossy dielectrics together with linear piecewise homogeneous and lossless d ielectric materials, does not admit undumped resonances.