The objective of this paper is the establishment of a formal theory of the scattering of time-harmonic electromagnetic waves from impenetrable, immobile obstacles, with given linear, homogeneous, and generally nonlocal, boundary conditions of Leontovich (i.e., impedance) type for the wave on the obstacle's surface partial derivative-OMEGA. As in an analogous treatment of acoustic-wave diffraction by the author [G.E. Hahne, Phys. Rev. A 43, 976 (1991); 43, 990 (1991)], the theory is modeled on the theory of the complete Green's function and the transition (T) operator in time-independent formal scattering theory of nonrelativistic quantum mechanics. For each nonzero free-space wave number k0, the electromagnetic field is described kinematically in terms of a six-component entity comprising the direct sum of the electric and the magnetic three-vector field at each point of position space; an electromagnetic source is described correspondingly as a six-component entity comprising the direct sum of the time-harmonic electric and magnetic current distributions. Accordingly, the Green's function and the T operator are 6 x 6 matrices of two-point, complex-valued, k0-dependent functions. A simplified expression is obtained for the T operator for a general case of nonlocal, homogeneous Leontovich boundary conditions for the electromagnetic wave on partial derivative-OMEGA. Analogous to the acoustic case, all the nonelementary operators that enter the expression for the T operator are formally simple, rational algebraic functions of a certain invertible, linear, k0-dependent operator Z(k)0+ which is called the radiation impedance operator; Z(k)0+ is an operator of the class that maps the linear space of complex tangent-vector fields on partial derivative-OMEGA onto itself. The nonlocal operator Z(k)0+ is defined only implicitly, in that, apart from a simple transformation made for technical reasons, it is the operator that maps the tangential magnetic field on partial derivative-OMEGA of an outgoing-wave solution to the source-free Maxwell equations into the uniquely corresponding tangential electric field. The paper concludes with a derivation of an expression for the differential scattering cross section for plane electromagnetic waves in terms of certain matrix elements of the T operator for the obstacle, and a proposal for a class of Leontovich boundary conditions that, if realized, would yield exactly zero scattering amplitude at a given k0. There are four appendixes: The first appendix recapitulates the theory of the free-space Green's function for the time-harmonic Maxwell field and the relationship of this Green's function to certain linear functional operators defined on the space of tangent-vector fields on the obstacle's boundary. The second appendix establishes mathematical conditions on the defining operators for the Leontovich boundary conditions, which conditions are sufficient to guarantee the uniqueness and existence of the complete Green's function, and reciprocity for the Green's functions of purely outgoing-wave type. The third appendix argues that any of a certain class of time-harmonic, linear electromagnetic scattering problems admits to a partial decoupling into a separate problem for the region interior and the region exterior to a dividing surface; a complete set of interior solutions determines exactly one equivalence class of Leontovich boundary conditions for the exterior electromagnetic field, so that the solution of a scattering problem then reduces to a problem in functional analysis in the space of tangent-vector fields on the dividing surface, as described in the main part of the paper. The fourth appendix describes a linear network analog to the formal scattering theory established herein.
