It has been shown in the past that the Ewald-Oseen extinction theorem can be generalized into a nonlocal boundary-value problem and that the scattering of an electromagnetic wave on a medium of arbitrary response can be described in terms of this boundary-value problem. The scattered field inside the medium (the interior-scattering problem) is determined, without any reference to the scattered field outside the medium, by solving a set of coupled partial differential equations, subject to certain nonlocal boundary conditions which are generalizations of the Ewald-Oseen extinction theorem. Once the field on the boundary of the medium is known, the exterior field (the exterior-scattering problem) is evaluated by direct integration. Moreover, a hypothesis was put forward according to which these nonlocal boundary conditions completely and uniquely specify the solution of the interior-scattering problem. In this paper it is shown that this hypothesis is true. The equivalence of the interior- and exterior-scattering problems to Maxwell’s equations and boundary conditions is proven. For simplicity, the proof is confined to nonmagnetic media. Thus, if Maxwell’s equations and boundary conditions have a unique solution, the interior-scattering problem will also have a unique solution, namely, that obtained from the former. Some illustrative examples are presented in the special case of a linear medium.
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