  Invariance in duality transformation, the self-dual property, has important
applications in electromagnetic engineering. In the present paper, the problem
of most general linear and local boundary conditions with self-dual property is
studied. Expressing the boundary conditions in terms of a generalized impedance
dyadic, the self-dual boundaries fall in two sets depending on symmetry or
antisymmetry of the impedance dyadic. Previously known cases are found to
appear as special cases of the general theory. Plane-wave reflection from
boundaries defined by each of the two cases of self-dual conditions are
analyzed and waves matched to the corresponding boundaries are determined. As a
numerical example, reflection from a special case, the self-dual EH boundary,
is computed for two planes of incidence.
